Attitude estimation apparatus and transportation machine

Abstract

An attitude estimation apparatus for estimating the attitude of a movable body includes an attitude estimation unit for estimating the roll angle of the movable body and for using a calculation process to estimate the offset error for at least one of first and second angular velocity detection units and first, second and third acceleration detection units. The attitude estimation unit includes a plurality of Kalman filters that each receive at least two or more imaginary offset quantities for a detection unit of interest, the imaginary offset quantities being different from each other. Each of the Kalman filters uses detected values from the detection units, estimated values from the previous estimation operation and the imaginary offset quantities to calculate a likelihood, which indicates how reliable the estimated values are. The attitude estimation unit weights the estimated values from the Kalman filters based on the likelihood to estimate the roll angle of the movable body.

Claims

1. An attitude estimation apparatus for estimating an attitude of a movable body, comprising: a first angular velocity detection unit configured to detect a first angular velocity, the first angular velocity being an angular velocity of the movable body about a first axis; a second angular velocity detection unit configured to detect a second angular velocity, the second angular velocity being an angular velocity of the movable body about a second axis, the second axis being in a different direction than that of the first axis; a first acceleration detection unit configured to detect a first acceleration, the first acceleration being an acceleration of the movable body in a first direction; a second acceleration detection unit configured to detect a second acceleration, the second acceleration being an acceleration of the movable body in a second direction, the second direction being different from the first direction; a third acceleration detection unit configured to detect a third acceleration, the third acceleration being an acceleration of the movable body in a third direction, the third direction being different from the first and second directions; a velocity information detection unit configured to detect information about a moving velocity in a direction of advance of the movable body; and an attitude estimation unit configured to estimate a roll angle of the movable body and estimate a first offset error using a calculation process, the first offset error being an offset error in at least one of the first angular velocity detection unit, the second angular velocity detection unit, the first acceleration detection unit, the second acceleration detection unit, or the third acceleration detection unit, wherein the attitude estimation unit includes: a plurality of Kalman filters each configured to receive, as an imaginary offset quantity for the first offset error, an associated one of a plurality of values including at least two values different from each other, and each of the plurality of Kalman filters uses, in a current estimation operation, a detected value from the first angular velocity detection unit, a detected value from the second angular velocity detection unit, a detected value from the first acceleration detection unit, a detected value from the second acceleration detection unit, a detected value from the third acceleration detection unit, a detected value from the velocity information detection unit, an estimated value of the roll angle from a previous estimation operation, and the imaginary offset quantity to calculate the estimated value of the roll angle of the movable body and a likelihood in the current estimation operation, the likelihood representing a reliability of an estimation result, and the attitude estimation unit estimates the first offset error based on the likelihoods obtained from the plurality of Kalman filters and the imaginary offset quantities provided to the plurality of Kalman filters.

2. The attitude estimation apparatus according to claim 1, wherein the attitude estimation unit estimates the first offset error by weighting the imaginary offset quantity received by each of the plurality of Kalman filters based on the likelihood obtained from each respective one of the plurality of Kalman filters.

3. The attitude estimation apparatus according to claim 1, wherein the attitude estimation unit estimates the roll angle of the movable body based on the likelihoods obtained from the plurality of Kalman filters and the roll angles of the movable body obtained from the plurality of Kalman filters.

4. The attitude estimation apparatus according to claim 1, wherein each of the plurality of Kalman filters includes: a first Kalman filter configured to receive, as the imaginary offset quantity, a value larger than a maximum possible value of an offset quantity for a detection unit of interest from among the first angular velocity detection unit, the second angular velocity detection unit, the first acceleration detection unit, the second acceleration detection unit, and the third acceleration detection unit, the detection unit of interest being the detection unit from among the first angular velocity detection unit, the second angular velocity detection unit, the first acceleration detection unit, the second acceleration detection unit, and the third acceleration detection unit with which the first offset error is associated; a second Kalman filter configured to receive, as the imaginary offset quantity, a value smaller than a minimum possible value of the offset quantity of the detection unit of interest; and a third Kalman filter configured to receive, as the imaginary offset quantity, a value between the minimum possible value and the maximum possible value of the offset quantity of the detection unit of interest.

5. The attitude estimation apparatus according to claim 1, wherein the first offset error is the offset error from one of the first acceleration detection unit, the second acceleration detection unit, and the third acceleration detection unit.

6. The attitude estimation apparatus according to claim 1, wherein each of the plurality of Kalman filters calculates a second offset error in addition to the roll angle of the movable body and the likelihood, the second offset error being the offset error from one of the first angular velocity detection unit, the second angular velocity detection unit, the first acceleration detection unit, the second acceleration detection unit, and the third acceleration detection unit, other than a detection unit of interest, and, in a current estimation operation, calculates the estimated value of the roll angle of the movable body, an estimated value of the second offset error and the likelihood using the detected value from the first angular velocity detection unit, the detected value from the second angular velocity detection unit, the detected value from the first acceleration detection unit, the detected value from the second acceleration detection unit, the detected value from the third acceleration detection unit, the detected value from the velocity information detection unit, the estimated value of the roll angle from the previous estimation operation, an estimated value of the second offset error from the previous estimation operation, and the imaginary offset quantity, wherein the attitude estimation unit estimates the second offset error based on the likelihoods obtained from the plurality of Kalman filters and the second offset errors obtained from the plurality of Kalman filters.

7. The attitude estimation apparatus according to claim 6, wherein the second offset error is the offset error from a detection unit, from among the first angular velocity detection unit, the second angular velocity detection unit, the first acceleration detection unit, the second acceleration detection unit, and the third acceleration detection unit, other than the detection unit of interest.

8. The attitude estimation apparatus according to claim 7, wherein the second offset error includes the offset errors from the first angular velocity detection unit and the second angular velocity detection unit.

9. The attitude estimation apparatus according to claim 8, wherein the second offset error includes the offset error from a detection unit, from among the first angular velocity detection unit, the second angular velocity detection unit, the first acceleration detection unit, the second acceleration detection unit, and the third acceleration detection unit, other than the detection unit of interest.

10. The attitude estimation apparatus according to claim 9, wherein: the first angular velocity detection unit detects a roll angular velocity of the movable body, the second angular velocity detection unit detects a yaw angular velocity of the movable body, and the second offset error includes the offset error from the first angular velocity detection unit, the offset error from the second angular velocity detection unit and the offset error from one of the first acceleration detection unit and the second acceleration detection unit that is other than the detection unit of interest.

11. The attitude estimation apparatus according to claim 1, wherein the first acceleration detection unit detects an acceleration in a top-bottom direction of the movable body, the second acceleration detection unit detects an acceleration in a left-right direction of the movable body, the third acceleration detection unit detects an acceleration in a front-rear direction of the movable body, and the first offset error is the offset error from the first acceleration detection unit or the offset error from the second acceleration detection unit.

12. The attitude estimation apparatus according to claim 6, further comprising: a third angular velocity detection unit configured to detect a third angular velocity, the third angular velocity being an angular velocity of the movable body about a third axis, the third axis being different from the first and second axes, wherein each of the plurality of Kalman filters, in a current estimation operation, calculates the estimated value of the roll angle of the movable body, an estimated value of the pitch angle of the movable body and the likelihood using the detected value from the first angular velocity detection unit, the detected value from the second angular velocity detection unit, a detected value from the third angular velocity detection unit, the detected value from the first acceleration detection unit, the detected value from the second acceleration detection unit, the detected value from the third acceleration detection unit, the detected value from the velocity information detection unit, the estimated value of the roll angle from the previous estimation operation, the estimated value of the pitch angle from the previous estimation operation, the imaginary offset quantity, and an estimated value of the second offset error from the previous estimation operation, the attitude estimation unit estimates the first offset quantity based on the likelihoods obtained from the plurality of Kalman filters and the imaginary offset quantities provided to the plurality of Kalman filters, estimates the roll angle of the movable body based on the likelihoods obtained from the plurality of Kalman filters and the roll angles of the movable body obtained from the plurality of Kalman filters, and estimates the pitch angle of the movable body based on the likelihoods obtained from the plurality of Kalman filters and the pitch angles of the movable body obtained from the plurality of Kalman filters.

13. The attitude estimation apparatus according to claim 12, wherein each of the plurality of Kalman filters, in the current estimation operation, calculates the estimated value of the roll angle of the movable body, the estimated value of the pitch angle of the movable body and the likelihood using a characteristic equation in which a value of a predetermined function is a constant, the function having, as its elements, the detected value from the first angular velocity detection unit, the detected value from the second angular velocity detection unit, the detected value from the third angular velocity detection unit, the detected value from the first acceleration detection unit, the detected value from the second acceleration detection unit, the detected value from the third acceleration detection unit, the detected value from the velocity information detection unit, the estimated value of the roll angle from the previous estimation operation, the estimated value of the pitch angle from the previous estimation operation, the imaginary offset quantity, and the estimated value of the second offset error from the previous estimation operation.

14. The attitude estimation apparatus according to claim 12, further comprising: a load estimation unit configured to estimate a load applied to at least one of a front wheel and a rear wheel included in the movable body, wherein the load estimation unit estimates the load based on the detected value from the first angular velocity detection unit, the detected value from the second angular velocity detection unit, the detected value from the third angular velocity detection unit, the detected value from the first acceleration detection unit, the detected value from the second acceleration detection unit, the detected value from the third acceleration detection unit, the detected value from the velocity information detection unit, and the roll angle of the movable body, the pitch angle of the movable body and the first offset error estimated by the attitude estimation unit.

15. The attitude estimation apparatus according to claim 14, further comprising: a suspension stroke quantity estimation unit configured to estimate a stroke quantity of a suspension provided on at least one of the front wheel and the rear wheel of the movable body, wherein the load estimation unit estimates the load applied to both the front wheel and the rear wheel provided on the movable body, and the suspension stroke quantity estimation unit estimates the stroke quantity of the suspension based on an estimated value of the load applied to both the front wheel and the rear wheel estimated by the load estimation unit.

16. The attitude estimation apparatus according to claim 15, further comprising: an elevation/depression angle estimation unit configured to estimate an elevation/depression angle based on an estimated value of the stroke quantity of the suspension estimated by the suspension stroke quantity estimation unit, the elevation/depression angle being an angle between an axis in a vehicle-body coordinate system fixed to the movable body and an axis in a road-surface coordinate system fixed to a road surface in contact with the front wheel or the rear wheel.

17. The attitude estimation apparatus according to claim 16, wherein each of the plurality of Kalman filters calculates the estimated value of the roll angle of the movable body, the estimated value of the pitch angle of the movable body, and the likelihood taking account of an estimated value of the elevation/depression angle estimated by the elevation/depression angle estimation unit.

18. The attitude estimation apparatus according to claim 16, further comprising: a slope estimation unit configured to estimate a longitudinal slope of the road surface on which the movable body is placed based on an estimated value of the elevation/depression angle estimated by the elevation/depression angle estimation unit and the estimated values of the roll angle and the pitch angle of the movable body estimated by the attitude estimation unit.

19. A transportation machine comprising: the movable body; and the attitude estimation apparatus according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates the relationship between the basis vector e.sub.o of an inertia coordinate system, the basis vector e.sub.b of a vehicle coordinate system, and the basis vector e.sub.r of a road-surface coordinate system.

(2) FIG. 2 is a schematic view of a vehicle including an attitude estimation apparatus according to an embodiment.

(3) FIG. 3 is a schematic block diagram of an exemplary configuration of the attitude estimation apparatus.

(4) FIG. 4 is a schematic block diagram of an exemplary configuration of the calculation unit.

(5) FIG. 5 illustrates where the group of sensors are mounted.

(6) FIG. 6 is a schematic cross-sectional view of the rear wheel.

(7) FIG. 7 illustrates where the group of sensors are mounted by means of vectors.

(8) FIG. 8 is a schematic block diagram of an exemplary configuration of the calculation unit.

(9) FIG. 9A illustrates how the estimated values of various parameters change over time.

(10) FIG. 9B illustrates how the estimated values of various parameters change over time.

(11) FIG. 9C illustrates how the estimated values of various parameters change over time.

(12) FIG. 9D illustrates how the estimated values of various parameters change over time.

(13) FIG. 9E illustrates how the estimated values of various parameters change over time.

(14) FIG. 9F illustrates how the estimated values of various parameters change over time.

(15) FIG. 9G illustrates how the estimated values of various parameters change over time.

(16) FIG. 9H illustrates how the estimated values of various parameters change over time.

(17) FIG. 9I illustrates how the estimated values of various parameters change over time.

(18) FIG. 9J illustrates how the estimated values of various parameters change over time.

(19) FIG. 9K illustrates how the estimated values of various parameters change over time.

(20) FIG. 9L illustrates how the estimated values of various parameters change over time.

(21) FIG. 10 is a schematic block diagram of an exemplary configuration of the attitude estimation apparatus.

(22) FIG. 11 illustrates an elevation/depression angle.

(23) FIG. 12 is a schematic block diagram of an exemplary configuration of the calculation unit.

(24) FIG. 13 illustrates the vectors of forces acting on the road-surface grounding points for the front and rear wheels.

(25) FIG. 14 illustrates the caster angle and the rear arm angle.

(26) FIG. 15 is a graph illustrating an exemplary relationship between .sub.R and .sub.W.

(27) FIG. 16 shows an equivalent circuit modelling the shock absorber of the suspension.

(28) FIG. 17 is a schematic block diagram of an exemplary configuration of the attitude estimation apparatus.

(29) FIG. 18A illustrates how the estimated values of various parameters change over time.

(30) FIG. 18B illustrates how the estimated values of various parameters change over time.

(31) FIG. 18C illustrates how the estimated values of various parameters change over time.

(32) FIG. 18D illustrates how the estimated values of various parameters change over time.

(33) FIG. 18E illustrates how the estimated values of various parameters change over time.

(34) FIG. 18F illustrates how the estimated values of various parameters change over time.

(35) FIG. 18G illustrates how the estimated values of various parameters change over time.

(36) FIG. 19A illustrates how the estimated values of various parameters change over time.

(37) FIG. 19B illustrates how the estimated values of various parameters change over time.

(38) FIG. 19C illustrates how the estimated values of various parameters change over time.

(39) FIG. 19D illustrates how the estimated values of various parameters change over time.

(40) FIG. 19E illustrates how the estimated values of various parameters change over time.

(41) FIG. 19F illustrates how the estimated values of various parameters change over time.

(42) FIG. 19G illustrates how the estimated values of various parameters change over time.

(43) FIG. 20A illustrates how the estimated values of various parameters change over time.

(44) FIG. 20B illustrates how the estimated values of various parameters change over time.

(45) FIG. 20C illustrates how the estimated values of various parameters change over time.

(46) FIG. 20D illustrates how the estimated values of various parameters change over time.

(47) FIG. 20E illustrates how the estimated values of various parameters change over time.

(48) FIG. 20F illustrates how the estimated values of various parameters change over time.

(49) FIG. 20G illustrates how the estimated values of various parameters change over time.

(50) FIG. 21A illustrates how the estimated values of various parameters change over time.

(51) FIG. 21B illustrates how the estimated values of various parameters change over time.

(52) FIG. 22 is a schematic view of a vehicle including the attitude estimation apparatus according to an embodiment.

EMBODIMENTS FOR CARRYING OUT THE INVENTION

(53) Embodiments of the present invention will be described with reference to the drawings. In the drawings referred to below, the size ratios in the drawings and the actual size ratios are not necessarily identical.

(54) <Definitions>

(55) The coordinate axes will be defined below with reference to the drawings. FIG. 1 illustrates the relationship between the basis vector e.sub.o of an inertia coordinate system, the basis vector e.sub.b of a vehicle coordinate system, and the basis vector e.sub.r of a road-surface coordinate system. In the following formulas, vectors may be expressed by bold letters. Each coordinate system includes an x-axis, a y-axis, and a z-axis. In FIG. 1, the vehicle 100 that represents a reference with respect to which a vehicle coordinate system and a road-surface coordinate system are set is a motorcycle.
e.sub.o=(e.sub.ox,e.sub.oy,e.sub.oz)
e.sub.b=(e.sub.bx,e.sub.by,e.sub.bz)
e.sub.r=(e.sub.rx,e.sub.ry,e.sub.rz) [Formula 1]

(56) The inertia coordinate system e.sub.o is a coordinate system fixed to the horizontal plane of the earth, and the z-axis is defined as the upward vertical direction.

(57) In the vehicle coordinate system e.sub.b, when the vehicle is standing upright on the horizontal road surface, the x- and y-axes are in the horizontal plane and the x-axis is fixed to the vehicle body so as to be the forward direction with respect to the vehicle. The angle formed by the vehicle coordinate system e.sub.b and the inertia coordinate system e.sub.o changes as the suspension of the vehicle moves. The suspension is a shock absorber provided between the vehicle wheels 2 and 3 and the vehicle body 1.

(58) In the road-surface coordinate system e.sub.r, the y-axis is the same as the y-axis of the vehicle coordinate system e.sub.b, and the vehicle coordinate system e.sub.b has been rotated about the y-axis such that the direction extending from the grounding point P3 between the rear wheel 3 and road surface 200 to the grounding point P2 between the front wheel 2 and road surface 200 is the same as the x-axis.

(59) As used herein, yaw angle means a rotational angle about the z-axis of the inertia coordinate system e.sub.o (e.sub.oz), yaw angular velocity means a rate of change over time of the yaw angle, and yaw angular acceleration means a rate of change over time of the yaw angular velocity. As used herein, pitch angle means a rotational angle about the y-axis of the inertia coordinate system e.sub.o (e.sub.oy), pitch angular velocity means a rate of change over time of the pitch angle, and pitch angular acceleration means a rate of change over time of the pitch angular velocity. As used herein, roll angle means a rotational angle about the x-axis of the vehicle coordinate system e.sub.b (e.sub.bx), roll angular velocity means a rate of change over time of the roll angle, and roll angular acceleration means a rate of change over time of the roll angular velocity.

(60) As used herein, top-bottom direction means the direction of the z-axis of the vehicle coordinate system e.sub.b (e.sub.bz), front-rear direction means the direction of the x-axis of the vehicle coordinate system e.sub.b (e.sub.bx), and left-right direction means the direction of the y-axis of the vehicle coordinate system e.sub.b (e.sub.by).

(61) Roll angle, roll angular velocity, roll angular acceleration, yaw angle, yaw angular velocity, yaw angular acceleration, pitch angle, pitch angular velocity, pitch angular acceleration, top-bottom acceleration, front-rear acceleration, and left-right acceleration will be denoted by the following characters. One dot on the character denoting a parameter means first-order temporal differential.

(62) TABLE-US-00001 TABLE 1 Parameter Meaning yaw angle .sub.ya yaw angular velocity {dot over ()}.sub.ya yaw angular acceleration pitch angle .sub.pi pitch angular velocity {dot over ()}.sub.pi pitch angular acceleration roll angle .sub.ro roll angular velocity {dot over ()}.sub.ro roll angular acceleration G.sub.z top bottom acceleration G.sub.x front-rear acceleration G.sub.y left-right acceleration

[First Embodiment]

(63) A first embodiment of the present invention will be described.

(64) <Vehicle>

(65) FIG. 2 is a schematic view of a vehicle including an attitude estimation apparatus according to the present embodiment. The vehicle 100 shown in FIG. 2 is a motorcycle.

(66) As shown in FIG. 2, the vehicle 100 includes a vehicle body 1. A front wheel 2 is attached to a front portion of the vehicle body 1, and a rear wheel 3 is attached to a rear portion of the vehicle body 1. Further, a group of sensors 5 are attached to a central portion of the vehicle body 1. The group of sensors 5 will be described in detail further below.

(67) A rear-wheel velocity sensor 7 is attached to the wheel body of the rear wheel 3 for detecting the rotational velocity of the rear wheel 3. According to the present embodiment, the rear-wheel velocity sensor 7 corresponds to the velocity information detection unit.

(68) Handlebars 11 are attached to the top of the front portion of the vehicle body 1 so as to be swingable to the left and right. In the implementation shown in FIG. 1, a navigation system 12 is provided near the handlebars 11, and a headlight 14 and a headlight driving device 15 are provided on the front portion of the vehicle body 1. The headlight driving device 15 controls the direction of the headlight 14. An electronic control unit 20 is provided on the rear portion of the vehicle body 1. The electronic control unit 20 will be referred to simply as ECU 20 as appropriate below. The positions of the ECU 20 and the group of sensors 5 are not limited to those in FIG. 2.

(69) Output signals from the group of sensors 5 and rear-wheel velocity sensor 7 are provided to the ECU 20. The ECU 20 controls the various parts of the vehicle body 1, and estimates the roll angle and other parameters of the vehicle body 1 and provide these estimated values to the navigation system 12 and headlight driving device 15, for example.

(70) According to the present embodiment, the group of sensors 5, rear-wheel velocity sensor 7 and ECU 20 constitute the attitude estimation apparatus.

(71) <Configuration of Attitude Estimation Apparatus>

(72) FIG. 3 is a schematic block diagram of an exemplary configuration of the attitude estimation apparatus. The attitude estimation apparatus 10 shown in FIG. 3 includes the group of sensors 5, the rear-wheel velocity sensor 7, low-pass filters 31, 32, 34, 35 and 36, differentiators 41 and 42, and a calculation unit 49. The functionality of the calculation unit 49 is realized by the ECU 20 shown in FIG. 2 and a program. The calculation unit 49 corresponds to the attitude estimation unit.

(73) The group of sensors 5 include a roll angular velocity sensor 21, a yaw angular velocity sensor 22, a top-bottom acceleration sensor 24, a front-rear acceleration sensor 25 and a left-right acceleration sensor 26.

(74) The roll angular acceleration sensor 21 is provided on the vehicle body 1 so as to detect the roll angular velocity of the vehicle body 1. The yaw angular velocity sensor 22 is provided on the vehicle body 1 so as to detect the yaw angular velocity of the vehicle body 1. According to the present embodiment, the roll angular velocity sensor 21 corresponds to the first angular velocity detection unit and the yaw angular velocity sensor 22 corresponds to the second angular velocity detection unit.

(75) The top-bottom acceleration sensor 24 is provided on the vehicle body 1 so as to detect the acceleration in the top-bottom direction of the vehicle body 1. The front-rear acceleration sensor 25 is provided on the vehicle body 1 so as to detect the acceleration in the front-rear direction of the vehicle body 1. The left-right acceleration sensor 26 is provided on the vehicle body 1 so as to detect the acceleration in the left-right direction of the vehicle body 1. According to the present embodiment, the top-bottom acceleration sensor 24 corresponds to the first acceleration detection unit, the front-rear acceleration sensor 25 corresponds to the second acceleration detection unit, and the left-right acceleration sensor 26 corresponds to the third acceleration detection unit.

(76) In this exemplary implementation, the top-bottom acceleration sensor 24, front-rear acceleration sensor 25 and left-right acceleration sensor 26 detect the accelerations in directions that are perpendicular to each other. This is not essential and it is only required that the accelerations in at least three different directions be detected.

(77) The output signal from the roll angular velocity sensor 21 is passed through the low-pass filter 31 and is fed into the calculation unit 49 and differentiator 41 as a roll angular velocity. The low-pass filter 31 removes noise from the output signal from of the roll angular velocity sensor 21. The differentiator 41 provides, to the calculation unit 49, the differential value of the roll angular velocity as a roll angular acceleration.

(78) The output signal from the yaw angular velocity sensor 22 is passed through the low-pass filter 32 and is fed into the calculation unit 49 and differentiator 42 as a yaw angular velocity. The low-pass filter 32 removes noise from the output signal from the yaw angular velocity sensor 22. The differentiator 42 provides, to the calculation unit 49, the differential value of the yaw angular velocity as a yaw angular acceleration.

(79) The output signal from the top-bottom acceleration sensor 24 is passed through the low-pass filter 34 and is provided to the calculation unit 49 as a top-bottom acceleration. The output signal from the front-rear acceleration sensor 25 is passed through the low-pass filter 35 and is fed into the calculation unit 49 as a front-rear acceleration. The output signal from the left-right acceleration sensor 26 is passed through the low-pass filter 36 and is provided to the calculation unit 49 as a left-right acceleration.

(80) The frequency characteristics of the low-pass filters 31, 32, 34, 35 and 36 are decided depending on the output characteristics of the corresponding sensors 21, 22, 24, 25 and 26. More specifically, the frequency characteristics of the noise components contained in the output signals from the sensors 21, 22, 24, 25 and 26 can be identified in advance, at the stage of apparatus design. The low-pass filters 31, 32, 34, 35 and 36 may be designed to block these noise components and pass the detection signals of the sensors 21, 22, 24, 25 and 26, which will be needed.

(81) The output signal from the rear-wheel velocity sensor 7 is fed into the calculation unit 49 as a rear-wheel velocity. The rear-wheel velocity is a rotational velocity of the outermost periphery of the tire, assuming that there is no slide between the road surface and the tire of the rear wheel 3 and, in reality, calculated based on the output signal of the rear-wheel velocity sensor 7 and the size of the tire. To simplify the explanation, FIG. 3 shows a signal indicative of rear-wheel velocity as if it were provided by the rear-wheel velocity sensor 7.

(82) The calculation unit 49 receives detected values relating to roll angular velocity, roll angular acceleration, yaw acceleration, yaw angular acceleration, top-bottom acceleration, front-rear acceleration, left-right acceleration, and rear-wheel velocity. Based on these values, the calculation unit 49 estimates the roll angle, front-rear direction vehicle velocity, roll angular velocity sensor offset, yaw angular velocity sensor offset, left-right acceleration sensor offset and top-bottom acceleration sensor offset before outputting them.

(83) The roll angular velocity sensor offset is the offset error for the roll angular velocity sensor 21. The yaw angular velocity sensor offset is the offset error for the yaw angular velocity sensor 22. The left-right acceleration sensor offset is the offset error for the left-right acceleration sensor 26. The top-bottom acceleration sensor offset is the offset error for the top-bottom acceleration sensor 24.

(84) The rear-wheel velocity detected by the rear-wheel velocity sensor 7, and the front-rear direction vehicle velocity, roll angular velocity sensor offset, yaw angular velocity sensor offset, left-right acceleration sensor offset, and top-bottom acceleration sensor offset estimated by the calculation unit 49 will be denoted by the following characters.

(85) TABLE-US-00002 TABLE 2 Parameter Meaning v.sub.r rear-wheel velocity V.sub.x front-rear-direction vehicle velocity b.sub.ro roll angular velocity sensor offset b.sub.ya yaw angular velocity sensor offset b.sub.y left-right acceleration sensor offset b.sub.z top-bottom acceleration sensor offset

(86) <Configuration of Kalman Filter>

(87) FIG. 4 is a schematic block diagram of an exemplary configuration of the calculation unit 49. As shown in FIG. 4, the calculation unit 49 includes a plurality of Kalman filters 50_1, 50_2 and 50_3, and a state quantity determination unit 503. In the following description, the Kalman filters 50_1, 50_2 and 50_3 may be collectively referred to as Kalman filters 50.

(88) FIG. 4 shows an implementation where the calculation unit 49 includes three Kalman filters 50; however, this number is merely an example. The calculation unit 49 may include two Kalman filters 50, or four or more Kalman filters 50.

(89) The Kalman filters 50 (50_1, 50_2 and 50_3) use a kinematic model for the vehicle 100, described below.

(90) In FIG. 4, the Kalman filters 50 (50_1, 50_2 and 50_3) each include a system equation calculation unit 51, an observation equation calculation unit 52, a subtractor 53, an adder 54, an integrator 55, a Kalman gain calculation unit 56, a likelihood calculation unit 57, a low-pass filter 58, and an imaginary offset input unit 59.

(91) The system equation that is an equation used for the calculation at the system equation calculation unit 51 includes the function f(x,u). The observation equation that is an equation used for the calculation at the observation equation calculation unit 52 includes the function h(x,u). The Kalman gain calculation unit 56 includes a fifth-degree Kalman gain K.

(92) The imaginary offset input unit 59 provides, as an offset value for a predetermined one of the sensors of the group 5, a predetermined value for each of the Kalman filters 50 (50_1, 50_2 and 50_3) to the observation equation calculation unit 52. According to the present embodiment, the imaginary offset input unit 59 is configured to provide the offset value b.sub.y for the left-right acceleration sensor 26 to the observation equation calculation unit 52. In this implementation, the left-right acceleration sensor 26 corresponds to the detection unit of interest, or in other words, in this example the left-right acceleration sensor 26 is a detection unit associated with the offset error whose imaginary offset quantity is provided in each of the Kalman filters 50 (50_1, 50_2 and 50_3).

(93) In FIG. 4, the offset value for the left-right acceleration sensor 26 provided by the imaginary offset input unit 59 of the Kalman filter 50_1 to the observation equation calculation unit 52 is denoted by b.sub.y. Similarly, the offset value for the left-right acceleration sensor 26 provided by the imaginary offset input unit 59 of the Kalman filter 50_2 to the observation equation calculation unit 52 is denoted by b.sub.y2. The offset value for the left-right acceleration sensor 26 provided by the imaginary offset input unit 59 of the Kalman filter 50_3 to the observation equation calculation unit 52 is denoted by b.sub.y3.

(94) The likelihood calculation unit 57 determines a likelihood using calculation, the likelihood being indicative of the reliability of the result from the estimation by the Kalman filter 50 (50_1, 50_2 or 50_3). The low-pass filter 58 is a calculation unit for filtering the value calculated by the likelihood calculation unit 57. The low-pass filter 58 may be replaced by any other calculation unit that can implement the same functionality. It is optional whether the low-pass filter 58 is included. Examples of the calculation performed by the likelihood calculation unit 57 will be described further below.

(95) The calculation units 51, 52, 53, 54, 55, 56, 57 and 58 constituting a Kalman filter 50 may be implemented by, for example, a program that has been prepared in advance being performed by the ECU 20. Alternatively, some or all of the calculation units 51, 52, 53, 54, 55, 56, 57 and 58 may be implemented by independent hardware mounted.

(96) In the current estimation operation, the following values are provided as the input parameter u of the function f(x,u) included in the system equation is the detected value of the roll angular velocity .sub.ro, the detected value of the roll angular acceleration (differential value of the roll angular velocity .sub.ro), the detected value of the yaw angular velocity .sub.ya, the yaw angular acceleration (differential value of the yaw angular velocity .sub.ya), and the detected value of the front-rear acceleration G.sub.x.

(97) Further, the following values are provided as the input parameter x of the function f(x,u) included in the system equation: the estimated value of the roll angle , the estimated value of the vehicle velocity V.sub.x, the estimated value of the roll angular velocity sensor offset b.sub.ro, the estimated value of the yaw angular velocity sensor offset b.sub.ya, and the estimated value of the top-bottom acceleration sensor offset b.sub.z from the previous estimation operation.

(98) The output from the system equation calculation unit 51 is the predicted differential value of the roll angle , the predicted differential value of the vehicle velocity V.sub.x, the predicted differential value of the roll angular velocity sensor offset b.sub.ro, the predicted differential value of the yaw angular velocity sensor offset b.sub.ya, and the predicted differential value of the top-bottom acceleration sensor offset b.sub.z.

(99) The adder 54 adds the fifth-degree Kalman gain K obtained by the previous estimation operation to the predicted differential value of the roll angle , the predicted differential value of the vehicle velocity V.sub.x, the predicted differential value of the roll angular velocity sensor offset b.sub.ro, the predicted differential value of the yaw angular velocity sensor offset b.sub.ya, and the predicted differential value of the top-bottom acceleration sensor offset b.sub.z.

(100) The predicted differential value of the roll angle , the predicted differential value of the vehicle velocity V.sub.x, the predicted differential value of the roll angular velocity sensor offset b.sub.ro, the predicted differential value of the yaw angular velocity sensor offset b.sub.ya, and the predicted differential value of the top-bottom acceleration sensor offset b.sub.z to which the Kalman gain K has been added are integrated by the integrator 55. This provides the estimated value of the roll angle , the estimated value of the vehicle velocity V.sub.x, the estimated value of the roll angular velocity sensor offset b.sub.ro, the estimated value of the yaw angular velocity sensor offset b.sub.ya, and the estimated value of the top-bottom acceleration sensor offset b.sub.z from the current estimation operation.

(101) The following values are provided as the input parameter x of the function h(x,u) included in the observation equation: the estimated value of the roll angle , the estimated value of the vehicle velocity V.sub.x, the estimated value of the roll angular velocity sensor offset b.sub.ro, the estimated value of the yaw angular velocity sensor offset b.sub.ya, and the estimated value of the top-bottom acceleration sensor offset b.sub.z. Further, as discussed above, the offset value for left-right acceleration sensor 26 provided by the imaginary offset input unit 59 is provided as the input parameter x of the function h(x,u) included in the observation equation.

(102) The output from the observation equation calculation unit 52 is the calculated value of the top-bottom acceleration G.sub.z, the calculated value of the left-right acceleration G.sub.y, and the calculated value of the rear-wheel velocity v.sub.r.

(103) The Kalman filters 50 each receive, as the input parameter y, the detected value of the top-bottom acceleration G.sub.z, the detected value of the left-right acceleration G.sub.y, and the detected value of the rear-wheel velocity v.sub.r. The Kalman gain calculation unit 56 calculates the Kalman gain K based on the difference between the detected values of the top-bottom acceleration G.sub.z, left-right acceleration G.sub.y and rear-wheel velocity v.sub.r and the calculated values (this difference may be hereinafter referred to as observation/prediction error e).

(104) Finding this kinematic model's system equation f(x,u) and observation equation h(x,u) gives the relational expression for the input parameters u and y and the output parameter x.

(105) <Finding of System Equation and Observation Equation>

(106) The present embodiment supposes the following points to simplify the kinematic model.

(107) (a) There is no rotational slide between the rear wheel 3 and road surface.

(108) (b) The side-skid velocity of the rear wheel 3 is zero.

(109) (c) The road surface is flat. Flat as used herein means a plane without irregularities, and may be inclined.

(110) (d) The vehicle 100 does not pitch.

(111) Based on suppositions (a) to (d), the kinematic model equation is found in the following manner. The differential value of the yaw angle, the differential value of the pitch angle, and the differential value of the roll angle will be denoted by the following characters.

(112) TABLE-US-00003 TABLE 3 Parameter Meaning {dot over ()} differential value of roll angle {dot over ()} differential value of yaw angle {dot over ()} differential value of pitch angle

(113) First, the following equation may be established based on a common relational expression between Euler angle and angular velocity.

(114) $\begin{array}{cc}\left[\mathrm{Formula}2\right]& \\ \left[\begin{array}{c}\stackrel{.}{}\\ \stackrel{.}{}\\ \stackrel{.}{}\end{array}\right]=\left[\begin{array}{ccc}1& \tan \sin & \tan \cos \\ 0& \cos & -\sin \\ 0& \sin \sec & \cos \sec \end{array}\right]\left[\begin{array}{c}{}_{\mathrm{ro}}\\ {}_{\mathrm{pi}}\\ {}_{\mathrm{ya}}\end{array}\right]& \left(1\right)\end{array}$

(115) Supposition (d) provided above means that the pitch angle and its differential value are zero. Thus, the following equation is derived from equation (1).

(116) $\begin{array}{cc}\left[\mathrm{Formula}3\right]& \\ \left[\begin{array}{c}\stackrel{.}{}\\ \stackrel{.}{}\\ \stackrel{.}{}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos & -\sin \\ 0& \sin & \cos \end{array}\right]\left[\begin{array}{c}{}_{\mathrm{ro}}\\ {}_{\mathrm{pi}}\\ {}_{\mathrm{ya}}\end{array}\right]& \left(2\right)\end{array}$

(117) Based on the second row of equation (2), the pitch angular velocity .sub.pi may be deleted. This gives the following equation.

(118) $\begin{array}{cc}\left[\mathrm{Formula}4\right]& \\ \left[\begin{array}{c}\stackrel{.}{}\\ \stackrel{.}{}\end{array}\right]=\left[\begin{array}{c}{}_{\mathrm{ro}}\\ {}_{\mathrm{ya}}\sec \end{array}\right]& \left(3\right)\end{array}$

(119) FIG. 5 illustrates where the group of sensors 5 are mounted. In FIG. 5, (a) shows the left side of the vehicle 100 while (b) shows the front of the vehicle 100. FIG. 6 is a schematic cross-sectional view of the rear wheel 3. FIG. 7 illustrates where the group of sensors 5 are mounted by means of vectors.

(120) In FIG. 5, the position at which the group of sensors 5 are mounted is denoted by PS. The horizontal distance between the mounting position PS and the center of the rear wheel 3 is denoted by L, and the height of the mounting position PS relative to the road surface 200 is denoted by h.

(121) The positional vector of the mounting position PS for the group of sensors 5 relative to the origin O of the inertia coordinate system, the positional vector of the grounding point P3 of the rear wheel 3 relative to the origin O of the inertia coordinate system, the vector from the grounding point P3 of the rear wheel 3 to the mounting position PS for the group of sensors 5, and the second-order differential vector of various vectors will be denoted by the following characters. The two dots on top of the character indicating a parameter means second-order temporal differential.

(122) TABLE-US-00004 TABLE 4 Parameter Meaning r positional vector of mounting position PS for group of sensors 5 {umlaut over (r)} second-order differential vector of positional vector r r.sub.0 positional vector of grounding point P {umlaut over (r)}.sub.0 second-order differential vector of positional vector r.sub.0 vector from grounding point P to mounting position PS of group of sensors 5 {umlaut over ()} second-order differential vector of vector

(123) This gives Equation (4) below.
[Formula 5]
r=r.sub.0+(4)

(124) Gravity acceleration vector and acceleration vector detected at the mounting position PS will be denoted by the following characters. The acceleration vector G is detected by the top-bottom acceleration sensor 24 provided at the mounting position PS, front-rear acceleration sensor 25 and left-right acceleration sensor 26.

(125) TABLE-US-00005 TABLE 5 Parameter Meaning g Gravity acceleration vector G acceleration vector at mounting position PS for group of sensors 5

(126) The acceleration vector G is obtained by Equation (5) below.
[Formula 6]
G={umlaut over (r)}+g={umlaut over (r)}.sub.0+{umlaut over ()}+g (5)

(127) The right side of Equation (5) will be calculated below. The vector shown in FIG 7 is expressed by the following equation.
[Formula 7]
=[e.sub.b]=[e.sub.bx,e.sub.by,e.sub.bz](6)

(128) As discussed above, the vector e.sub.b is the basis vector of the vehicle coordinate system, where e.sub.bx corresponds to the component in the forward direction with respect to the vehicle body 1, e.sub.by corresponds to the component in the left direction with respect to the vehicle body 1, and e.sub.bz corresponds to the component in the upward direction with respect to the vehicle body 1. Based on FIGS. 6 and 7, the matrix shown in the right side of Equation (6) is expressed by the equation below. In FIG. 7, the radius of a cross section of the rear wheel 3 is denoted by R.sub.cr, and the radius of the rear wheel 3 is denoted by R.sub.e. As discussed above, the roll angle of the vehicle body 1 is denoted by .

(129) $\begin{array}{cc}\left[\mathrm{Formula}8\right]& \\ =\left[\begin{array}{c}L\\ R_{\mathrm{cr}}\sin \\ h-R_{\mathrm{cr}}\left(1-\cos \right)\end{array}\right]& \left(7\right)\end{array}$

(130) When movements of the suspension of the vehicle 100 are considered, to speak exactly, L and h vary; however, such variances are sufficiently small compared with the values of L and h, and thus the values of L and h can be considered approximately constant.

(131) From Equation (7) provided above, the second-order differential vector of the vector can be expressed by the following equation.

(132) $\begin{array}{cc}\left[\mathrm{Formula}9\right]& \\ \stackrel{\mathrm{.Math.}}{}=\left[e_b\right]\left[\begin{array}{c}{a}_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)\\ a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)\\ a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)\end{array}\right]& \left(8\right)\end{array}$

(133) In Equation (8), a.sub.x, a.sub.y and a.sub.z are functions. The functions a.sub.x, a.sub.y and a.sub.z can be determined by calculating Equations (6) and (7). Using Equation (1) provided above to rearrange Equation (7) into Equation (8) removes the differential value of the roll angle and the differential value of the yaw angle .

(134) Next, the side-skid velocity of the vehicle 100 is denoted by V.sub.y. The first-order differential vector of the positional vector r.sub.0 in FIG. 7 is expressed by the following equation using the vehicle velocity V.sub.x and side-skid velocity V.sub.y. The vector e.sub.0 is the basis vector of the inertia coordinate system.

(135) $\begin{array}{cc}\left[\mathrm{Formula}10\right]& \\ {\stackrel{.}{r}}_0=\left[e_o\right]\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]& \left(9\right)\end{array}$

(136) From Supposition (b), V.sub.y=0; when Equation (9) is first-order-differentiated, the second-order differential vector of the positional vector r is expressed by the following equation.

(137) $\begin{array}{cc}\left[\mathrm{Formula}11\right]& \\ {\stackrel{\mathrm{.Math.}}{r}}_0=\left[e_b\right]\left[\begin{array}{c}{\stackrel{.}{V}}_x\\ V_x{}_{\mathrm{ya}}\\ -V_x{}_{\mathrm{ya}}\tan \end{array}\right]& \left(10\right)\end{array}$

(138) Next, the gravity acceleration vector may be expressed by the following equation. g in the right side of Equation (11) indicates the magnitude of the gravity acceleration.

(139) $\begin{array}{cc}\left[\mathrm{Formula}12\right]& \\ g=\left[e_b\right]\left[\begin{array}{c}0\\ g\sin \\ g\cos \end{array}\right]& \left(11\right)\end{array}$

(140) Based on Equations (5), (8), (10) and (11), the acceleration vector G detected at the mounting position PS may be expressed by the following equation.

(141) $\begin{array}{cc}\left[\mathrm{Formula}13\right]& \\ G=\stackrel{\mathrm{.Math.}}{r}+g={\stackrel{\mathrm{.Math.}}{r}}_0+\stackrel{\mathrm{.Math.}}{}+g=[e_b][\begin{array}{c}{\stackrel{.}{V}}_x+a_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)\\ V_x{}_{\mathrm{ya}}+a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\sin \\ -V_x{}_{\mathrm{ya}}\tan +a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\cos \end{array}]& \left(12\right)\end{array}$

(142) The acceleration vector G detected at the mounting position PS may be expressed by the following equation using the front-rear acceleration G.sub.x detected by the front-rear acceleration sensor 25, the left-right acceleration G.sub.y detected by the left-right acceleration sensor 26, and the top-bottom acceleration G.sub.z detected by the top-bottom acceleration sensor 24.

(143) 0$\begin{array}{cc}\left[\mathrm{Formula}14\right]& \\ G=\left[e_b\right]\left[\begin{array}{c}{G}_x\\ G_y\\ G_z\end{array}\right]& \left(13\right)\end{array}$

(144) Thus, based on Equations (12) and (13), the front-rear acceleration G.sub.x, the left-right acceleration G.sub.y and the top-bottom acceleration G.sub.z may be expressed by the following equation.

(145) $\begin{array}{cc}\left[\mathrm{Formula}15\right]& \\ \left[\begin{array}{c}{G}_x\\ G_y\\ G_z\end{array}\right]=\left[\begin{array}{c}{\stackrel{.}{V}}_x+a_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)\\ V_x{}_{\mathrm{ya}}+a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\sin \\ -V_x{}_{\mathrm{ya}}\tan +a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\cos \end{array}\right]& \left(14\right)\end{array}$

(146) Next, the relationship between the rear-wheel velocity v.sub.r and vehicle velocity V.sub.x is determined. Supposition (a) means that there is no slide between the rear wheel 3 and road surface 200, and thus the relationship expressed by the following equation can be established between the rear-wheel velocity v.sub.r and vehicle velocity V.sub.x.

(147) $\begin{array}{cc}\left[\mathrm{Formula}16\right]& \\ \frac{V_x}{R_e-R_{\mathrm{cr}}\left(1-\cos \right)}=\frac{v_r}{R_e}& \left(15\right)\end{array}$

(148) Equation (15) gives the following equation.

(149) $\begin{array}{cc}\left[\mathrm{Formula}17\right]& \\ v_r=\frac{R_e}{R_e-R_{\mathrm{cr}}\left(1-\cos \right)}{V}_x=\frac{1}{1-R_{\mathrm{cr}}/R_e\left(1-\cos \right)}{V}_x& \left(16\right)\end{array}$

(150) Equations (1), (14) and (16) give the following equations.

(151) $\begin{array}{cc}\left[\mathrm{Formula}18\right]& \\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}\\ V_x\end{array}\right]=\left[\begin{array}{c}{}_{\mathrm{ro}}\\ G_x-a_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)\end{array}\right]& \left(17\right)\\ \left[\mathrm{Formula}19\right]& \\ \left[\begin{array}{c}{G}_y\\ G_z\\ v_r\end{array}\right]=\left[\begin{array}{c}{V}_x{}_{\mathrm{ya}}+a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\sin \\ -V_x{}_{\mathrm{ya}}\tan +a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\cos \\ \frac{1}{1-R_{\mathrm{cr}}/R_e\left(1-\cos \right)}{V}_x\end{array}\right]& \left(18\right)\end{array}$

(152) Each of the Kalman filters 50, at the system equation calculation unit 51, uses Equation (17) as the system equation to perform calculation, and, at the observation equation calculation unit 52, uses Equation (18) as the observation equation to perform calculation.

(153) Even if the roll angular velocity offset b.sub.ro, yaw angular velocity offset b.sub.ya, pitch angular velocity offset b.sub.pi and top-bottom acceleration offset b.sub.z vary, such variances are small compared with movements of the vehicle 100. Thus, the differential value of the roll angular velocity offset b.sub.ro, the differential value of the yaw angular velocity offset b.sub.ya, the differential value of the pitch angular velocity offset b.sub.pi, and the differential value of the top-bottom acceleration offset b.sub.z can be considered to be zero.

(154) Further, replacing some values in Equations (17) and (18) with values reflecting offset errors gives the following equations.

(155) $\begin{array}{cc}\left[\mathrm{Formula}20\right]& \\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}\\ V_x\\ b_{\mathrm{ro}}\\ b_{\mathrm{ya}}\\ b_z\end{array}\right]=\left[\begin{array}{c}{}_{\mathrm{ro}}-b_{\mathrm{ro}}\\ G_x-a_x\left({}_{\mathrm{ro}}-b_{\mathrm{ro}},{}_{\mathrm{ya}}-b_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)\\ 0\\ 0\\ 0\end{array}\right]& \left(19\right)\\ \left[\mathrm{Formula}21\right]& \\ \left[\begin{array}{c}{G}_y\\ G_z\\ v_r\end{array}\right]=\left[\begin{array}{c}{V}_x{}_{\mathrm{ya}}+a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\sin \\ -V_x{}_{\mathrm{ya}}\tan +a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\cos +b_z\\ \frac{1}{1-R_{\mathrm{cr}}/R_e\left(1-\cos \right)}{V}_x\end{array}\right]& \left(20\right)\end{array}$

(156) When the offset errors are taken into consideration, each of the Kalman filters 50, at the system equation calculation unit 51, uses Equation (19) as the system equation to perform calculation, and, at the observation equation calculation unit 52, uses Equation (20) as the observation equation to perform calculation. Equations (19) and (20) take account of the roll angular velocity offset b.sub.ro, yaw angular velocity offset b.sub.ya, and top-bottom acceleration offset b.sub.z.

(157) As the Kalman filters 50 use Equation (19) as the system equation and use Equation (20) as the observation equation to perform calculation, the roll angle , vehicle velocity V.sub.x, roll angular velocity offset b.sub.ro, yaw angular velocity offset b.sub.ya, and top-bottom acceleration offset b.sub.z may be estimated. The right side of Equation (19) corresponds to the function f(x,u) and the right side of Equation (20) corresponds to the function h(x,u).

(158) An angular velocity sensor is more likely to have an offset error than an acceleration sensor. In view of this, according to the present embodiment, the offset error of the roll angular velocity sensor 21 (roll angular velocity sensor offset b.sub.ro) and the offset error of the yaw angular velocity sensor 22 (yaw angular velocity sensor offset b.sub.ya) are estimated. Using the estimated values of the roll angular velocity offset b.sub.ro and yaw angular velocity offset b.sub.ya in a subsequent estimation operation improves the estimation accuracy for the roll angle .

(159) Further, if the offset errors of the three acceleration sensors (top-bottom acceleration sensor 24, front-rear acceleration sensor 25 and left-right acceleration sensor 26) can be estimated, the estimation accuracy for the roll angle is expected to further improve. However, when the offset errors of the three acceleration sensors are to be estimated, observability cannot be maintained. In view of this, according to the present embodiment, the offset error of the top-bottom acceleration sensor 24 (top-bottom acceleration sensor offset b.sub.z) is estimated for the following reasons. When the roll angle of the vehicle body 1 is in a small range, the top-bottom acceleration of the vehicle body 1 does not change significantly. If the detected value of the top-bottom acceleration in such a case is changed by the top-bottom acceleration sensor offset b.sub.z, the effect of a change in the detected value of the top-bottom acceleration when the roll angle is to be estimated is large. Thus, using the estimated value of the top-bottom acceleration sensor offset b.sub.z in a subsequent estimation operation further improves the estimation accuracy found when the roll angle is in a small range.

(160) When the roll angle is to be estimated, in addition to the change in the detected value of the top-bottom acceleration, although to a lesser degree, a change in the detected value of the left-right acceleration is likely to affect the result. In view of this, as discussed above with reference to FIG. 4, the calculation unit 49 according to the present embodiment uses a plurality of Kalman filters 50 to take account of the effects of the left-right acceleration sensor offset b.sub.y. Specifically, the observation equation calculation unit 52 of each of the Kalman filters 50 (50_1, 50_2 and 50_3) receives the left-right acceleration sensor offset b.sub.y (b.sub.y1, b.sub.y2 and b.sub.y3) from the imaginary offset input unit 59.

(161) The observation equation calculation unit 52 according to the present embodiment uses, instead of Equation (20) provided above, the following equation as the observation equation to perform calculation.

(162) $\begin{array}{cc}\left[\mathrm{Formula}22\right]& \\ \left[\begin{array}{c}{G}_y\\ G_z\\ v_r\end{array}\right]=\left[\begin{array}{c}{V}_x{}_{\mathrm{ya}}+a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\sin +b_y\\ -V_x{}_{\mathrm{ya}}\tan +a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},,L,h,R_{\mathrm{cr}}\right)+g\cos +b_z\\ \frac{1}{1-R_{\mathrm{cr}}/R_e\left(1-\cos \right)}{V}_x\end{array}\right]& \left(21\right)\end{array}$

(163) That is, each of the Kalman filters 50 according to the present embodiment, at the system equation calculation unit 51, uses Equation (19) as the system equation to perform calculation, and, at the observation equation calculation unit 52, uses Equation (21) as the observation equation to perform calculation.

(164) The value of b.sub.y in the first row of Equation (21) is the value of the left-right acceleration sensor offset b.sub.y(b.sub.y1,b.sub.y2,b.sub.y3) provided by the imaginary offset input unit 59 of each of the Kalman filters 50 (50_1, 50_2 and 50_3).

(165) Based on the observation equation including the left-right acceleration sensor offset b.sub.y(b.sub.y1,b.sub.y2,b.sub.y3) provided by the imaginary offset input unit 59, the observation equation calculation unit 52 calculates the estimated values of the top-bottom acceleration G.sub.z, left-right acceleration G.sub.y and rear-wheel velocity v.sub.r. These estimated values are provided to the likelihood calculation unit 57 to calculate the value relating to the likelihood indicative of the reliability of the estimation results of the Kalman filters 50 (50_1, 50_2 and 50_3).

(166) Preferably, the largest one of the values of the left-right acceleration sensor offset b.sub.y(b.sub.y1,b.sub.y2,b.sub.y3) provided by the imaginary offset input unit 59 is larger than the maximum value of the zero-point offset that can be provided by the left-right acceleration sensor 26, and the smallest value is smaller than the minimum value of the zero-point offset that can be provided by the left-right acceleration sensor 26. Thus, the observation equation calculation unit 52 can calculate the estimated values of the top-bottom acceleration G.sub.z, left-right acceleration G.sub.y and rear-wheel velocity v.sub.r taking account of situations where the value of the zero-point offset of the left-right acceleration sensor 26 is the largest.

(167) For example, if it is ensured that the value of the zero-point offset that can be provided by the left-right acceleration sensor 26 is in a range of 100 mG, then, the offset value provided by the imaginary offset input unit 59 of the Kalman filter 50_1 may be b.sub.y1100 mG and the offset value provided by the imaginary offset input unit 59 of the Kalman filter 50_3 may be b.sub.y3100 mG. In this case, the offset value provided by the imaginary offset input unit 59 of the Kalman filter 50_2 may be b.sub.y2=0 mG.

(168) As discussed above, the above-described embodiment describes an implementation where the calculation unit 49 includes three Kalman filters 50 (50_1, 50_2 and 50_3); alternatively, the value of the left-right acceleration sensor offset b.sub.y may be set in a similar way if the calculation unit 49 includes two Kalman filters 50 or four or more Kalman filters 50.

(169) Next, the likelihood calculated by the likelihood calculation unit 57 will be described. As discussed above, if the difference between an estimated value and an actual detected value is expressed by the observation/prediction error e, e is defined by the following equation.

(170) $\begin{array}{cc}\left[\mathrm{Formula}23\right]& \\ \begin{array}{c}e=y-h\left(x\right)\\ =\left[\begin{array}{c}{G}_y\\ G_z\\ v_r\end{array}\right]-h\left(x\right)\end{array}& \left(22\right)\end{array}$

(171) In Equation (22), y is the detected value of the top-bottom acceleration G.sub.z, the detected value of the left-right acceleration G.sub.y, and the detected value of the rear-wheel velocity v.sub.r provided by the Kalman filters 50 as input parameters. h(x) is the calculation result from the observation equation calculation unit 52.

(172) If the detection error in the top-bottom acceleration G.sub.z detected by the top-bottom acceleration sensor 24 is denoted by G.sub.z, the detection error in the left-right acceleration G.sub.y detected by the left-right acceleration sensor 26 is denoted by G.sub.y, and the detection error in the rear-wheel velocity v.sub.r detected by the rear-wheel velocity sensor 7 is denoted by v.sub.r, then, the variance-covariance matrix R of these detection errors can be expressed by the equation below. In the equation below, E(a) means the expected value of a.

(173) $\begin{array}{cc}\left[\mathrm{Formula}24\right]& \\ R=\left[\begin{array}{ccc}E\left(G_y{G}_y\right)& E\left(G_y{G}_z\right)& E\left(G_y{v}_r\right)\\ E\left(G_z{G}_y\right)& E\left(G_z{G}_z\right)& E\left(G_z{v}_r\right)\\ E\left(v_r{G}_y\right)& E\left(v_r{G}_z\right)& E\left(v_r{v}_r\right)\end{array}\right]& \left(23\right)\end{array}$

(174) Further, if the estimation error in the roll angle is denoted by , the estimation error in the vehicle velocity V.sub.x is denoted by V.sub.x, the estimation error in the roll angular velocity sensor offset b.sub.ro is denoted by b.sub.ro, the estimation error in the yaw angular velocity sensor offset b.sub.ya is denoted by b.sub.ya, and the estimation error in the top-bottom acceleration sensor offset b.sub.z is denoted by b.sub.z, then, the variance-covariance matrix P of these detection errors can be expressed by the following equation.

(175) $\begin{array}{cc}\left[\mathrm{Formula}25\right]& \\ P=\left[\begin{array}{ccccc}E\left(\right)& E\left(V_x\right)& E\left(b_{\mathrm{ro}}\right)& E\left(b_{\mathrm{ya}}\right)& E\left(b_z\right)\\ E\left(V_x\right)& E\left(V_x{V}_x\right)& E\left(V_x{b}_{\mathrm{ro}}\right)& E\left(V_x{b}_{\mathrm{ya}}\right)& E\left(V_x{b}_z\right)\\ E\left(b_{\mathrm{ro}}\right)& E\left(b_{\mathrm{ro}}{V}_x\right)& E\left(b_{\mathrm{ro}}{b}_{\mathrm{ro}}\right)& E\left(b_{\mathrm{ro}}{b}_{\mathrm{ya}}\right)& E\left(b_{\mathrm{ro}}{b}_z\right)\\ E\left(b_{\mathrm{ya}}\right)& E\left(b_{\mathrm{ya}}{V}_x\right)& E\left(b_{\mathrm{ya}}{b}_{\mathrm{ro}}\right)& E\left(b_{\mathrm{ya}}{b}_{\mathrm{ya}}\right)& E\left(b_{\mathrm{ya}}{b}_z\right)\\ E\left(b_z\right)& E\left(b_z{V}_x\right)& E\left(b_z{b}_{\mathrm{ro}}\right)& E\left(b_z{b}_{\mathrm{ya}}\right)& E\left(b_z{b}_z\right)\end{array}\right]& \left(24\right)\end{array}$

(176) The Kalman filters 50 (50_1, 50_2 and 50_3) successively calculate the matrix P and matrix R.

(177) The variance-covariance matrix S for the error contained in the observation/prediction error e is expressed by the following equation.
[Formula 26]
S=R+HPH.sup.t (25)

(178) The superscript tin the equation provided above means transposed matrix. That is, H.sup.t means the transposed matrix of the matrix H. H is the Jacobian matrix of h(x), defined by the following equation.

(179) 0$\begin{array}{cc}\left[\mathrm{Formula}27\right]& \\ H=\left[\begin{array}{ccccc}\frac{h\left(x\right)}{}& \frac{h\left(x\right)}{V_x}& \frac{h\left(x\right)}{b_{\mathrm{ro}}}& \frac{h\left(x\right)}{b_{\mathrm{ya}}}& \frac{h\left(x\right)}{b_z}\end{array}\right]& \left(26\right)\end{array}$

(180) The likelihood calculation unit 57 calculates the likelihood based on the equation provided below, for example. This likelihood is a likelihood value that is momentary, and may be called momentary likelihood.

(181) $\begin{array}{cc}\left[\mathrm{Formula}28\right]& \\ =\frac{1}{\sqrt{\det \left(S\right)}}\exp \left[-\frac{1}{2}{\left\{y-h\left(x\right)\right\}}^t{S}^{-1}\left\{y-h\left(x\right)\right\}\right]& \left(27\right)\end{array}$

(182) The likelihood calculation unit 57 is only required to be configured to calculate the likelihood based on the observation/prediction error e=yh(x), and the calculation method is not limited to Equation (27).

(183) x(,V.sub.x,b.sub.ro,b.sub.ya,b.sub.z) estimated by the Kalman filter 50_1 is denoted by x.sub.1, and the likelihood calculated by the likelihood calculation unit 57 of the Kalman filter 50_1 is denoted by .sub.1. Similarly, x(,V.sub.x,b.sub.ro,b.sub.ya,b.sub.z) estimated by the Kalman filter 50_2 is denoted by x.sub.2, and the likelihood calculated by the likelihood calculation unit 57 of the Kalman filter 50_2 is denoted by .sub.2. Similarly, x(,V.sub.x,b.sub.ro,b.sub.ya,b.sub.z) estimated by the Kalman filter 50_3 is denoted by x.sub.3, and the likelihood calculated by the likelihood calculation unit 57 of the Kalman filter 50_3 is denoted by .sub.3. Then, the left-right acceleration sensor offset b.sub.y is calculated by the following equation.

(184) $\begin{array}{cc}\left[\mathrm{Formula}29\right]& \\ b_y=\frac{\underset{i=1}{\overset{n}{.Math.}}{\stackrel{~}{}}_i.Math.b_{\mathrm{yi}}}{\underset{i=1}{\overset{n}{.Math.}}{\stackrel{~}{}}_i}& \left(28\right)\end{array}$

(185) In Equation 28, the character with a tilde () on top of means a value obtained after the momentary likelihood has been filtered by the low-pass filter 58. It does not mean that filtering is necessary. If filtering is not performed, the value of the momentary likelihood may be used. In Equation (28), n is the number of Kalman filters 50 included in the calculation unit 49. According to the present embodiment, n=3.

(186) Each Kalman filter 50 performs the estimation process taking account of the left-right acceleration sensor offset b.sub.y(b.sub.y1,b.sub.y2,b.sub.y3) provided by the imaginary offset input unit 59. Then, the indicators that show how reliable these estimation results are are calculated, which are (.sub.1, .sub.2, .sub.3). Thus, the value of the left-right acceleration sensor offset b.sub.y provided to the imaginary offset input unit 59 included in each of the Kalman filters 50 (50_1, 50_2 and 50_3) is weighted depending on the likelihood (.sub.1, .sub.2, .sub.3), which indicates how reliable the estimation results of the Kalman filters 50 (50_1, 50_2 and 50_3) are, thereby determining the estimated value of the left-right acceleration sensor offset b.sub.y.

(187) Further, based on the same reasoning, as expressed by the equation below, x(,V.sub.x,b.sub.ro,b.sub.ya,b.sub.z) estimated by each Kalman filter 50 is weighted depending on the likelihood (.sub.1, .sub.2, .sub.3), which indicates how reliable the estimation results of the Kalman filters 50 (50_1, 50_2 and 50_3) are, thereby providing the estimation results taking account of the left-right acceleration sensor offset b.sub.y.

(188) $\begin{array}{cc}\left[\mathrm{Formula}30\right]& \\ x=\frac{\underset{i=1}{\overset{n}{.Math.}}{\stackrel{~}{}}_i.Math.x_i}{\underset{i=1}{\overset{n}{.Math.}}{\stackrel{~}{}}_i}& \left(29\right)\end{array}$

(189) The state quantity determination unit 503 performs the calculation represented by Equations (28) and (29). Thus, the calculation unit 49 estimates the left-right acceleration sensor offset b.sub.y, in addition to the roll angle , vehicle velocity V.sub.x, roll angular velocity offset b.sub.ro, yaw angular velocity offset b.sub.ya, and top-bottom acceleration offset b.sub.z. These estimated values are estimation results taking account of the left-right acceleration sensor offset b.sub.y, and thus have improved accuracy over the conventional art.

(190) Equations (28) and (29) perform calculation with proportional distribution depending on the value of the likelihood ; however, this calculation is merely an example. The state quantity determination unit 503 may use any other calculation method that performs weighting depending on the value of the likelihood .

(191) <Alternative Configurations>

(192) The attitude estimation apparatus 10 according to the present embodiment may use the following variations.

(193) (1) In the embodiment described above, the state quantity determination unit 503 performs a calculation where the left-right acceleration sensor offset b.sub.y provided to each Kalman filter 50 and the estimated value x estimated by the Kalman filter are weighted depending on the likelihood . Alternatively, a Kalman filter 50 that is most likely to be reliable may be selected based on the likelihood calculated by the Kalman filters 50, the left-right acceleration sensor offset b.sub.y provided to this Kalman filter 50 may be treated as the estimated value of the left-right acceleration sensor offset and the estimation results of this Kalman filter 50 may be treated as the estimation results of the calculation unit 49. This will simplify the calculation process by the state quantity determination unit 503.

(194) (2) In the embodiment described above, each Kalman filter 50 estimates the roll angle , vehicle velocity V.sub.x, roll angular velocity sensor offset b.sub.ro, yaw angular velocity sensor offset b.sub.ya, and top-bottom acceleration sensor offset b.sub.z, and the left-right acceleration sensor offset b.sub.y is estimated taking account of the likelihood obtained based on the estimation results of the Kalman filters 50. Alternatively, each Kalman filter 50 may estimate the roll angle , vehicle velocity V.sub.x, roll angular velocity sensor offset b.sub.ro, yaw angular velocity sensor offset b.sub.ya, and left-right acceleration sensor offset b.sub.y, and the top-bottom acceleration sensor offset b.sub.z may be estimated taking account of the likelihood obtained based on the estimation results of the Kalman filters 50. In this case, the top-bottom acceleration sensor 24 corresponds to the detection unit of interest or in other words, in this example the top-bottom acceleration sensor 24 is a detection unit associated with the offset error which is estimated by using the likelihood.

(195) In this case, the calculation unit 49 has the configuration shown in FIG. 8, instead of FIG. 4. That is, the imaginary offset input unit 59 is configured to provide the offset value b.sub.z for the top-bottom acceleration sensor 24 to the observation equation calculation unit 52. The observation equation calculation unit 52 uses Equation (21) as the observation equation to perform calculation. However, unlike in the above-described embodiment, the value of bz in the second row of Equation (21) is the value of the top-bottom acceleration sensor offset b.sub.z(b.sub.z1,b.sub.z2,b.sub.z3) provided by the imaginary offset input unit 59 of each Kalman filter 50 (50_1, 50_2 and 50_3). Based on the observation equation including the top-bottom acceleration sensor offset b.sub.z(b.sub.z1,b.sub.z2,b.sub.z3) provided by this imaginary offset input unit 59, the observation equation calculation unit 52 calculates the estimated values of the top-bottom acceleration G.sub.z, left-right acceleration G.sub.y and rear-wheel velocity v.sub.r. These estimated values are provided to the likelihood calculation unit 57 to calculate the value relating to the likelihood indicative of how reliable the estimation results of the Kalman filters 50 (50_1, 50_2 and 50_3) are.

(196) In this case, the state quantity determination unit 503 calculates the top-bottom acceleration sensor offset b.sub.z by performing calculation based on Equation (30), instead of Equation (28). Further, calculating the estimated value x by Equation (29) provides estimated values taking account of the roll angle , vehicle velocity V.sub.x, roll angle velocity offset b.sub.ro, yaw angle velocity offset b.sub.ya, top-bottom acceleration offset b.sub.z, and left-right acceleration sensor offset b.sub.y.

(197) $\begin{array}{cc}\left[\mathrm{Formula}31\right]& \\ b_z=\frac{\underset{i=1}{\overset{n}{.Math.}}{\stackrel{~}{}}_i.Math.b_{\mathrm{zi}}}{\underset{i=1}{\overset{n}{.Math.}}{\stackrel{~}{}}_i}& \left(30\right)\end{array}$

(198) Similarly, each Kalman filter 50 may estimate the roll angle , vehicle velocity V.sub.x, roll angle velocity sensor offset b.sub.ro, yaw angle velocity sensor offset b.sub.ya, and top-bottom acceleration sensor offset b.sub.z, and the front-rear acceleration sensor offset b.sub.x may be estimated taking account of the likelihood obtained based on the estimation results of the Kalman filters 50. In this case, the front-rear acceleration sensor 25 corresponds to the detection unit of interest, or in other words, in this example the front-rear acceleration sensor 25 is a detection unit associated with the offset error which is estimated by using the likelihood. The offset value for the front-rear acceleration sensor 25 provided by the imaginary offset input unit 59 is provided as the input parameter u for the function f(x,u) included in the system equation.

(199) Similarly, each Kalman filter 50 may estimate the roll angle , vehicle velocity V.sub.x, roll angle velocity sensor offset b.sub.ro, yaw angle velocity sensor offset b.sub.ya, and left-right acceleration sensor offset b.sub.y, and the front-rear acceleration sensor offset b.sub.x may be estimated taking account of the likelihood obtained based on the estimation results of the Kalman filters 50. Again, the front-rear acceleration sensor 25 corresponds to the detection unit of interest, or in other words, in this example the front-rear acceleration sensor 25 is a detection unit associated with the offset error which is estimated by using the likelihood. The offset value for the front-rear acceleration sensor 25 provided by the imaginary offset input unit 59 is provided as the input parameter u for the function f(x,u) included in the system equation.

(200) <Calculation of Estimated Values of Parameters>

(201) Now, the ability of the attitude estimation apparatus according to the present embodiment to estimate the attitude of the vehicle 100 with high accuracy will be proven with reference to examples.

(202) FIGS. 9A to 9L are graphs showing the estimation results for the attitude of the vehicle 100 using the attitude estimation apparatus while the vehicle 100 was travelling on a predetermined road surface. FIGS. 9A to 9L are the results of simulations made while the vehicle 100 traveled freely on a road surface having a horizontal surface portions and slopes. The figures show the calculation results of the estimated values of the various parameters based on the detected values of the mounted roll angle velocity sensor 21, yaw angle velocity sensor 22, top-bottom acceleration sensor 24, front-rear acceleration sensor 25, left-right acceleration sensor 26, and rear-wheel velocity sensor 7 having no offset error when an offset error was intentionally generated at a predetermined moment in a predetermined sensor. To simulate actual situations, white noise is superimposed on the detected values from the sensors provided to the Kalman filters 50.

(203) In FIGS. 9A to 9F, the estimation results by the calculation unit 49 according to the present embodiment described with reference to FIG. 4 are represented by solid lines. That is, the calculation unit 49 presupposed for FIGS. 9A to 9F is configured such that each Kalman filter 50 estimates the roll angle , vehicle velocity V.sub.x, roll angular velocity sensor offset b.sub.ro, yaw angular velocity sensor offset b.sub.ya, and top-bottom acceleration sensor offset b.sub.z, and the left-right acceleration sensor offset b.sub.y is estimated taking account of the likelihood obtained based on the estimation results by the Kalman filters 50.

(204) FIGS. 9A and 9B are graphs showing the estimated values resulting when an offset error with 250 mG was superimposed in the left-right acceleration sensor 26 at a predetermined moment. In FIGS. 9A and 9B, a dotted line represents a true value, a broken line represents a value estimated using one Kalman filter 50, and a solid line represents a value estimated using a plurality of Kalman filters. The estimation results from the calculation unit 49 according to the present embodiment described with reference to FIG. 4 are represented by solid lines.

(205) In FIG. 9A, the estimated value of the left-right acceleration sensor offset b.sub.y increases after a predetermined moment, indicating that an estimation close to the true value was achieved. The estimated values of the other sensor offsets are zero, again indicating that an estimation close to the true value was achieved.

(206) FIG. 9B demonstrates that the solid line achieves estimation results closer to the true value than the broken line. This shows that arranging a plurality of Kalman filters 50 in parallel and additionally estimating an offset error based on a likelihood improves estimation accuracy.

(207) FIGS. 9C to 9F are graphs showing the estimated values resulting when an offset error was generated in sensors other than the left-right acceleration sensor 26. In FIGS. 9C to 9F, a dotted line represents a true value, and a solid line represents a value estimated using a plurality of Kalman filters 50.

(208) FIG. 9C shows the estimated values found when an offset of 1 deg/sec was superimposed in the roll angular velocity sensor 21 after a predetermined period of time. FIG. 9D shows the estimated values found when an offset of 1 deg/sec was superimposed in the yaw angular velocity sensor 22 after a predetermined period of time. FIG. 9E shows the estimated values found when an offset of 250 mG was superimposed in the top-bottom acceleration sensor 24 after a predetermined period of time.

(209) FIG. 9F shows the estimated values found when offsets were superimposed in all the sensors in a combined manner. Specifically, an offset of 1 deg/sec was superimposed in the roll angular velocity sensor 21, an offset of 1 deg/sec was superimposed in the yaw angular velocity sensor 22, an offset of 250 mG was superimposed in the top-bottom acceleration sensor 24, and an offset of 250 mG was superimposed in the left-right acceleration sensor 26.

(210) FIGS. 9C to 9F demonstrate that, immediately after an offset was superimposed, the estimated values of some other sensor offsets temporarily fluctuated, but converged over time. This verifies that, in each case, the values of the sensor offsets were estimated with high accuracy without being interfered with by other offsets.

(211) The calculation unit 49 presupposed for FIGS. 9G to 9L is configured such that each Kalman filter 50 estimates the roll angle , vehicle velocity V.sub.x, roll angle velocity sensor offset b.sub.ro, yaw angle velocity sensor offset b.sub.ya, and top-bottom acceleration sensor offset b.sub.z, and the front-rear acceleration sensor offset b.sub.x was estimated taking account of the likelihood obtained based on the estimation results of the Kalman filters 50. In FIGS. 9G to 9L, the estimation results by the calculation unit 49 are represented by solid lines.

(212) FIGS. 9G and 9H are graphs showing the estimated values resulting when an offset error of 100 mG was superimposed in the front-rear acceleration sensor 25 at a predetermined moment. In FIGS. 9G and 9H, a dotted line represents a true value, a broken line represents a value estimated using one Kalman filter 50, and a solid line represents a value estimated using a plurality of Kalman filters 50.

(213) FIG. 9G demonstrates that the estimated value of the front-rear acceleration sensor offset b.sub.x increased after a predetermined moment and an estimation close to the true value was achieved. Further, the estimated values of the other sensor offsets were zero, again demonstrating that an estimation close to the true value was achieved.

(214) FIG. 9H demonstrates that the solid line achieves estimation results closer to the true value than the broken line. This shows that arranging a plurality of Kalman filters 50 in parallel and additionally estimating an offset error based on a likelihood improves estimation accuracy.

(215) FIGS. 9I to 9L are graphs showing the estimation results found when an offset error was generated in sensors other than the front-rear acceleration sensor 26. In FIGS. 9I to 9L, a dotted line represents a true value, and a solid line represents a value estimated using a plurality of Kalman filters 50.

(216) FIG. 9I shows the estimated values found when an offset of 1 deg/sec was superimposed in the roll angle velocity sensor 21 after a predetermined period of time. FIG. 9J shows the estimated values found when an offset of 1 deg/sec was superimposed in the yaw angular velocity sensor 22 after a predetermined period of time. FIG. 9K shows the estimated values found when an offset of 100 mG was superimposed in the top-bottom acceleration sensor 24 after a predetermined period of time.

(217) Further, FIG. 9L shows the estimated values found when offsets were superimposed in all the sensors in a combined manner. Specifically, an offset of 1 deg/sec was superimposed in the roll angle velocity sensor 21, an offset of 1 deg/sec was superimposed in the yaw angle velocity sensor 22, an offset of 100 mG was superimposed in the top-bottom acceleration sensor 24, and an offset of 100 mG was superimposed in the front-rear acceleration sensor 25.

(218) FIGS. 9I to 9L demonstrate that, immediately after an offset was superimposed, the estimated values of some other sensor offsets temporarily fluctuated, but converged over time. This verifies that, in each case, the values of the sensor offsets were estimated with high accuracy without being interfered with by other offsets.

Second Embodiment

(219) A second embodiment of the present invention will be described. The vehicle body 100 is the same as in the first embodiment and will not be described again.

(220) <Configuration of Attitude Estimation Apparatus>

(221) FIG. 10 is a schematic block diagram of an exemplary configuration of the attitude estimation apparatus according to the present embodiment. The attitude estimation apparatus 10 shown in FIG. 10 includes a group of sensors 5, a rear-wheel velocity sensor 7, low-pass filters 31, 32, 33, 34, 35 and 36, differentiators 41, 42, 43 and 45, a calculation unit 49, a load estimation unit 60, a suspension stroke quantity estimation unit 70, an elevation/depression angle estimation unit 80, and a slope estimation unit 90. The functionality of the calculation unit 49, load estimation unit 60, suspension stroke quantity estimation unit 70, elevation/depression angle estimation unit 80 and slope estimation unit 90 is implemented by the ECU 20 shown in FIG. 2 operating in accordance with a program. The calculation unit 49 corresponds to the attitude estimation unit.

(222) According to the present embodiment, the group of sensors 5 includes a roll angular velocity sensor 21, a yaw angular velocity sensor 22, a pitch angular velocity sensor 23, a top-bottom acceleration sensor 24, a front-rear acceleration sensor 25, and a left-right acceleration sensor 26. That is, the present embodiment is different from the first embodiment in that the group of sensors 5 further includes a pitch angular velocity sensor 23. The pitch angular velocity sensor 23 is provided on the vehicle body 1 so as to detect the pitch angular velocity of the vehicle body 1, and corresponds to the third angular velocity detection unit.

(223) The output signal from the pitch angular velocity sensor 23 is passed through the low-pass filter 33 and is fed into the calculation unit 49 and differentiator 43 as the pitch angular velocity. The low-pass filter 33 removes noise from the output signal from the pitch angular velocity sensor 23. The differentiator 43 provides, as a pitch angular acceleration, the differential value of the pitch angular velocity to the calculation unit 49.

(224) The frequency characteristics of the low-pass filter 33 are decided depending on the output characteristics of the pitch angular velocity sensor 23. More specifically, the frequency characteristics of the noise components contained in the output signal from the pitch angular velocity sensor 23 can be identified in advance, at the stage of apparatus design. The low-pass filter 33 may be designed to block these noise components and pass the detection signal of the pitch angular velocity sensor 23.

(225) In the present embodiment, the calculation unit 49 receives detected values relating to the roll angular velocity, roll angular acceleration, yaw acceleration, yaw angular acceleration, pitch angular velocity, pitch angular acceleration, top-bottom acceleration, front-rear acceleration, left-right acceleration, and rear-wheel velocity. Then, based on these values, the calculation unit 49 estimates the roll angle, pitch angle, front-rear direction vehicle velocity, roll angular velocity sensor offset, yaw angular velocity sensor offset, pitch angular velocity sensor offset, top-bottom acceleration sensor offset, and front-rear acceleration sensor offset, and output them. The pitch angular velocity sensor offset is the offset error for the pitch angular velocity sensor 23.

(226) The attitude estimation apparatus 10 according to the present embodiment includes an elevation/depression angle estimation unit 80, and is configured such that the calculation unit 49 also receives an estimated value of the elevation/depression angle from the elevation/depression angle estimation unit 80.

(227) The pitch angular velocity sensor offset estimated by the calculation unit 49, the elevation/depression angle estimated by the elevation/depression angle estimation unit 80, and the first-order differential value of the elevation/depression angle will be denoted by the following characters.

(228) TABLE-US-00006 TABLE 6 Parameter Meaning b.sub.pi pitch angular velocity sensor offset elevation/depression angle differential value of {dot over ()} elevation/depression angle

(229) FIG. 11 illustrates the elevation/depression angle . The elevation/depression angle is defined as the angle formed by the road-surface coordinate system e.sub.r and vehicle coordinate system e.sub.b found when a stroke quantity of the suspension of the vehicle 100 is present. In the following description, the elevation/depression angle is the angle formed by the x-axis e.sub.bx of the vehicle coordinate system e.sub.b and the x-axis e.sub.rx of the road-surface coordinate system.

(230) <Configuration of Kalman Filters>

(231) FIG. 12 is a schematic block diagram of an exemplary configuration of the calculation unit 49 according to the present embodiment. According to the present embodiment, similar to the first embodiment described with reference to FIG. 4, the calculation unit 49 includes a plurality of Kalman filters 50_1, 50_2 and 50_3 and a state quantity determination unit 503. FIG. 12 shows an implementation where the calculation unit 49 includes three Kalman filters 50; however, this number is merely an example. The calculation unit 49 may include two Kalman filters 50, or four or more Kalman filters 50.

(232) The Kalman filters 50 (50_1, 50_2 and 50_3) use a kinematic model for the vehicle 100, described below. Similar to FIG. 4, in FIG. 12, the Kalman filters 50 (50_1, 50_2 and 50_3) each include a system equation calculation unit 51, an observation equation calculation unit 52, a subtractor 53, an adder 54, an integrator 55, a Kalman gain calculation unit 56, a likelihood calculation unit 57, a low-pass filter 58, and an imaginary offset input unit 59.

(233) The system equation that is an equation used for the calculation at the system equation calculation unit 51 includes the function f(x,u). The observation equation that is an equation used for the calculation at the observation equation calculation unit 52 includes the function h(x,u). The Kalman gain calculation unit 56 includes a seventh-degree Kalman gain K.

(234) The imaginary offset input unit 59 provides, as an offset value for a predetermined one of the sensors of the group 5, a predetermined value for each of the Kalman filters 50 (50_1, 50_2 and 50_3) to the system equation calculation unit 51 and observation equation calculation unit 52. According to the present embodiment, the imaginary offset input unit 59 is configured to provide the offset value b.sub.x for the front-rear acceleration sensor 52 to the system equation calculation unit 51 and observation equation calculation unit 52. In this implementation, the front-rear acceleration sensor 25 corresponds to the detection unit of interest, or in other words, in this example the front-rear acceleration sensor 25 is a detection unit associated with the offset error whose imaginary offset quantity is provided in each of the Kalman filters 50 (50_1, 50_2 and 50_3).

(235) In FIG. 12, the offset value for the front-rear acceleration sensor 25 provided by the imaginary offset input unit 59 of the Kalman filter 50_1 to the system equation calculation unit 51 and observation equation calculation unit 52 is denoted by b.sub.x1. Similarly, the offset value for the front-rear acceleration sensor 25 provided by the imaginary offset input unit 59 of the Kalman filter 50_2 to the system equation calculation unit 51 and observation equation calculation unit 52 is denoted by b.sub.x2. The offset value for the front-rear acceleration sensor 25 provided by the imaginary offset input unit 59 of the Kalman filter 50_3 to the system equation calculation unit 51 and observation equation calculation unit 52 is denoted by b.sub.x3.

(236) The likelihood calculation unit 57 determines a likelihood using calculation, the likelihood being indicative of the reliability of the result from the estimation by the Kalman filter 50 (50_1, 50_2 or 50_3). The low-pass filter 58 is a calculation unit for filtering the value calculated by the likelihood calculation unit 57. The low-pass filter 58 may be replaced by any other calculation unit that can implement the same functionality. It is optional whether the low-pass filter 58 is included. The calculation performed by the likelihood calculation unit 57 will be described further below.

(237) The calculation units 51, 52, 53, 54, 55, 56, 57 and 58 constituting a Kalman filter 50 may be implemented by, for example, a program that has been prepared in advance being performed by the ECU 20. Alternatively, some or all of the calculation units 51, 52, 53, 54, 55, 56, 57 and 58 may be implemented by independent hardware mounted.

(238) According to the present embodiment, in the current estimation operation, the following values are provided as the input parameter u of the function f(x,u) included in the system equation: the detected value of the roll angular velocity .sub.ro, the detected value of the roll angular acceleration (differential value of the roll angular velocity .sub.ro), the detected value of the yaw angular velocity .sub.ya, the yaw angular acceleration (differential value of the yaw angular velocity .sub.ya), the detected value of the pitch angular velocity .sub.pi, the detected value of the pitch angular acceleration (differential value of the pitch angular velocity .sub.pi) and the detected value of the front-rear acceleration G.sub.x.

(239) Further, the following values are provided as the input parameter x of the function f(x,u) included in the system equation: the estimated value of the roll angle , the estimated value of the pitch angle , the estimated value of the vehicle velocity V.sub.x, the estimated value of the roll angular velocity sensor offset b.sub.ro, the estimated value of the yaw angular velocity sensor offset b.sub.ya, the estimated value of the pitch angular velocity sensor offset b.sub.pi, and the estimated value of the top-bottom acceleration sensor offset b.sub.z from the previous estimation operation. Further, as discussed above, the offset value for the front-rear acceleration sensor 25 provided by the imaginary offset input unit 59 is provided as the input parameter u of the function f (x,u) included in the system equation.

(240) The output from the system equation calculation unit 51 is the predicted differential value of the roll angle , the predicted differential value of the pitch angle , the predicted differential value of the vehicle velocity V.sub.x, the predicted differential value of the roll angular velocity sensor offset b.sub.ro, the predicted differential value of the yaw angular velocity sensor offset b.sub.ya, the predicted differential value of the pitch angular velocity sensor offset b.sub.pi, and the predicted differential value of the top-bottom acceleration sensor offset b.sub.z.

(241) The adder 54 adds the seventh-degree Kalman gain K obtained by the previous estimation operation to the predicted differential value of the roll angle , the predicted differential value of the pitch angle , the predicted differential value of the vehicle velocity V.sub.x, the predicted differential value of the roll angular velocity sensor offset b.sub.ro, the predicted differential value of the yaw angular velocity sensor offset b.sub.ya, the predicted differential value of the pitch angular velocity sensor offset b.sub.pi, and the predicted differential value of the top-bottom acceleration sensor offset b.sub.z.

(242) The predicted differential value of the roll angle , the predicted differential value of the pitch angle , the predicted differential value of the vehicle velocity V.sub.x, the predicted differential value of the roll angular velocity sensor offset b.sub.ro, the predicted differential value of the yaw angular velocity sensor offset b.sub.ya, the predicted differential value of the pitch angular velocity sensor offset b.sub.pi, and the predicted differential value of the top-bottom acceleration sensor offset b.sub.z to which the Kalman gain K has been added are integrated by the integrator 55. This provides the estimated value of the roll angle , the estimated value of the pitch angle , the estimated value of the vehicle velocity V.sub.x, the estimated value of the roll angular velocity sensor offset b.sub.ro, the estimated value of the yaw angular velocity sensor offset b.sub.ya, the estimated value of the pitch angular velocity sensor offset b.sub.pi, and the estimated value of the top-bottom acceleration sensor offset b.sub.z from the current estimation operation.

(243) The following values are provided as the input parameter x of the function h(x,u) included in the observation equation: the estimated value of the roll angle , the estimated value of the pitch angle , the estimated value of the vehicle velocity V.sub.x, the estimated value of the roll angular velocity sensor offset b.sub.ro, the estimated value of the yaw angular velocity sensor offset b.sub.ya, the estimated value of the pitch angular velocity sensor offset b.sub.pi, and the estimated value of the top-bottom acceleration sensor offset b.sub.z. Further, as discussed above, the offset value for front-rear acceleration sensor 25 provided by the imaginary offset input unit 59 is provided as the input parameter x of the function h(x,u) included in the observation equation.

(244) The output from the observation equation calculation unit 52 is the calculated value of the top-bottom acceleration G.sub.z, the calculated value of the left-right acceleration G.sub.y, the calculated value of the rear-wheel velocity v.sub.r, and the calculated value of the characteristic equation discussed below.

(245) The Kalman filters 50 each receive, as the input parameter y, the detected value of the top-bottom acceleration G.sub.z, the detected value of the left-right acceleration G.sub.y, the detected value of the rear-wheel velocity v.sub.r and a constant that serves as the detected value of the characteristic equation. The Kalman gain calculation unit 56 calculates the Kalman gain K based on the difference between the detected values of the top-bottom acceleration G.sub.z, left-right acceleration G.sub.y, rear-wheel velocity v.sub.r and the detected value of the characteristic equation, and the calculated values. In the description further below, the detected value of the characteristic equation is zero; however, it is not limited to zero and may be any constant that does not change over time.

(246) Finding this kinematic model's system equation f(x,u) and observation equation h(x,u) gives the relational expression for the input parameters u and y and the output parameter x.

(247) <Finding of System Equation and Observation Equation>

(248) The present embodiment supposes the following points to simplify the kinematic model.

(249) (a) There is no rotational slide between the rear wheel 3 and road surface.

(250) (b) The side-skid velocity of the rear wheel 3 is zero.

(251) (c) The road surface is flat. Flat as used herein means a plane without irregularities, and may be inclined.

(252) Based on suppositions (a) to (c), the kinematic model equation is found in the following manner. That is, it is different from the first embodiment in that the finding of the kinematic model does not incorporate supposition (d).

(253) Based on Equation (7) provided above, the second-order differential vector of the vector is determined by the equation provided below. It is different from Equation (8) in that the second-order differential vector of the vector takes account of the pitch angular velocity .sub.pi and its first-order differential value.

(254) $\begin{array}{cc}\left[\mathrm{Formula}32\right]& \\ \stackrel{\mathrm{.Math.}}{}=\left[e_b\right]\left[\begin{array}{c}{a}_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)\\ a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)\\ a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)\end{array}\right]& \left(31\right)\end{array}$

(255) In Equation (31), a.sub.x, a.sub.y and a.sub.z are functions. The functions a.sub.x, a.sub.y and a.sub.z may be determined by calculating Equations (6) and (7) provided above. Using Equation (1) to rearrange Equation (6) into Equation (7) removes the differential value of the roll angle , the differential value of the yaw angle and the differential value of the pitch angle .

(256) Next, the side-skid velocity of the vehicle 100 is denoted by V.sub.y. The first-order differential vector of the positional vector r.sub.0 in FIG. 7 is expressed by the equation below using the vehicle velocity V.sub.x and side-skid velocity V.sub.y. As discussed above, the vector e.sub.b is the basis vector of the vehicle coordinate system. According to the present embodiment, the elevation/depression angle caused by the slope of the road surface 200 and the stroke of the suspension is also taken into consideration for estimation, and thus the velocity V.sub.z for the z-direction of the vehicle 100 is generated. That is, the first-order differential vector of the positional vector r.sub.0 in FIG. 7 is expressed by the following equation using V.sub.x, V.sub.y and V.sub.z.

(257) $\begin{array}{cc}\left[\mathrm{Formula}33\right]& \\ \stackrel{.}{r_0}=\left[e_b\right]\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]& \left(32\right)\end{array}$

(258) From Supposition (b), V.sub.y=0; when Equation (32) is first-order differentiated, the second-order differential vector of the positional vector r is expressed by the equation provided below. The present embodiment is different from the first embodiment in that the pitching of the vehicle 100 is taken into consideration, and thus the equation is different from Equation (10) provided above.

(259) $\begin{array}{cc}\left[\mathrm{Formula}34\right]& \\ \stackrel{\mathrm{.Math.}}{r_0}=\left[e_b\right]\left[\begin{array}{c}\stackrel{.}{V_x}+V_z{}_{\mathrm{pi}}\\ V_x{}_{\mathrm{ya}}-V_z{}_{\mathrm{ro}}\\ \stackrel{.}{V_z}-V_x{}_{\mathrm{pi}}\end{array}\right]& \left(33\right)\end{array}$

(260) As discussed above, the elevation/depression angle is the angle formed by the x-axis of the vehicle coordinate system e.sub.b and the x-axis of the road-surface coordinate system e.sub.r. This definition gives the following equation.
[Formula 35]
V.sub.z=V.sub.x tan (34)

(261) Thus, Equation (33) may be rewritten into the following equation, Equation (35).

(262) $\begin{array}{cc}\left[\mathrm{Formula}36\right]& \\ \stackrel{\mathrm{.Math.}}{r_0}=\left[e_b\right]\left[\begin{array}{c}\stackrel{.}{V_x}+V_x{}_{\mathrm{pi}}\tan \\ V_x\left({}_{\mathrm{ya}}-{}_{\mathrm{ro}}\tan \right)\\ \stackrel{.}{V_x}\tan +V_x\left(\stackrel{.}{}{\sec }^2-{}_{\mathrm{pi}}\right)\end{array}\right]& \left(35\right)\end{array}$

(263) Next, the gravity acceleration vector may be expressed by the equation below. g in the right side of Equation (36) below indicates the magnitude of the gravity acceleration.

(264) $\begin{array}{cc}\left[\mathrm{Formula}37\right]& \\ g=\left[e_b\right]\left[\begin{array}{c}-g\sin \\ g\cos \sin \\ g\cos \cos \end{array}\right]& \left(36\right)\end{array}$

(265) Based on Equations (5), (31), (35) and (36), the acceleration vector G detected at the mounting position PS may be expressed by the following equation.

(266) 0$\begin{array}{cc}\left[\mathrm{Formula}38\right]& \\ G=\stackrel{\mathrm{.Math.}}{r}+g=\stackrel{\mathrm{.Math.}}{r_0}+\stackrel{\mathrm{.Math.}}{}+g=\left[e_b\right]\left[\begin{array}{c}\begin{array}{c}\stackrel{.}{V_x}+V_x{}_{\mathrm{pi}}\tan +\\ a_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)-\\ g\sin \end{array}\\ \begin{array}{c}{V}_x\left({}_{\mathrm{ya}}-{}_{\mathrm{ro}}\tan \right)+\\ a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)+\\ g\cos \sin \end{array}\\ \begin{array}{c}\stackrel{.}{V_x}\tan +V_x\left(\stackrel{.}{}{\sec }^2-{}_{\mathrm{pi}}\right)+\\ a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)+\\ g\cos \cos \end{array}\end{array}\right]& \left(37\right)\end{array}$

(267) The acceleration vector G detected at the mounting position PS may be expressed by Equation (13) provided above using the front-rear acceleration G.sub.x detected by the front-rear acceleration sensor 25, the left-right acceleration G.sub.y detected by the left-right acceleration sensor 26, and the top-bottom acceleration G.sub.z detected by the top-bottom acceleration sensor 24. Thus, based on Equations (13) and (37), the front-rear acceleration G.sub.x, left-right acceleration G.sub.y and top-bottom acceleration G.sub.z may be expressed by the following equation.

(268) $\begin{array}{cc}\left[\mathrm{Formula}39\right]& \\ \left[\begin{array}{c}{G}_x\\ G_y\\ G_z\end{array}\right]=\left[\begin{array}{c}\begin{array}{c}\stackrel{.}{V_x}+V_x{}_{\mathrm{pi}}\tan +\\ a_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)-\\ g\sin \end{array}\\ \begin{array}{c}{V}_x\left({}_{\mathrm{ya}}-{}_{\mathrm{ro}}\tan \right)+\\ a_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)+\\ g\cos \sin \end{array}\\ \begin{array}{c}\stackrel{.}{V_x}\tan +V_x\left(\stackrel{.}{}{\sec }^2-{}_{\mathrm{pi}}\right)+\\ a_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)+\\ g\cos \cos \end{array}\end{array}\right]& \left(38\right)\end{array}$

(269) Next, the relationship between the rear-wheel velocity v.sub.r and vehicle velocity V.sub.x is determined. Supposition (a) means that there is no slide between the rear wheel 3 and road surface 200, and thus the relationship expressed by the following equation can be established between the rear-wheel velocity v.sub.r and vehicle velocity V.sub.x.

(270) $\begin{array}{cc}\left[\mathrm{Formula}40\right]& \\ \frac{V_x\sec }{R_e-R_{\mathrm{cr}}\left(1-\cos \right)}=\frac{v_r}{R_e}& \left(39\right)\end{array}$

(271) Equation (39) gives the following equation.

(272) $\begin{array}{cc}\left[\mathrm{Formula}41\right]& \\ v_r=\frac{R_e\sec }{R_e-R_{\mathrm{cr}}\left(1-\cos \right)}{V}_x=\frac{\sec }{1-R_{\mathrm{cr}}/R_e\left(1-\cos \right)}{V}_x& \left(40\right)\end{array}$

(273) Equations (1), (38) and (40) give the following equation.

(274) $\begin{array}{cc}\left[\mathrm{Formula}42\right]& \\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}\\ \\ V_x\end{array}\right]=\left[\begin{array}{c}{}_{\mathrm{pi}}\cos -{}_{\mathrm{ya}}\sin \\ {}_{\mathrm{ro}}+{}_{\mathrm{pi}}\tan \sin +{}_{\mathrm{ya}}\tan \cos \\ \begin{array}{c}{G}_x-V_x{}_{\mathrm{pi}}\tan -\\ a_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},,L,h,R_{\mathrm{cr}}\right)+g\sin \end{array}\end{array}\right]& \left(41\right)\end{array}$

(275) As shown in FIG. 7, the vector from the mounting position PS for the group of sensors 5 to the gravity point MP of the main body of the vehicle body 1 is denoted by W. The gravity point MP does not take account of the weight of those portions of the vehicle body 1 that are located below the spring. The weight of the portions of the vehicle body 1 that are located below the spring are the total weight of those parts of the vehicle body 1 that are closer to the road surface than the suspension as determined along the routes of transfer of forces from the road surface. The parts closer to the road surface than the suspension include, for example, the tires 2 and 3, the wheels, the brakes etc. The vector W is expressed by the following equation.

(276) $\begin{array}{cc}\left[\mathrm{Formula}43\right]& \\ W=\left[e_b\right]\left[\begin{array}{c}{W}_x\\ W_y\\ W_z\end{array}\right]& \left(42\right)\end{array}$

(277) Since the weight of the vehicle body 1 is generally distributed symmetrically with respect to the vertical centerline, W.sub.y=0. If the mass of the main body of the vehicle body 1 is denoted by M and the inertia moment tensor is denoted by I, the angular momentum vector L of the vehicle 100 as viewed from the reference point O is calculated in the manner described below. In the following vector calculation equation, .circle-solid. means an inner product and means an outer product.

(278) $\begin{array}{cc}\left[\mathrm{Formula}44\right]& \\ \begin{array}{c}L=M\left(r+W\right)\frac{d}{\mathrm{dt}}\left(r+W\right)+I.Math.\\ =M\left(r+W\right)\left(\frac{d}{\mathrm{dt}}r+\frac{d}{\mathrm{dt}}W\right)+I.Math.\end{array}& \left(43\right)\end{array}$

(279) In Equation (43), the angular velocity vector and tensor I are defined by the following equations.

(280) $\begin{array}{cc}\left[\mathrm{Formula}45\right]& \\ =\left[e_b\right]\left[\begin{array}{c}{}_{\mathrm{ro}}\\ {}_{\mathrm{pi}}\\ {}_{\mathrm{ya}}\end{array}\right]& \left(44\right)\\ \left[\mathrm{Formula}46\right]& \\ \begin{array}{c}I=I_{\mathrm{xx}}\left(e_{\mathrm{bx}}.Math.e_{\mathrm{bx}}\right)+I_{\mathrm{xy}}\left(e_{\mathrm{bx}}.Math.e_{\mathrm{by}}\right)+I_{\mathrm{xz}}\left(e_{\mathrm{bx}}.Math.e_{\mathrm{bz}}\right)\\ I_{\mathrm{xy}}\left(e_{\mathrm{by}}.Math.e_{\mathrm{bx}}\right)+I_{\mathrm{yy}}\left(e_{\mathrm{by}}.Math.e_{\mathrm{by}}\right)+I_{\mathrm{yz}}\left(e_{\mathrm{by}}.Math.e_{\mathrm{bz}}\right)\\ I_{\mathrm{xz}}\left(e_{\mathrm{bz}}.Math.e_{\mathrm{bx}}\right)+I_{\mathrm{yz}}\left(e_{\mathrm{bz}}.Math.e_{\mathrm{by}}\right)+I_{\mathrm{zz}}\left(e_{\mathrm{bz}}.Math.e_{\mathrm{bz}}\right)\end{array}& \left(45\right)\end{array}$

(281) In Equation (45), an operator with a circle including a cross means a tensor product.

(282) Temporally differentiating both sides of Equation (43) gives the following equation.

(283) $\begin{array}{cc}\left[\mathrm{Formula}47\right]& \\ \begin{array}{c}\stackrel{.}{L}=M\left(\stackrel{.}{r}+\stackrel{.}{W}\right)\left(\stackrel{.}{r}+\stackrel{.}{W}\right)+M\left(r+W\right)\left(\stackrel{\mathrm{.Math.}}{r}+\stackrel{\mathrm{.Math.}}{W}\right)+I.Math.\stackrel{.}{}\\ =M\left(r+W\right)\left(\stackrel{\mathrm{.Math.}}{r}+\stackrel{\mathrm{.Math.}}{W}\right)+I.Math.\stackrel{.}{}\\ =M\left(r_0++W\right)\left(\stackrel{\mathrm{.Math.}}{r_0}+\stackrel{\mathrm{.Math.}}{}+\stackrel{\mathrm{.Math.}}{W}\right)+I.Math.\stackrel{.}{}\\ =r_{0}M\left(\stackrel{\mathrm{.Math.}}{r_0}+\stackrel{\mathrm{.Math.}}{}+\stackrel{\mathrm{.Math.}}{W}\right)+M\left(+W\right)\left(\stackrel{\mathrm{.Math.}}{r_0}+\stackrel{\mathrm{.Math.}}{}+\stackrel{\mathrm{.Math.}}{W}\right)+I.Math.\stackrel{.}{}\end{array}& \left(46\right)\end{array}$

(284) If it is rearranged in a manner similar to that for the rearrangement of Equation (7) into Equation (31), the second-order differential vector of the vector W and the inner product of the tensor I and angular acceleration vector dot (first-order differential vector of the angular velocity vector ) are expressed by the following equations.

(285) $\begin{array}{cc}\left[\mathrm{Formula}48\right]& \\ \stackrel{\mathrm{.Math.}}{W}=\left[e_b\right]\left[\begin{array}{c}{w}_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},W_x,W_z\right)\\ w_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},W_x,W_z\right)\\ w_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},W_x,W_z\right)\end{array}\right]& \left(47\right)\\ \left[\mathrm{Formula}49\right]& \\ I.Math.\stackrel{.}{}=\left[e_b\right]\left[\begin{array}{c}{q}_x\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},I_{\mathrm{xx}},I_{\mathrm{yy}},I_{\mathrm{zz}},I_{\mathrm{xz}}\right)\\ q_y\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},I_{\mathrm{xx}},I_{\mathrm{yy}},I_{\mathrm{zz}},I_{\mathrm{xz}}\right)\\ q_z\left({}_{\mathrm{ro}},{}_{\mathrm{ya}},{}_{\mathrm{pi}},{\stackrel{.}{}}_{\mathrm{ro}},{\stackrel{.}{}}_{\mathrm{ya}},{\stackrel{.}{}}_{\mathrm{pi}},I_{\mathrm{xx}},I_{\mathrm{yy}},I_{\mathrm{zz}},I_{\mathrm{xz}}\right)\end{array}\right]& \left(48\right)\end{array}$