Vehicle state estimation device

Abstract

Provided is a vehicle state estimation device (10) having a calculation unit (28) that calculates state quantities of at least a sprung of a vehicle based on wheel speeds of front left and right wheels and rear left and right wheels detected by detection devices. The calculation unit (28) calculates in-phase and reverse phase components of wheel speeds of left and right wheels for the front and rear wheels and calculates a pitch angular speed and a yaw angular speed of the sprung based on the in-phase and reverse phase components of the wheel speeds, respectively. The calculation unit (28) calculates in-phase and reverse phase components of vertical strokes of left and right suspensions for the front and rear wheels and calculates a vertical speed and a roll angular speed of the sprung based on the in-phase and reverse phase components of vertical strokes of the suspensions, respectively.

Claims

1. A vehicle state estimation device which is applied to a vehicle having four wheels, including front left and right wheels and rear left and right wheels, and a sprung including a portion of the vehicle body from which the wheels are suspended by suspensions that can expand and contract at least vertically, comprising: wheel speed detection devices that detect wheel speeds of the four wheels; and an electronic control unit (ECU) configured to: calculate state quantities of at least the sprung on the basis of detected wheel speeds of the four wheels; calculate an in-phase component of wheel speeds of left and right wheels and a reverse phase component of wheel speeds of left and right wheels for the front and rear wheels; calculate a pitch angular speed of the sprung and a yaw angular speed of the sprung on the basis of the in-phase component of wheel speeds of left and right wheels and the reverse phase component of wheel speeds of left and right wheels, respectively; and based on the calculated in-phase component, control an actuator of at least one shock absorber of the vehicle in order to control the damping force of the at least one shock absorber.

2. A vehicle state estimation device according to claim 1, wherein: the ECU is further configured to: acquire information of vertical strokes of the suspensions of the four wheels caused by expansions and contractions of the suspensions, and calculate an in-phase component of vertical strokes of the left and right suspensions and a reverse phase component of vertical strokes of the left and right suspensions for the front and rear wheels, and calculate a vertical speed of the sprung and a roll angular speed of the sprung on the basis of the in-phase component of vertical strokes of left and right suspensions and the reverse phase component of vertical strokes of left and right suspensions, respectively.

3. A vehicle state estimation device according to claim 1, wherein: the four wheels include tires, the ECU is further configured to, on the presupposition that a vertical transmitting force of each tire is the same as a vertical transmitting force of the associated suspension: calculate an in-phase component of vertical strokes of left and right suspensions and a reverse phase component of vertical strokes of left and right suspensions for the front and rear wheels on the basis of wheel speeds of the four wheels, and calculate a vertical speed of the sprung and a roll angular speed of the sprung on the basis of the in-phase component of vertical strokes of left and right suspensions and the reverse phase component of vertical strokes of left and right suspensions, respectively.

4. A vehicle state estimation device according to claim 2, wherein: the ECU is further configured to: calculate an in-phase component of vertical speeds of unsprungs of the front left and right wheels on the basis of the pitch angular speed of the sprung and the in-phase component of vertical strokes of left and right suspensions for the front and rear wheels, calculate a reverse phase component of vertical speeds of the unsprungs of the front left and right wheels on the basis of the reverse phase component of vertical strokes of left and right suspensions for the front and rear wheels, to calculate vertical speeds of unsprungs of the front left and right wheels on the basis of the in-phase component of vertical speeds of the unsprungs of the front left and right wheels and the reverse phase component of vertical speeds of the unsprungs of the front left and right wheels, and calculate vertical speeds of the unsprungs of the rear left and right wheels on the basis of a delay time that is a wheel base of the vehicle divided by a vehicle speed and the vertical speeds of the unsprungs of the front left and right wheels.

5. A vehicle state estimation device according to claim 4, wherein: the ECU is further configured to: calculate vertical displacements of a road surface at positions of the front left and right wheels on the basis of the in-phase component of vertical speeds of the unsprings of the front left and right wheels and the reverse phase component of vertical speeds of the unsprungs of the front left and right wheels, and calculate vertical displacements of the road surface at positions of the rear left and right wheels on the basis of the delay time and the vertical displacements of the road surface at positions of the front left and right wheels, respectively.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic view for illustrating a vehicle state estimation device according to a first embodiment of the present invention.

(2) FIG. 2 illustrates a block diagram for use in the first embodiment with calculating various state quantities of the sprung and a state quantity (vertical speed) of the unsprung of each wheel.

(3) FIG. 3 illustrates a block diagram for use in the first embodiment with calculating vertical displacements of a road surface at positions of the wheels.

(4) FIG. 4 illustrates a change in rotation angle of a tire caused by a change in longitudinal displacement of an unsprung.

(5) FIG. 5 illustrates a situation where the position of the sprung changes in a longitudinal direction of the vehicle.

(6) FIG. 6 illustrates a situation where pitching of the vehicle occurs.

(7) FIG. 7 illustrates a situation where yawing of the vehicle occurs.

(8) FIG. 8 illustrates a situation where a front wheel is displaced vertically by a vertical stroke of a suspension.

(9) FIG. 9 illustrates a situation where a pitch angle of an unsprung is generated by pitching of the vehicle.

(10) FIG. 10 illustrates a situation where the suspension of the front wheel expands and contracts due to input from a road surface but the suspension of the rear wheel does not expand nor contract.

(11) FIG. 11 illustrates a block diagram for use in a second embodiment with calculating various state quantities of the sprung and a state quantity (vertical speed) of the unsprung of each wheel.

(12) FIG. 12 illustrates a block diagram for use in a third embodiment with calculating various state quantities of the sprung and a state quantity (vertical speed) of the unsprung of each wheel.

(13) FIG. 13 illustrates a block diagram for use in a fourth embodiment with calculating various state quantities of the sprung and a state quantity (vertical speed) of the unsprung of each wheel.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(14) Now, with reference to the accompanying drawings, preferred embodiments of the present invention are described in detail.

First Embodiment

(15) FIG. 1 is a schematic view for illustrating a vehicle state estimation device 10 according to a first embodiment of the present invention.

(16) As shown in FIG. 1, the vehicle state estimation device 10 is applied to a vehicle 14 which has front left and right wheels 12FL and 12FR that are steered wheels and rear left and right wheels 12RL and 12RR that are non-steered wheels. Although not shown in detail in FIG. 1, the front wheels 12FL and 12FR have tires 13FL and 13FR, respectively, mounted around metal wheel members, and the rear wheels 12RL and 12RR have tires 13 RL and 13RR, respectively, mounted around metal wheel members. The front wheels 12FL and 12FR are suspended by suspensions 16FL and 16FR, respectively, from a vehicle body 18 and the rear wheels 12RL and 12RR are suspended by suspensions 16 RL and 18RR, respectively, from the vehicle body 18.

(17) The suspensions 16FL-16RR include shock absorbers 20FL-20RR and suspension springs 22FL-22RR, respectively. The shock absorbers 20FL-20RR and the suspension springs 22FL-22RR extend vertically slightly inclined in longitudinal and lateral directions of the vehicle 14. The wheels 12FL-12RR are rotatably supported by wheel carriers 24FL-24RR, respectively, which are coupled to the vehicle body 18 by suspension arms, not shown, so as to displace mainly in vertical direction. The shock absorbers 20FL-20RR are arranged between the vehicle body 18 and the wheel carriers 24FL-24RR or the suspension arms, respectively.

(18) The vehicle body 18 can displace at least vertically relative to the wheels 12FL-12RR by means of expansion and contraction of the shock absorbers 20FL-20RR and the suspension springs 22FL-22RR. Thus, the vehicle body 18, portions of the shock absorbers 20FL-20RR and portions of the suspension arms and the like form a sprung of the vehicle 14. The wheels 12FL-12RR, the wheel carriers 24FL-24RR, the other portions of the shock absorbers 20FL-20RR and the other portions of the suspension arms and the like form unsprungs of the vehicle 14.

(19) The suspension springs 22FL-22RR restrict vertical displacement of a road surface and shocks and the like that the wheels 12FL-12RR receive from the road surface from being transmitted to the sprung. The shock absorbers 20FL-20RR generate damping forces that damp vibrations caused by relative displacement of the sprung and the unsprungs. In the first embodiment, the shock absorbers 20FL-20RR are damping force variable shock absorbers having actuators 26FL-26RR, respectively. The actuators 26FL-26RR variably control damping forces of the shock absorbers 20FL-20RR, respectively, in multistage or continually between the lowest damping force and the highest damping force by controlling openings of damping force generation valves incorporated in the shock absorbers 20FL-20RR.

(20) The actuators 26FL-26RR are controlled by an electronic control unit 28 that serves as calculation unit. The wheels 12FL-12RR are provided with wheel speed sensors 30FL-30RR that detect wheel speeds .sub.1-.sub.4 of the associated wheels, respectively. The wheel speed sensors 30FL-30RR detect as wheel speeds .sub.1-.sub.4 rotational speed of the wheels 12FL-12RR relative to the sprung, respectively. The suspensions 16FL-16RR are provided with stroke sensors 32FL-32RR that detect vertical strokes Z.sub.1-Z.sub.4 of the associated suspensions 16FL-16RR, respectively. Signals indicative of the detected wheel speeds .sub.1-.sub.4 and vertical strokes Z.sub.1-Z.sub.4 are input into the electronic control unit 28.

(21) It is to be noted that suffixes 1-4 which are attached to wheel speeds , strokes and below-described other parameters represent that they are parameters of the front left, front right, rear left and rear right wheels, respectively, as FL, FR, RL and RR do. Suffixes F and R which are fixed to the parameters represent that they are parameters of the front and rear wheels, respectively. When the members and the parameters of the front left, front right, rear left and rear right wheels are totally referred to, the suffixes are omitted such as, for example, the wheels 12 and wheel speeds .

(22) In the first embodiment, as described later in detail, the electronic control unit 28 estimates various state quantities of the sprung such as, for example, vertical speed, pitch angular speed, roll angular speed and yaw angular speed of the sprung on the basis of wheel speeds .sub.1-.sub.4 and vertical strokes Z.sub.1-Z.sub.4. In addition, the electronic control unit 28 estimates vertical speeds of the wheels 12FL-12RR as state quantities of the unsprungs on the basis of wheel speeds .sub.1-.sub.4 and vertical strokes Z.sub.1-Z.sub.4.

(23) The electronic control unit 28 controls the actuators 26FL-26RR in accordance with the estimated state quantities of the vehicle 14 so as to control the damping forces of the associated shock absorbers 20FL-20RR so that operation stability and ride comfort of the vehicle 14 are enhanced. Notably, a control executed in accordance with the estimated state quantities of the vehicle 14 is not limited to the damping force control but may be any other control of the vehicle 14 such as a running motion control for a vehicle.

(24) Although not illustrated in detail in FIG. 1, the electronic control unit 28 has a microcomputer and a drive circuit. The microcomputer may have a general configuration having CPU, ROM, RAM and an input/output port connected with one another via a bidirectional common bus. ROM stores a control program corresponding to a block diagram shown in FIG. 2 and CPU executes the program.

(25) Summary of State Quantities Estimation

(26) Next, a summary of estimation of state quantities of the sprung and the unsprungs in the first embodiment will be described. As described in detail later, in the first embodiment, various state quantities of the sprung are estimated in the following manner and vertical speeds of the unsprungs are additionally estimated for the wheels.

(27) It is to be noted that in the following description, positive directions of the various parameters and their changes are forward, upward and leftward. In addition, it is assumed that the tires 13FL-13RR, the suspensions 16FL-16RR and the like of the left and right wheels have the same characteristics with each other.

(28) 1. Wheel speeds .sub.1-.sub.4 of the wheels 12FL-12RR and vertical strokes Z.sub.1-Z.sub.4 of the suspensions 16FL-16RR are detected.

(29) 2. Behaviors of the sprung include pitching, rolling and yawing. The behavior which influences on components of wheel speeds .sub.1-.sub.4 that are in the same phase to the left and right wheels is pitching only and the behavior which influences on components of wheel speeds .sub.e-.sub.4 that are in the reverse phase to the left and right wheels is yawing only. Accordingly, a pitch angular speed of the sprung is estimated on the basis of the components of wheel speeds .sub.1-.sub.4 that are in the same phase to the left and right wheels and a yaw angular speed of the sprung is estimated on the basis of the components of wheel speeds .sub.1-.sub.4 that are in the reverse phase to the left and right wheels.

(30) 3. Components of vertical stroke speeds of the front and rear suspensions 16 which are in the same phase to the left and right wheels and components of vertical stroke speeds of the front and rear suspensions 16 which are in the reverse phase to the left and right wheels are estimated on the basis of the vertical strokes Z.sub.1-Z.sub.4.

(31) 4. A vertical speed of the sprung is estimated on the basis of the pitch angular speed of the sprung and the component of vertical stroke speeds of the front suspensions 16 which are in the same phase to the left and right wheels, and a roll angular speed of the sprung is estimated on the basis of the components of vertical stroke speeds of the front and rear suspensions 16 which are in the reverse phase to the left and right wheels.

(32) 5. The unsprungs of the rear wheels make the same displacements as the unsprungs of the front wheels with a delay time L/U that is the wheel base L of the vehicle divided by a vehicle speed U. Accordingly, a component of vertical speeds of the unsprungs of the front wheels which are in the same phase to the left and right wheels is estimated on the basis of the pitch angular speed of the sprung and the component of vertical stroke speeds of the rear suspensions 16 which are in the same phase to the left and right wheels. In addition, a component of vertical speeds of the unsprungs of the front wheels which are in the reverse phase to the left and right wheels is estimated on the basis of the components of vertical stroke speeds of the front and rear suspensions 16 which are in the reverse phase to the left and right wheels.

(33) 6. Vertical speeds of the unsprungs of the front wheels 12FL and 12FR are estimated on the basis of the component of vertical speeds of the unsprungs of the front wheels which are in the same phase to the left and right wheels and the component of vertical speeds of the unsprungs of the front wheels which are in the reverse phase to the left and right wheels.

(34) 7. Vertical speeds of the unsprungs of the rear wheels 12RL and 12RR are estimated on the basis of the vertical speeds of the unsprungs of the front wheels 12FL and 12FR and the delay time L/U.

(35) Theoretical Formulae of State Quantities Estimation

(36) Next, theoretical formulae will be described with which estimations of state quantities of the sprung and the unsprungs executed in the above-described manners are based. It is to be noted that in the following descriptions, differential values and second order differential values of parameters in formulae are written as parameters having a dot (.) that indicates a differential value and two dots (..) that indicates a second order differential value. In the following explanatory descriptions, however, since a dot and two dots cannot be written, differential values and second order differential values of parameters are written as parameters having a foregoing d that means a differential value and a foregoing dd that means a second order differential value.

(37) FIG. 4 illustrates a change in rotation angle of a tire 13 caused by a change in longitudinal displacement of an unsprung. In FIG. 4, a dot line indicates a position of the tire 13 in a situation where it is not influenced by an input from a road surface to a wheel and driving operation by a driver, and a solid line indicates a position of the tire 13 in a situation where it is subjected to the above influences. Denoting a change amount in longitudinal displacement of the unsprung by X.sub.A and a radius of the tire 13 by r, a rotation angle of the tire 13 can be approximated by X.sub.A/r.

(38) If the radius of the tire 13 changes due to deformation of the tire, a change in rotation angle of the tire 13 can be caused by the change in the radius. A change amount in the radius of the tire 13 due to its deformation is represented by r; a ratio of a change amount in the radius of the tire 13 due to dynamic load to a change amount in the radius due to static load is represented by ; and a rotational speed in a situation where the change amount r in the radius is 0 is represented by .sub.0. Then, a change amount in the radius of the tire 13 in a situation where the radius r of the tire 13 changes by r is represented by *.sub.0(r/r). As a rotational speed of the tire 13 is a differential value of a rotation angle , a rotational speed of the tire 13 in a situation where a change amount in the radius r of the tire 13 due to its deformation is r is represented by the following Formula (1.)

(39) $\begin{array}{cc}={\stackrel{.}{X}}_A/r-{}_0\frac{r}{r}& \left(1\right)\end{array}$

(40) The Formula (1) can be transformed into the following Formula (2.) Notably, dX.sub.A is a differential value of a longitudinal displacement X.sub.A of the unsprung and dX.sub.B is a differential value of a longitudinal displacement X.sub.B of the sprung at axle position TC (see FIG. 5.) The axle position TC is on a center line of the wheel 12 and a center point of the wheel 12 in its lateral direction. In addition, Z.sub.A is a vertical displacement of the unsprung and Z.sub.0 is a vertical displacement of the unsprung in a situation where it is not influenced by an input from a road surface to the wheel and driving operation by a driver
=[{dot over (X)}.sub.B+({dot over (X)}.sub.A{dot over (X)}.sub.B).sub.0(Z.sub.AZ.sub.0)]/r(2)

(41) The first term dX.sub.B in the bracket on the right side of the above Formula (2) will be described. The first term is that of differential value of a longitudinal displacement of the axle position TC due to a behavior of the sprung. A longitudinal displacement X.sub.B of the axle position TC due to a behavior of the sprung is represented by a total of a longitudinal displacement due to longitudinal movement of the sprung illustrated in FIG. 5, a longitudinal displacement due to pitching of the sprung illustrated in FIG. 6 and a longitudinal displacement due to yawing of the sprung illustrated in FIG. 7.

(42) As illustrated in FIG. 5, when the position of the sprung changes in a longitudinal direction of the vehicle, a longitudinal displacement X.sub.B of the sprung at axle position TC includes a component X.sub.Ba generated by a change in the position of the sprung in the longitudinal direction of the vehicle 14. Denoting a longitudinal displacement of the sprung at a gravity center PG by X.sub.BG, as represented by the following Formula (3), the longitudinal displacement X.sub.Ba due to a longitudinal movement of the sprung is the same as the change amount X.sub.BG.
X.sub.Ba=X.sub.BG(3)

(43) As illustrated in FIG. 6, when pitching of the vehicle 14 occurs, a longitudinal displacement X.sub.B of the sprung at the axle position TC includes a component X.sub.Bb generated by the pitching. Denoting a pitch angle of the sprung by .sub.BG and denoting a vertical distance between the axle position TC and the gravity center PG by H, a longitudinal displacement X.sub.Bb of the sprung due to pitching is represented by the following Formula (4.)
X.sub.Bb=.sub.BG*H(4)

(44) As illustrated in FIG. 7, when yawing of the vehicle 14 occurs, a longitudinal displacement X.sub.B of the sprung at the axle position TC includes a component X.sub.Bc generated by the yawing. Denoting a yaw angle of the sprung by .sub.BG and denoting a lateral distance between the gravity center PG and the axle position TC by W, a longitudinal displacement X.sub.Bc of the sprung due to yawing is represented by the following Formula (5.)
X.sub.Bc=.sub.BG*W(5)

(45) A longitudinal displacement X.sub.B of the sprung at the axle position TC due to behaviors of the sprung is a total of the above three components X.sub.Ba, X.sub.Bb and X.sub.Bc. Thus, a differential value dX.sub.B of the longitudinal displacement is represented by the following Formula (6.)
dX.sub.B=d.sub.BG*H+dX.sub.BG+d.sub.BG*W(6)

(46) Next, the second term (dX.sub.A-dX.sub.B) in the bracket on the right side of the above Formula (2) will be described. The second term is that of differential value of a longitudinal displacement of the axle position TC due to a relative vertical displacement of the sprung and the unsprung, i.e., a vertical stroke of the suspension 16. As illustrated in FIG. 8 with respect to the front wheel 12F, the vehicle body 18 which forms a part of the sprung and the front wheel 12F displaces vertically by a vertical stroke of the suspension 16. As described above, since the suspension 16 is inclined relative to the vertical direction in the longitudinal direction of the vehicle 14, the wheel 12 and the vehicle body 18 displaces as well in the longitudinal direction of the vehicle. A difference (dX.sub.AdX.sub.B) between differential values of longitudinal displacements of the sprung and the unsprung is represented by the following Formula (7.)
dX.sub.AdX.sub.B=.sub.X(dZ.sub.AdZ.sub.B)(7)

(47) Here, dZ.sub.A is a vertical speed of the sprung; dZ.sub.B is a vertical speed of the unsprung at the axle position TC; and .sub.X is a relative displacement of the sprung and the unsprung in the longitudinal direction of the vehicle 14 per a unit stroke amount of the suspension 16.

(48) In addition, the third term *.sub.0(Z.sub.AZ.sub.0) in the bracket on the right side of the above Formula (2) will be described. r in the second term on the right side of the above Formula (1), i.e., a change amount in the radius r of the tire 13 due to its deformation is equal to a difference between a vertical displacement Z.sub.A of the unsprung and a vertical displacement Z.sub.0 of the unsprung in a situation where a change amount r in the radius r of the tire 13 is 0. Thus, the following Formula (8) holds.
r=Z.sub.AZ.sub.0(8)

(49) According to the above Formulae (6)-(8), the above Formula (2) can be transformed into the following Formula (9.)
=({dot over ()}.sub.BGH+{dot over (X)}.sub.BG+{dot over ()}W)+.sub.X(.sub.A.sub.B).sub.0(Z.sub.AZ.sub.0)/r(9)

(50) Next, referring to FIGS. 9 and 10, a pitch angle .sub.A of the unsprung will be described. A pitch angle .sub.A of the unsprung is an inclined angle of the unsprung relative to a road surface in the longitudinal direction of the vehicle 14. In the vehicle 14, as the suspension 16 expands and contracts, there arises a case where a pitch angle .sub.BG of the sprung and a pitch angle .sub.A of the unsprung differ from each other. In other words, a pitch angle .sub.A of the unsprung includes a component .sub.A, that corresponds to a pitch angle .sub.BG of the sprung and a component .sub.Ab generated by expansion and contraction of the suspension 16.

(51) As illustrated in FIG. 9, a component .sub.A, that corresponds to a pitch angle .sub.BG of the sprung is equal to a pitch angle .sub.BG of the sprung. Thus, a component .sub.A, that corresponds to a pitch angle .sub.BG of the sprung is represented by the following Formula (10.)
.sub.Aa=.sub.BG(10)

(52) FIG. 10 illustrates a situation where the suspension 16 of the front wheel 12F of the vehicle 14 expands and contracts due to input from a road surface and the like, but the suspension 16 of the rear wheel 12R does not expand nor contract. Denoting a pitch angle of the unsprung per a unit stroke amount of the suspension 16 by .sub., as illustrated in FIG. 10, a component .sub.Ab of a pitch angle .sub.A generated by expansion and contraction of the suspension 16 is represented by the following Formula (11.)
.sub.Ab=.sub.e(Z.sub.AZ.sub.B)(11)

(53) A rotational speed caused by a change in a pitch angle .sub.A of the unsprung, i.e., a differential value of a pitch angle .sub.A of the unsprung is represented by the following Formula (12.)
{dot over ()}.sub.A={dot over ()}.sub.BG+.sub.e(.sub.A.sub.B)(12)

(54) Next, a wheel speed will be described. Each wheel speed is a value detected by an associated wheel speed sensor 30. As described above, the wheel speed sensor 30 detects a rotational speed of the unsprung relative to the sprung as a wheel speed . Thus, a wheel speed is a difference between a rotational speed of the tire 13 and a rotational speed caused by a change in a pitch angle .sub.A of the unsprung, and, accordingly, the following Formula (13) holds.
=.sub.A(13)

(55) The following Formula (14) is derived by substituting the above Formulae (9) and (12) for the above Formula (13.)
=({dot over ()}.sub.BGH+{dot over (X)}.sub.BG+{dot over ()}W)+.sub.X(.sub.A.sub.B).sub.0(Z.sub.AZ.sub.0)/r{dot over ()}.sub.BG+.sub.(.sub.A.sub.B) (14)

(56) Next, a vertical displacement of the sprung will be described. A vertical displacement X.sub.B of the sprung at the axle position TC can be expressed with the following Formula (15.) The first term on the right side of the following Formula (15) is a vertical displacement of the axle position TC. The second term on the right side of the following Formula (15) is a vertical displacement (an approximated value) caused by pitching of the sprung. The third term on the right side of the following Formula (15) is a vertical displacement (an approximated value) caused by rolling of the sprung.
Z.sub.B=Z.sub.BGL.sub.FR*.sub.BGW*.sub.BG(15)

(57) In the above Formula (15), L.sub.FR is a distance between the axle position TC and the gravity center position PG in the longitudinal direction of the vehicle (see FIG. 5), and .sub.BG is a roll angle of the sprung. A distance L.sub.FR between the axle position TC and the gravity center position PG in the longitudinal direction is a distance L.sub.F in the case of the front wheel 12FR or 12FL and a distance L.sub.R in the case of the rear wheel 12RR or 12 RL. The distances L.sub.F and L.sub.R may take different values.

(58) Describing the Formula (15) with regard to the front left wheel 12FL, for example, a vertical displacement Z.sub.B1 of the sprung at the axle position TC of the front left wheel 12FL can be obtained by adding or subtracting a vertical displacement caused by pitching of the sprung and a vertical displacement caused by rolling of the sprung to or from a vertical displacement Z.sub.BG of the gravity center position PG. For example, when the sprung is pitched such that the front wheel side sinks in, a vertical displacement (L.sub.FR*.sub.BG) caused by pitching of the sprung is subtracted from a vertical displacement Z.sub.BG of the gravity center position PG. When the sprung is rolled such that the left side of the vehicle sinks in, a vertical displacement (W.sub.BG*.sub.BG) caused by rolling of the sprung is subtracted from a vertical displacement Z.sub.BG of the gravity center position PG.

(59) On the contrary, when the sprung is pitched such that the front wheel side lifts up, a vertical displacement (L.sub.FR*.sub.BG) caused by pitching of the sprung is added to a vertical displacement Z.sub.BG of the gravity center position PG. When the sprung is rolled such that the left side of the vehicle lifts up, a vertical displacement (W.sub.BG*.sub.BG) caused by rolling of the sprung is added. With respect to each of the other wheels 12FL, 12RR and 12 RL as well, a vertical displacement Z.sub.B of the sprung at the axle position TC is similarly calculated.

(60) According to the above Formula (15), a change speed dZ.sub.B of a vertical displacement of the sprung at the axle position TC is expressed with the following Formula (16.)
.sub.B=.sub.BG+L.sub.FR{dot over ()}.sub.BG+W{dot over ()}.sub.BG(16)

(61) Applying the above Formula (14) to the four wheels, and notating the wheel speeds for the four wheels in a matrix form, the following Formula (17) is obtained. Notably, in the following Formula (17), the matrixes [D], [G], [E], [F] and [H] are indicated in the following Formulae (18)-(22), respectively.

(62) $\begin{array}{cc}\left(\begin{array}{c}{}_1\\ {}_2\\ {}_3\\ {}_4\end{array}\right)=\left(\begin{array}{c}{}_1-{}_{A1}S\\ {}_2-{}_{A2}S\\ {}_3-{}_{A3}S\\ {}_4-{}_{A4}S\end{array}\right)=D\left(\begin{array}{c}{\stackrel{.}{Z}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{X}}_{\mathrm{BG}}\\ {\stackrel{.}{Y}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{\stackrel{.}{}}}_{\mathrm{BG}}\end{array}\right)-G\left(\begin{array}{c}{\stackrel{.}{Z}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{X}}_{\mathrm{BG}}\\ {\stackrel{.}{Y}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{\stackrel{.}{}}}_{\mathrm{BG}}\end{array}\right)+E\left(\begin{array}{c}{\stackrel{.}{Z}}_{A1}-{\stackrel{.}{Z}}_{B1}\\ {\stackrel{.}{Z}}_{A2}-{\stackrel{.}{Z}}_{B2}\\ {\stackrel{.}{Z}}_{A3}-{\stackrel{.}{Z}}_{B3}\\ {\stackrel{.}{Z}}_{A4}-{\stackrel{.}{Z}}_{B4}\end{array}\right)-F\left(\begin{array}{c}{\stackrel{.}{Z}}_{A1}-{\stackrel{.}{Z}}_{B1}\\ {\stackrel{.}{Z}}_{A2}-{\stackrel{.}{Z}}_{B2}\\ {\stackrel{.}{Z}}_{A3}-{\stackrel{.}{Z}}_{B3}\\ {\stackrel{.}{Z}}_{A4}-{\stackrel{.}{Z}}_{B4}\end{array}\right)-H\left(\begin{array}{c}{Z}_{A1}-Z_{01}\\ Z_{A2}-Z_{02}\\ Z_{A3}-Z_{03}\\ Z_{A4}-Z_{04}\end{array}\right)=\left(D-G\right)\left(\begin{array}{c}{\stackrel{.}{Z}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{X}}_{\mathrm{BG}}\\ {\stackrel{.}{Y}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{\stackrel{.}{}}}_{\mathrm{BG}}\end{array}\right)+\left(E-F\right)\left(\begin{array}{c}{\stackrel{.}{Z}}_{A1}-{\stackrel{.}{Z}}_{B1}\\ {\stackrel{.}{Z}}_{A2}-{\stackrel{.}{Z}}_{B2}\\ {\stackrel{.}{Z}}_{A3}-{\stackrel{.}{Z}}_{B3}\\ {\stackrel{.}{Z}}_{A4}-{\stackrel{.}{Z}}_{B4}\end{array}\right)+H\left(\begin{array}{c}{Z}_{01}-Z_{\mathrm{A1}}\\ Z_{02}-Z_{\mathrm{A2}}\\ Z_{03}-Z_{\mathrm{A3}}\\ Z_{04}-Z_{\mathrm{A4}}\end{array}\right)& \left(17\right)\\ \left[D\right]=\left(\begin{array}{cccccc}0& -H_F/r_F& 1/r_F& 0& 0& W_F/r_F\\ 0& -H_F/r_F& 1/r_F& 0& 0& -W_F/r_F\\ 0& -H_R/r_R& 1/r_R& 0& 0& W_R/r_R\\ 0& -H_R/r_R& 1/r_R& 0& 0& -W_R/r_R\end{array}\right)& \left(18\right)\\ \left[G\right]=\left(\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\end{array}\right)& \left(19\right)\\ \left[E\right]=\left(\begin{array}{cccc}{}_{\mathrm{XF}}/r_F& 0& 0& 0\\ 0& {}_{\mathrm{XF}}/r_F& 0& 0\\ 0& 0& {}_{\mathrm{XR}}/r_R& 0\\ 0& 0& 0& {}_{\mathrm{XR}}/r_R\end{array}\right)& \left(20\right)\\ \left[F\right]=\left(\begin{array}{cccc}{}_F& 0& 0& 0\\ 0& {}_F& 0& 0\\ 0& 0& {}_R& 0\\ 0& 0& 0& {}_R\end{array}\right)& \left(21\right)\\ \left[H\right]=\left(\begin{array}{cccc}{}_F{}_F/r_F& 0& 0& 0\\ 0& {}_F{}_F/r_F& 0& 0\\ 0& 0& {}_R{}_R/r_R& 0\\ 0& 0& 0& {}_R{}_R/r_R\end{array}\right)& \left(22\right)\end{array}$

(63) The above Formula (17) is developed to obtain the following Formula (23.)

(64) $\begin{array}{cc}\begin{array}{c}\left(\begin{array}{c}{}_1\\ {}_2\\ {}_3\\ {}_4\end{array}\right)=\left(D-G\right)\left(\begin{array}{c}{\stackrel{.}{Z}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{X}}_{\mathrm{BG}}\\ {\stackrel{.}{Y}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\\ {\stackrel{.}{}}_{\mathrm{BG}}\end{array}\right)+\left(E-F\right)\left(\begin{array}{c}{\stackrel{.}{Z}}_{A1}-{\stackrel{.}{Z}}_{B1}\\ {\stackrel{.}{Z}}_{A2}-{\stackrel{.}{Z}}_{B2}\\ {\stackrel{.}{Z}}_{A3}-{\stackrel{.}{Z}}_{B3}\\ {\stackrel{.}{Z}}_{A4}-{\stackrel{.}{Z}}_{B4}\end{array}\right)+H\left(\begin{array}{c}{Z}_{01}-Z_{A1}\\ Z_{02}-Z_{A2}\\ Z_{03}-Z_{A3}\\ Z_{04}-Z_{A4}\end{array}\right)\\ =\left(\begin{array}{cccccc}0& -H_F/r_F-1& 1/r_F& 0& 0& W_F/r_F\\ 0& -H_F/r_F-1& 1/r_F& 0& 0& -W_F/r_F\\ 0& -H_F/r_F-1& 1/r_R& 0& 0& W_R/r_R\\ 0& -H_F/r_F-1& 1/r_R& 0& 0& -W_R/r_R\end{array}\right)s\left(\begin{array}{c}{Z}_{\mathrm{BG}}\\ {}_{\mathrm{BG}}\\ X_{\mathrm{BG}}\\ Y_{\mathrm{BG}}\\ {}_{\mathrm{BG}}\\ {}_{\mathrm{BG}}\end{array}\right)+\\ \left(\begin{array}{cccc}{}_{\mathrm{XF}}/r_F-{}_F& 0& 0& 0\\ 0& {}_{\mathrm{XF}}/r_F-{}_F& 0& 0\\ 0& 0& {}_{\mathrm{XR}}/r_R-{}_R& 0\\ 0& 0& 0& {}_{\mathrm{XR}}/r_R-{}_R\end{array}\right)s\left(\begin{array}{c}{Z}_{A1}-Z_{B1}\\ Z_{A2}-Z_{B2}\\ Z_{A3}-Z_{B3}\\ Z_{A4}-Z_{B4}\end{array}\right)+\\ \left(\begin{array}{cccc}{}_F{}_F/r_F& 0& 0& 0\\ 0& {}_F{}_F/r_F& 0& 0\\ 0& 0& {}_R{}_R/r_R& 0\\ 0& 0& 0& {}_R{}_R/r_R\end{array}\right)\left(\begin{array}{c}{Z}_{01}-Z_{A1}\\ Z_{02}-Z_{A2}\\ Z_{03}-Z_{A3}\\ Z_{04}-Z_{A4}\end{array}\right)\end{array}& \left(23\right)\end{array}$

(65) According to the above Formula (23), an in-phase component (.sub.1+.sub.2)/2 of the wheel speeds of the front wheels 12FL and 12FR and an in-phase component (.sub.3+.sub.4)/2 of the wheel speeds of the rear wheels 12RL and 12RR are expressed with the following Formula (24.)

(66) $\begin{array}{cc}\begin{array}{c}\left[\begin{array}{c}\frac{{}_1+{}_2}{2}\\ \frac{{}_3+{}_4}{2}\end{array}\right]=\left[\begin{array}{c}-\left(\frac{H_F}{r_F}+1\right){}_{\mathrm{BG}}+\frac{X_{\mathrm{BG}}}{r_F}\\ -\left(\frac{H_R}{r_R}+1\right){}_{\mathrm{BG}}+\frac{X_{\mathrm{BG}}}{r_R}\end{array}\right]s+\\ \left[\begin{array}{c}\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{\left(Z_{A1}+Z_{A2}-Z_{B1}-Z_{B2}\right)}{2}\\ \left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{\left(Z_{A3}+Z_{A4}-Z_{B3}-Z_{B4}\right)}{2}\end{array}\right]+\\ \left[\begin{array}{c}\frac{{}_F{}_F}{r_F}\frac{\left(Z_{01}+Z_{02}-Z_{A1}-Z_{A2}\right)}{2}\\ \frac{{}_R{}_R}{r_R}\frac{\left(Z_{03}+Z_{04}-Z_{A3}-Z_{A4}\right)}{2}\end{array}\right]\\ -\left[\begin{array}{c}\frac{H}{r_F}{}_{\mathrm{BG}}\\ \frac{H}{r_R}{}_{\mathrm{BG}}\end{array}\right]s+\\ \left[\begin{array}{c}\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{\left(Z_{A1}+Z_{A2}-Z_{B1}-Z_{B2}\right)}{2}\\ \left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{\left(Z_{A3}+Z_{A4}-Z_{B3}-Z_{B4}\right)}{2}\end{array}\right]s+\\ \left[\begin{array}{c}\frac{{}_F{}_F}{r_F}\frac{\left(Z_{01}+Z_{02}-Z_{A1}-Z_{A2}\right)}{2}\\ \frac{{}_R{}_R}{r_R}\frac{\left(Z_{03}+Z_{04}-Z_{A3}-Z_{A4}\right)}{2}\end{array}\right]\end{array}& \left(24\right)\end{array}$

(67) As described above, as a time difference between the time point where the front and rear wheels pass the same position on a road surface is a value L/U that is derived by dividing a wheel base L (=L.sub.F+L.sub.R) by a vehicle speed U, displacements of the unsprungs of the rear wheels delay with the delay time L/U relative to displacemenst of the unsprungs of the front wheels. The above Formula (24) can be rewritten as the following Formula (25) with the delay time L/U.

(68) $\begin{array}{cc}\left[\begin{array}{c}\left({}_1+{}_2\right)/2\\ \left({}_3+{}_4\right)/2\end{array}\right]=-\left[\begin{array}{c}\frac{H}{r_F}{}_{\mathrm{BG}}\\ \frac{H}{r_R}{}_{\mathrm{BG}}\end{array}\right]s+\left[\begin{array}{c}\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\left(Z_{A1}+Z_{A2}-Z_{B1}-Z_{B2}\right)/2\\ \left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\left(Z_{A3}+Z_{A4}-Z_{B3}-Z_{B4}\right)/2\end{array}\right]s+\left[\begin{array}{c}\frac{{}_F{}_F}{r_F}\frac{\left(Z_{01}+Z_{02}-Z_{A1}-Z_{A2}\right)}{2}\\ \frac{{}_R{}_R}{r_R}\frac{\left(Z_{01}+Z_{02}-Z_{A1}-Z_{A2}\right)}{2}{e}^{-\frac{L}{U}s}\end{array}\right]& \left(25\right)\end{array}$

(69) The above Formula (25) is transformed into obtain the following Formula (26) and the latter Formula is transformed into obtain the following Formula (27.)

(70) $\begin{array}{cc}\left[\begin{array}{cc}-\frac{H}{r_F}& \frac{{}_F{}_F}{r_F}\frac{1}{s}\\ -\frac{H}{r_R}& \frac{{}_R{}_R}{r_R}\frac{1}{s}{e}^{-\frac{L}{U}s}\end{array}\right]\left[\begin{array}{c}{}_{\mathrm{BG}}\\ \left(Z_{01}+Z_{02}-Z_{A1}-Z_{A2}\right)/2\end{array}\right]s=\left[\begin{array}{c}\left({}_1+{}_2\right)/2-\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{\left(Z_{A1}+Z_{A2}-Z_{B1}-Z_{B2}\right)}{2}s\\ \left({}_3+{}_4\right)/2-\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{\left(Z_{A3}+Z_{A4}-Z_{B3}-Z_{B4}\right)}{2}s\end{array}\right]& \left(26\right)\\ \left[\begin{array}{c}{}_{\mathrm{BG}}\\ \left(Z_{01}+Z_{02}-Z_{A1}-Z_{A2}\right)/2\end{array}\right]s={\left[\begin{array}{cc}-\frac{H}{r_F}& \frac{{}_F{}_F}{r_F}\frac{1}{s}\\ -\frac{H}{r_R}& \frac{{}_R{}_R}{r_R}\frac{1}{s}{e}^{-\frac{L}{U}s}\end{array}\right]}^{-1}.Math.\left[\begin{array}{c}\left({}_1+{}_2\right)/2-\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{\left(Z_{A1}+Z_{A2}-Z_{B1}-Z_{B2}\right)}{2}s\\ \left({}_3+{}_4\right)/2-\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{\left(Z_{A3}+Z_{A4}-Z_{B3}-Z_{B4}\right)}{2}s\end{array}\right]& \left(27\right)\end{array}$

(71) An in-phase vertical stroke of the suspensions 16F of the front wheels 12F is represented by .sub.SFD and an in-phase vertical stroke of the suspensions 16R of the rear wheels 12R is represented by .sub.SRD. An in-phase deformation of the tires 13F of the front wheels 12F is represented by .sub.TFD and an in-phase deformation of the tires 13R of the rear wheels 12R is represented by .sub.TRD. According to the above Formula (27), the following Formula (28) holds. A pitch angle .sub.BG of the sprung and an in-phase deformation .sub.TFD of the tires 13F of the front wheels 12F can be calculated in accordance with the following Formula (28) on the basis of wheel speeds of the four wheels and vertical strokes Z of the four suspensions 16.

(72) $\begin{array}{cc}\left[\begin{array}{c}{}_{\mathrm{BG}}\\ {}_{\mathrm{TFD}}\end{array}\right]s={\left[\begin{array}{cc}-\frac{H}{r_F}& \frac{{}_F{}_F}{r_F}\frac{1}{s}\\ -\frac{H}{r_R}& \frac{{}_R{}_R}{r_R}\frac{1}{s}{e}^{-\frac{L}{U}s}\end{array}\right]}^{-1}\left[\begin{array}{c}\frac{{}_1+{}_2}{2}-\left({}_{\mathrm{XF}}/r_F-{}_F\right){}_{\mathrm{SFD}}s\\ \frac{{}_3+{}_4}{2}-\left({}_{\mathrm{XR}}/r_R-{}_R\right){}_{\mathrm{SRD}}s\end{array}\right]& \left(28\right)\end{array}$

(73) Notably, the following Formulae (29)-(32) hold with regard to in-phase vertical strokes .sub.SFD and .sub.SRD and in-phase deformations .sub.TFD and .sub.TRD, respectively. A vertical stroke .sub.SFD is a value which can be derived as an average value of strokes Z1 and Z2 detected by the stroke sensors 32FL, 32FR provided for the front wheels 12FL, 12FR, respectively. In similar, a vertical stroke .sub.SRD is a value which can be derived as an average value of strokes Z3 and Z4 detected by the stroke sensors 32RL, 32RR provided for the rear wheels 12RL, 12RR, respectively. In addition, Z.sub.01 and Z.sub.02 in the following Formula (31) are vertical displacements of the unsprungs of the front wheels 12FL, 12FR, respectively in a situation where a deformation of each tire is 0. In similar, Z.sub.03 and Z.sub.04 in the following Formula (32) are vertical displacements of the unsprungs of the rear wheels 12RL, 12RR, respectively in a situation where a deformation of each tire is 0.
.sub.SFD=(Z.sub.A1+Z.sub.A2Z.sub.B1Z.sub.B2)/2(29)
.sub.SRD=(Z.sub.A3+Z.sub.A4Z.sub.B3Z.sub.B4)/2(30)
.sub.TFD=(Z.sub.01+Z.sub.02Z.sub.A1+Z.sub.A2)/2(31)
.sub.TRD=(Z.sub.03+Z.sub.04Z.sub.A3+Z.sub.A4)/2(32)

(74) (Z.sub.B1+Z.sub.B2)/2 in the above Formula (29) is a vertical displacement of the sprung at the axle positions TC of the front wheels and is equal to Z.sub.BGL.sub.F*.sub.BG. (Z.sub.B3+Z.sub.B4)/2 in the above Formula (30) is a vertical displacement of the sprung at the axle positions TC of the rear wheels and is equal to Z.sub.BG+L.sub.R*.sub.13G. In addition, a vertical displacement (Z.sub.A3+Z.sub.A4)/2 of the unsprungs of the rear wheels delays with a delay time L/U relative to a vertical displacement (Z.sub.A1+Z.sub.A2)/2 of the unsprung of the front wheels. Thus, the following Formulae (33) and (34) hold corresponding to the above Formulae (29) and (30.)
(Z.sub.A1+Z.sub.A2Z.sub.B1Z.sub.B2)/2=(Z.sub.A1+Z.sub.A2)/2(Z.sub.BGL.sub.F.sub.BG)=.sub.SFD(33)
(Z.sub.A3+Z.sub.A4-Z.sub.B3-Z.sub.B4)/2=(Z.sub.A1+Z.sub.A2)/2=(Z.sub.A1+Z.sub.A2)/2e.sup.L/Us(Z.sub.BG+L.sub.R.sub.BG)=.sub.SRD(34)

(75) According to the above Formulae (33) and (34), the following Formula (35) holds and, by transforming the latter Formula, the following Formula (36) can be obtained. Thus, a vertical speed Z.sub.BG*s of the sprung and an in-phase component (Z.sub.A1+Z.sub.A2)s/2 of vertical speeds of the unsprungs of the front wheels can be calculated in accordance with the following Formula (36) on the basis of in-phase vertical strokes .sub.SFD and .sub.SRD and a pitch angle .sub.BG of the sprung.

(76) $\begin{array}{cc}\left[\begin{array}{cc}1& -1\\ e^{-\frac{L}{U}s}& -1\end{array}\right]\left[\begin{array}{c}\left(Z_{A1}+Z_{A2}\right)/2\\ Z_{\mathrm{BG}}\end{array}\right]s=\left[\begin{array}{c}{}_{\mathrm{SFD}}s-L_F{}_{\mathrm{BG}}s\\ {}_{\mathrm{SRD}}s+L_R{}_{\mathrm{BG}}s\end{array}\right]& \left(35\right)\\ \left[\begin{array}{c}\left(Z_{A1}+Z_{A2}\right)/2\\ Z_{\mathrm{BG}}\end{array}\right]s={\left[\begin{array}{cc}1& -1\\ e^{-\frac{L}{U}s}& -1\end{array}\right]}^{-1}\left[\begin{array}{c}{}_{\mathrm{SFD}}s-L_F{}_{\mathrm{BG}}s\\ {}_{\mathrm{SRD}}s+L_R{}_{\mathrm{BG}}s\end{array}\right]& \left(36\right)\end{array}$

(77) FIG. 2: Block Diagram for State Quantities Estimation

(78) FIG. 2 illustrates a block diagram for use in the first embodiment with estimating state quantities such as a vertical speed of the sprung and the like and vertical speeds of the unsprungs of the four wheels in the above-described manners. The calculations of a vertical speed of the sprung and the like executed in accordance with the block diagram illustrated in FIG. 2 are achieved by the electronic control unit 28.

(79) As illustrated in FIG. 2, a vertical speed Z.sub.BG*s, a pitch angular speed .sub.BG*s, a roll angular speed .sub.BG*s and a yaw angular speed .sub.BG*s of the sprung can be calculated on the basis of wheel speeds of the four wheels 12 and vertical strokes Z of the four suspensions 16. In-phase and reverse phase components of vertical speeds of the unsprungs of the front wheels can be calculated on the basis of wheel speeds and vertical strokes Z, and vertical speeds Z.sub.A1*sZ.sub.A4*s of the usprungs of the four wheels 12 can be calculated on the basis of the components.

(80) In the block diagram illustrated in FIG. 2, calculation blocks denoted by P-S execute the calculations of the above Formula (28), the following Formula (37), the above Formula (36) and the following Formula (38), respectively.

(81) $\begin{array}{cc}\left[\begin{array}{c}{}_{\mathrm{BG}}\\ {}_{\mathrm{TFG}}\end{array}\right]s={\left[\begin{array}{cc}-\frac{W_F}{r_F}& \frac{{}_F{}_F}{r_F}\frac{1}{s}\\ -\frac{W_R}{r_R}& \frac{{}_R{}_R}{r_R}\frac{1}{s}{e}^{-\frac{L}{U}s}\end{array}\right]}^{-1}\left[\begin{array}{c}\left(-{}_1+{}_2\right)/2-\left({}_{\mathrm{XF}}/r_F-{}_F\right){}_{\mathrm{SFG}}s\\ \left(-{}_3+{}_4\right)/2-\left({}_{\mathrm{XR}}/r_R-{}_R\right){}_{\mathrm{SRG}}s\end{array}\right]& \left(37\right)\\ \left[\begin{array}{c}\left(-Z_{A1}+Z_{A2}\right)/2\\ {}_{\mathrm{BG}}\end{array}\right]s={\left[\begin{array}{cc}1& -W_F\\ e^{-\frac{L}{U}s}& -W_R\end{array}\right]}^{-1}\left[\begin{array}{c}{}_{\mathrm{SFG}}s\\ {}_{\mathrm{SRG}}s\end{array}\right]& \left(38\right)\end{array}$

(82) It is to be noted that .sub.SFG in FIG. 2 and the above Formula (37) is a reverse phase vertical stroke of the suspensions 16F of the front wheels 12F and is calculated in accordance with the following Formula (39.) Z.sub.A1+Z.sub.B1 and Z.sub.A2Z.sub.B2 in the following Formula (39) are sign-inverted values of a stroke Z1 detected by the stroke sensor 32FL for the front wheel 12FL and a stroke Z2 detected by the stroke sensor 32FR for the front wheel 12FR, respectively. In similar, it is also to be noted that .sub.SRG is a reverse phase vertical stroke of the suspensions 16R of the rear wheels 12R and is calculated in accordance with the following Formula (40.) Z.sub.A3+Z.sub.B3 and Z.sub.A4Z.sub.B4 in the following Formula (40) are sign-inverted values of a stroke Z3 detected by the stroke sensor 32RL for the rear left wheel 12RL and a stroke Z4 detected by the stroke sensor 32RR for the rear right wheel 12RR, respectively.
.sub.SFG=(Z.sub.A1+Z.sub.A2+Z.sub.B1Z.sub.B2)/2(39)
.sub.SRG=(Z.sub.A3+Z.sub.A4+Z.sub.B3Z.sub.B4)/2(40)

(83) Values input to the calculation block P are those which form the second matrix on the right side of the above Formula (28.) The calculation block P calculates a pitch angular speed .sub.BG*s of the sprung and a change rate .sub.TFD*s of an in-phase component of deformations of the tires 13F of the front wheels 12F by multiplying the first and second matrixes on the right side of the above Formula (28.)

(84) Values input to the calculation block Q are those which form the second matrix on the right side of the above Formula (37.) The calculation block Q calculates a yaw angular speed .sub.BG*s of the sprung and a change rate .sub.TFG*s of a reverse phase component of deformations of the tires 13F of the front wheels 12F by multiplying the first and second matrixes on the right side of the above Formula (37.)

(85) Values input to the calculation block R are those which form the second matrix on the right side of the above Formula (36.) The calculation block R calculates a vertical speed (Z.sub.A1+Z.sub.A2)s/2 of the unsprungs of the front wheels and a vertical speed Z.sub.BG*s of the sprung by multiplying the first and second matrixes on the right side of the above Formula (36.)

(86) Values input to the calculation block S are those which form the second matrix on the right side of the above Formula (38.) The calculation block S calculates a roll speed (Z.sub.A1+Z.sub.A2)s/2 of the unsprungs of the front wheels and a roll speed .sub.BG*s of the sprung by multiplying the first and second matrixes on the right side of the above Formula (38.)

(87) FIG. 3: Block Diagram for Estimation of Vertical Displacement of Road Surface

(88) FIG. 3 illustrates a block diagram for use in the first embodiment with estimating vertical displacements Z.sub.01-Z.sub.04 of a road surface at positions of the wheels 12FL-12RR. The calculations of vertical displacements Z.sub.01-Z.sub.04 of a road surface executed in accordance with the block diagram illustrated in FIG. 3 are as well achieved by the electronic control unit 28.

(89) With the block diagram illustrated in FIG. 3, vertical displacements Z.sub.01-Z.sub.04 of a road surface are calculated on the basis of a change rate .sub.TFD*s of an in-phase deformation of the tires 13F of the front wheels 12F, a change rate .sub.TFG*s of a reverse phase deformation of the tires 13F of the front wheels 12F, a vertical speed (Z.sub.A1+Z.sub.A2)s/2 of the unsprungs of the front wheels and a roll speed (Z.sub.A1+Z.sub.A2)s/2 of the unsprungs of the front wheels that are calculated with the block diagram illustrated in FIG. 2. It is to be noted that in the other embodiments described later, vertical displacements Z.sub.01-Z.sub.04 of a road surface are calculated as well with the block diagram illustrated in FIG. 3.

(90) As will be understood from the above descriptions, according to the first embodiment, wheel speed components that are in the same phase to left and right wheels for the front and rear wheels are calculated on the basis of wheel speeds .sub.1-.sub.4. As described above, as the behavior of the sprung which influences on components of wheel speeds that are in the same phase to the left and right wheels is pitching, a pitch angular speed .sub.BG*s of the sprung is calculated on the basis of the components of wheel speeds that are in the same phase to the left and right wheels.

(91) Wheel speed components that are in the reverse phase to left and right wheels for the front and rear wheels are calculated on the basis of wheel speeds .sub.1-.sub.4. As described above, as the behavior of the sprung which influences on components of wheel speeds that are in the reverse phase to the left and right wheels is yawing, a yaw angular speed .sub.BG*s of the sprung is calculated on the basis of the components of wheel speeds that are in the reverse phase to the left and right wheels.

(92) In-phase vertical stroke speeds .sub.SFD*s and .sub.SRD*s of the suspensions 16 of the front and rear wheels and reverse phase vertical stroke speeds .sub.SFG*s and .sub.SRG*s of the suspensions 16 of the front and rear wheels are calculated on the basis of strokes Z.sub.1-Z.sub.4 of the suspensions 16 of the front and rear wheels.

(93) A vertical speed Z.sub.BG*s of the sprung can be calculated by removement an influence of pitching of the sprung from the in-phase vertical stroke speeds .sub.SFD*s and .sub.SRD*s of the suspensions 16 of the front and rear wheels. Changes in vertical stroke speeds of the suspensions 16 of the rear wheels delay with a delay time L/U relative to changes in vertical stroke speeds of the suspensions 16 of the front wheels. Thus, an in-phase vertical stroke speed .sub.SRD*s of the suspensions 16 of the rear wheels can be expressed using a delay time L/U and an in-phase vertical stroke speed .sub.SFD*s of the suspensions 16 of the front wheels. Accordingly, a vertical speed Z.sub.BG*s of the sprung can be calculated on the basis of a pitch angular speed .sub.BG*s of the sprung and an in-phase vertical stroke speed .sub.SFD*s of the suspensions 16 of the front wheels.

(94) As described above, the behavior of the sprung which influences on reverse phase components .sub.SFG*s and .sub.SRG*s of vertical stroke speeds of the suspensions 16 of the front and rear wheels is rolling. Thus, a roll angular speed .sub.BG*s of the sprung is calculated on the basis of reverse phase components .sub.SFG*S and .sub.SRG*S of vertical stroke speeds of the suspensions 16 of the front and rear wheels.

(95) An in-phase component (Z.sub.A1+Z.sub.A2)s/2 of vertical speeds of the unsprungs of the front wheels is calculated on the basis of a pitch angular speed .sub.BG*s of the sprung and in-phase vertical stroke speeds .sub.SFD*s and .sub.SRD*s of the suspensions 16 of the front and rear wheels. A reverse phase component (Z.sub.A1+Z.sub.A2)s/2 of vertical speeds of the unsprungs of the front wheels is calculated on the basis of reverse phase components .sub.SFG*S and .sub.SRG*s of vertical stroke speeds of the suspensions 16 of the front and rear wheels.

(96) Further, vertical speeds Z.sub.A1*s and Z.sub.A2*s of the usprungs of the front wheels 12FL and 12FR are calculated on the basis of an in-phase component (Z.sub.A1+Z.sub.A2)s/2 and a reverse phase component (Z.sub.A1+Z.sub.A2)s/2 of vertical speeds of the unsprungs of the front wheels. Changes in vertical stroke speeds of the unsprungs of the rear wheels 12RL and 12RR delay with a delay time L/U relative to changes in vertical stroke speeds of the unsprungs of the front wheels 12FL and 12FR. Thus, vertical speeds Z.sub.A3*s and Z.sub.A4*s of the usprungs of the rear wheels 12RL and 12RR are calculated on the basis of vertical speeds Z.sub.A1*s and Z.sub.A2*s of the usprungs of the front wheels 12FL and 12FR and the delay time L/U.

(97) As described above, wheel speeds .sub.1-.sub.4 are rotational speeds of the wheels 12FL-12RR, respectively, relative to the sprung. As expressed in the above Formula (13), wheel speeds are the same as rotational speeds w corresponding to longitudinal displacement of the wheels 12 (the tires 13) corrected with change amounts d.sub.A of rotational speeds of the wheels 12 caused by pitching behavior of the sprung.

(98) As expressed by the above Formulae (2) and (9), rotational speeds w corresponding to longitudinal displacement of the wheels 12 are corrected with change amounts (dX.sub.AdX.sub.B) of rotational speeds caused by the behavior of the sprung and change amounts *.sub.0(r/r) of rotational speeds caused by changes in the radiuses r of the tires 13 due to deformations. Consequently, state quantities of the sprung and the unsprung can be estimated with higher accuracy as compared to where rotational speeds w are not corrected with change amounts (dX.sub.AdX.sub.B) of rotational speeds caused by the behavior of the sprung and change amounts *.sub.0(r/r) of rotational speeds caused by changes in the radiuses r of the tires 13 due to deformations.

(99) A longitudinal displacement X.sub.B of the sprung used for calculating longitudinal speed dX.sub.B of the sprung is calculated as a total of three displacements X.sub.Ba, X.sub.Bb and X.sub.Bc. Accordingly, as compared to where at least one of the three displacements X.sub.Ba, X.sub.Bb and X.sub.Bc is not considered, a longitudinal speed dX.sub.B of the sprung can be calculated with higher accuracy, which enables to estimate state quantities of the sprung and the unsprung with higher accuracy.

(100) In addition, as expressed by the above Formula (12), a longitudinal speed dX.sub.A of the sprung is corrected with a correction amount .sub.(dX.sub.AdX.sub.B) based on a vertical stroke speed of the suspension 16. Consequently, state quantities of the sprung and the unsprung can be estimated with higher accuracy as compared to where a longitudinal speed dX.sub.A of the sprung is not corrected with a correction amount based on a vertical stroke speed of the suspension 16. The effects generated by the corrections can as well be obtained in the other embodiments described later.

Second Embodiment

(101) In a second embodiment, on the presupposition that a vertical transmitting force of each tire 13 is the same as a vertical transmitting force of the associated suspension 16, various state quantities of the sprung and vertical speeds of the unsprungs of the four wheels are estimated on the base of wheel speeds of the four wheels and strokes Z of the suspensions 16. Notably, in a vehicle such as an automobile and the like, when a frequency of vertical stroke speed of the suspension 16 is not higher than 10 Hz or so, estimation error due to the above presupposition is very small.

(102) First, an in-phase component of wheel speeds will be described. According to the Formula (24) and the Formulae (29)-(32) in the above-described first embodiment, the following Formula (41) holds.

(103) 0$\begin{array}{cc}\left[\begin{array}{c}\left({}_1+{}_2\right)/2\\ \left({}_3+{}_4\right)/2\end{array}\right]=-\left[\begin{array}{c}\frac{H}{r_F}{}_{\mathrm{BG}}\\ \frac{H}{r_R}{}_{\mathrm{BG}}\end{array}\right]s+\left[\begin{array}{c}\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right){}_{\mathrm{SFD}}\\ \left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right){}_{\mathrm{SRD}}\end{array}\right]s+\left[\begin{array}{c}\frac{{}_F{}_F}{r_F}{}_{\mathrm{TFD}}\\ \frac{{}_R{}_R}{r_R}{}_{\mathrm{TRD}}\end{array}\right]& \left(41\right)\end{array}$

(104) The unsprungs of the left and right front wheels 12FL and 12FR are assumed to have the same mass and the mass is denoted by m.sub.F. In similar, the unsprungs of the left and right rear wheels 12RL and 12RR are assumed to have the same mass and the mass is denoted by m.sub.R. Coefficients that transmit in-phase vertical strokes .sub.SFD and .sub.SRD of the suspensions 16 of the front and rear wheels to vertical forces are denoted by K.sub.SFD and K.sub.SRD, respectively. Similarly, coefficients that transmit in-phase deformations .sub.TFD and .sub.TRD of the tires 13 of the front and rear wheels to vertical forces are denoted by K.sub.TFD and K.sub.TRD, respectively.

(105) In addition, vertical acceleration of the unsprungs of the front wheels 12FL, 12FR and the rear wheels 12RL, 12RR are denoted by ddZ.sub.A1-ddZ.sub.A4, respectively. According to the relationship between vertical forces of the unsprungs of the front and rear wheels, the following Formulae (42) and (43) hold, respectively. It is to be noted that coefficients K.sub.SFD and K.sub.SRD are determined by specifications of the suspensions 16 of the front and rear wheels, respectively (damping coefficients of the shock absorbers 20 and spring rates of the suspension springs 22.) Coeficients K.sub.TFD and K.sub.TRD are determined by specifications of the tires 13 of the front and rear wheels.
.sub.SFDK.sub.SFD=.sub.TFDK.sub.TFDm.sub.F({umlaut over (Z)}.sub.A1+{umlaut over (Z)}.sub.A2)/2(42)
.sub.SRDK.sub.SRD=.sub.TRDK.sub.TRDm.sub.R({umlaut over (Z)}.sub.A3+{umlaut over (Z)}.sub.A4)/2(43)

(106) As inertia forces of the unsprungs, i.e. the second term on the right side of the above Formulae (42) and (43) are very small than the other forces, i.e. the term on the left side and the first term on the right side of the above Formulae (42) and (43), the following approximate Formulae (44) and (45) hold corresponding to the above Formulae (42) and (43.)
.sub.SFD.sub.TFDK.sub.TFD/K.sub.SFD(44)
.sub.SRD.sub.TRDK.sub.TRD/K.sub.SRD(45)

(107) The following Formula (46) is derived by substituting the above Formulae (44) and (45) for the above Formula (41.)

(108) $\begin{array}{cc}\begin{array}{c}\left[\begin{array}{c}\left({}_1+{}_2\right)/2\\ \left({}_3+{}_4\right)/2\end{array}\right]-\left[\begin{array}{c}\frac{H}{r_F}{}_{\mathrm{BG}}\\ \frac{H}{r_R}{}_{\mathrm{BG}}\end{array}\right]s+\left[\begin{array}{c}\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right){}_{\mathrm{SFD}}\\ \left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right){}_{\mathrm{SRD}}\end{array}\right]s+\\ \left[\begin{array}{c}\frac{{}_F{}_F}{r_F}{}_{\mathrm{TFD}}\\ \frac{{}_R{}_R}{r_R}{}_{\mathrm{TRD}}\end{array}\right]\\ =-\left[\begin{array}{c}\frac{H}{r_F}{}_{\mathrm{BG}}\\ \frac{H}{r_R}{}_{\mathrm{BG}}\end{array}\right]s+\\ \left[\begin{array}{c}\left\{\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{K_{\mathrm{TFD}}}{K_{\mathrm{SFD}}}+\frac{{}_F{}_F}{r_F}\frac{1}{s}\right\}{}_{\mathrm{TFD}}s\\ \left\{\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{K_{\mathrm{TRD}}}{K_{\mathrm{SRD}}}+\frac{{}_R{}_R}{r_R}\frac{1}{s}\right\}{}_{\mathrm{TRD}}s\end{array}\right]\end{array}& \left(46\right)\end{array}$

(109) As a change in an in-phase deformation .sub.TRD of the tire 13 of each rear wheel delays with a delay time L/U relative to a change in an in-phase deformation .sub.TFD of the tires 13 of the associated front wheel, the above Formula (46) can be rewritten as the following Formula (47.) In the following Formula (47), K.sub.TF and K.sub.TR are the same as K.sub.TFD and K.sub.TRD, respectively, and K.sub.SF and K.sub.SR are the same as K.sub.SFD and K.sub.SRD, respectively.

(110) $\begin{array}{cc}\left[\begin{array}{c}\left({}_1+{}_2\right)/2\\ \left({}_3+{}_4\right)/2\end{array}\right]=-\left[\begin{array}{c}\frac{H}{r_F}{}_{\mathrm{BG}}\\ \frac{H}{r_R}{}_{\mathrm{BG}}\end{array}\right]s+\left[\begin{array}{c}\left\{\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{K_{\mathrm{TF}}}{K_{\mathrm{SF}}}+\frac{{}_F{}_F}{r_F}\frac{1}{s}\right\}{}_{\mathrm{TFD}}s\\ \left\{\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{K_{\mathrm{TR}}}{K_{\mathrm{SR}}}+\frac{{}_R{}_R}{r_R}\frac{1}{s}\right\}{}_{\mathrm{TRD}}{\mathrm{se}}^{-\frac{L}{U}s}\end{array}\right]& \left(47\right)\end{array}$

(111) The above Formula (47) can be transformed into the following Formula (48) and can further be transformed into the following Formula (49.)

(112) $\begin{array}{cc}\left[\begin{array}{cc}-\frac{H}{r_F}& \left\{\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{K_{\mathrm{TF}}}{K_{\mathrm{SF}}}+\frac{{}_F{}_F}{r_F}\frac{1}{s}\right\}\\ -\frac{H}{r_F}& \left\{\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{K_{\mathrm{TR}}}{K_{\mathrm{SR}}}+\frac{{}_R{}_R}{r_R}\frac{1}{s}\right\}{e}^{-\frac{L}{U}s}\end{array}\right]\left[\begin{array}{c}{}_{\mathrm{BG}}\\ {}_{\mathrm{TFD}}\end{array}\right]s=\left[\begin{array}{c}\left({}_1+{}_2\right)/2\\ \left({}_3+{}_4\right)/2\end{array}\right]& \left(48\right)\\ \left[\begin{array}{c}{}_{\mathrm{BG}}\\ {}_{\mathrm{TFD}}\end{array}\right]s={\left[\begin{array}{cc}-\frac{H}{r_F}& \left\{\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{K_{\mathrm{TF}}}{K_{\mathrm{SF}}}+\frac{{}_F{}_F}{r_F}\frac{1}{s}\right\}\\ -\frac{H}{r_F}& \left\{\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{K_{\mathrm{TR}}}{K_{\mathrm{SR}}}+\frac{{}_R{}_R}{r_R}\frac{1}{s}\right\}{e}^{-\frac{L}{U}s}\end{array}\right]}^{-1}\left[\begin{array}{c}\left({}_1+{}_2\right)/2\\ \left({}_3+{}_4\right)/2\end{array}\right]& \left(49\right)\end{array}$

(113) As a change in an in-phase deformation .sub.TRD of the tire 13 of each rear wheel delays with a delay time L/U relative to a change in an in-phase deformation .sub.TFD of the tire 13 of the associated front wheel, the above Formula (45) can be rewritten as the following Formula (50) using the delay time L/U.

(114) $\begin{array}{cc}{}_{\mathrm{SRD}}{}_{\mathrm{TFD}}{e}^{-\frac{L}{U}s}{K}_{\mathrm{TRD}}/K_{\mathrm{SRD}}& \left(50\right)\end{array}$

(115) A pitch angle .sub.BG of the sprung and an in-phase deformation .sub.TFD of the tires 13 of the front wheels can be calculated on the basis of wheel speeds .sub.1-.sub.4 of the four wheels. If an in-phase deformation .sub.TFD is calculated, in-phase vertical stroke speeds .sub.SFD*s and .sub.SRD*s of the suspensions 16 of the front and rear wheels can be calculated in accordance with the above Formulae (44) and (45.)

(116) As already described in the description of the first embodiment, the above Formula (36) holds. Consequently, a vertical speed Z.sub.BG*s of the sprung and an in-phase component (Z.sub.A1+Z.sub.A2)s/2 of vertical speeds of the unsprungs of the front wheels can be calculated by substituting a pitch angle .sub.BG of the sprung and in-phase vertical strokes .sub.SFD and .sub.SRD that are calculated as above for the following Formula (36.) In other word, a vertical speed Z.sub.BG*s of the sprung and an in-phase component (Z.sub.A1+Z.sub.A2)s/2 of vertical speeds of the unsprungs of the front wheels can be calculated on the basis of in-phase vertical strokes .sub.SFD and .sub.SRD and a pitch angle .sub.BG of the sprung.

(117) Next, reverse phase components of wheel speeds will be described. According to the above Formulae (23), a reverse phase component (.sub.1+.sub.2)/2 of wheel speeds of the front wheels 12FL, 12FR and a reverse phase component (.sub.3+.sub.4)/2 of wheel speeds of the rear wheels 12RL, 12RR are expressed by the following Formula (51.)

(118) $\begin{array}{cc}\left[\begin{array}{c}-\frac{{}_1+{}_2}{2}\\ -\frac{{}_3+{}_4}{2}\end{array}\right]=-\left[\begin{array}{c}\frac{W_F}{r_F}{}_{\mathrm{BG}}\\ \frac{W_R}{r_R}{}_{\mathrm{BG}}\end{array}\right]s+\left[\begin{array}{c}\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{\left(-Z_{A1}+Z_{A2}\right)-\left(-Z_{B1}+Z_{B2}\right)}{2}\\ \left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{\left(-Z_{A3}+Z_{A4}\right)-\left(-Z_{B3}+Z_{B4}\right)}{2}\end{array}\right]s+\left[\begin{array}{c}\frac{{}_F{}_F}{r_F}\frac{\left(-Z_{01}+Z_{02}\right)-\left(-Z_{A1}+Z_{A2}\right)}{2}\\ \frac{{}_R{}_R}{r_R}\frac{\left(-Z_{03}+Z_{04}\right)-\left(-Z_{A3}+Z_{A4}\right)}{2}\end{array}\right]& \left(51\right)\end{array}$

(119) As displacements of the unsprungs of the rear wheels delay with a delay time L/U relative to displacements of the unsprungs of the front wheels, the above Formula (51) can be rewritten as the following Formula (52) using the delay time L/U. The following Formula (52) can be transformed into the following Formula (53.)

(120) $\begin{array}{cc}\left[\begin{array}{cc}-\frac{W_F}{r_F}s& \frac{{}_F{}_F}{r_F}\\ -\frac{W_F}{r_F}s& \frac{{}_F{}_F}{r_F}{e}^{-\frac{L}{U}s}\end{array}\right]\left[\begin{array}{c}{}_{\mathrm{BG}}\\ \frac{\left(-Z_{01}+Z_{02}\right)-\left(-Z_{A1}+Z_{A2}\right)}{2}\end{array}\right]=\left[\begin{array}{c}\frac{-{}_1+{}_2}{2}-\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{\left(-Z_{A1}+Z_{A2}\right)-\left(-Z_{B1}+Z_{B2}\right)}{2}s\\ \frac{-{}_3+{}_4}{2}-\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{\left(-Z_{A3}+Z_{A4}\right)-\left(-Z_{B3}+Z_{B4}\right)}{2}s\end{array}\right]& \left(52\right)\\ \left[\begin{array}{c}{}_{\mathrm{BG}}\\ \frac{\left(-Z_{01}+Z_{02}\right)-\left(-Z_{A1}+Z_{A2}\right)}{2}\end{array}\right]s={\left[\begin{array}{cc}-\frac{W_F}{r_F}& \frac{{}_F{}_F}{r_F}\frac{1}{s}\\ -\frac{W_F}{r_F}& \frac{{}_F{}_F}{r_F}\frac{1}{s}{e}^{-\frac{L}{U}s}\end{array}\right]}^{-1}\left[\begin{array}{c}\frac{-{}_1+{}_2}{2}-\left(\frac{{}_{\mathrm{XF}}-{}_F{r}_F}{r_F}\right)\frac{\left(-Z_{A1}+Z_{A2}\right)-\left(-Z_{B1}+Z_{B2}\right)}{2}s\\ \frac{-{}_3+{}_4}{2}-\left(\frac{{}_{\mathrm{XR}}-{}_R{r}_R}{r_R}\right)\frac{\left(-Z_{A3}+Z_{A4}\right)-\left(-Z_{B3}+Z_{B4}\right)}{2}s\end{array}\right]& \left(53\right)\end{array}$

(121) According to the above Formula (53) and the above Formulae (39) and (40), the above Formula (37) holds. Accordingly, a yaw angular speed .sub.BG*s of the sprung and a change rate .sub.TFG*s of a reverse phase deformation of the tires 13FL, 13FR of the front wheels 12FL, 12FR, respectively, can be calculated on the basis of wheel speeds of the four wheels and strokes Z of the four suspensions 16.

(122) It is to be noted that the following Formulae (54) and (55) hold for reverse phase deformations .sub.TFG and .sub.TRG of the tires.
.sub.TFG=(Z.sub.01+Z.sub.02+Z.sub.A1+Z.sub.A2)/2(54)
.sub.TRG=(Z.sub.03+Z.sub.04+Z.sub.A3+Z.sub.A4)/2(55)

(123) (Z.sub.A1+Z.sub.A2)/2 in the above Formula (39) is a roll angle of the sprung at the axle positions TC of the front wheels and is equal to W.sub.F*.sub.BG. Similarly, (Z.sub.A3+Z.sub.A4)/2 in the above Formula (40) is a roll angle of the sprung at the axle positions TC of the rear wheels and is equal to W.sub.R*.sub.BG. In addition, a roll angle (Z.sub.A3+Z.sub.A4)/2 of the sprung of the rear wheels delays with a delay time L/U relative to a roll angle (Z.sub.A1+Z.sub.A2)/2 of the sprung of the front wheels. Thus, the following Formulae (56) and (57) hold corresponding to the above Formulae (39) and (40.)

(124) $\begin{array}{cc}\frac{\left(-Z_{A1}+Z_{A2}\right)-\left(-Z_{B1}+Z_{B2}\right)}{2}=\frac{\left(-Z_{A1}+Z_{A2}\right)}{2}-W_F{}_{\mathrm{BG}}={}_{\mathrm{SFG}}& \left(56\right)\\ \frac{\left(-Z_{A3}+Z_{A4}\right)-\left(-Z_{B3}+Z_{B4}\right)}{2}=\frac{\left(-Z_{A1}+Z_{A2}\right)}{2}{e}^{-\frac{L}{U}s}-W_R{}_{\mathrm{BG}}={}_{\mathrm{SRG}}& \left(57\right)\end{array}$

(125) According to the above Formulae (56) and (57), the following Formula (58) holds and, by transforming the latter Formula, the above Formula (38) can be obtained. Thus, a roll speed (Z.sub.A1+Z.sub.A2)s/2 of the sprung of the front wheels and a roll angular speed .sub.BG*s of the sprung can be calculated in accordance with the above Formula (38) on the basis of strokes Z of the suspensions 16 of the wheels 12.

(126) $\begin{array}{cc}\left[\begin{array}{cc}1& -W_F\\ e^{-\frac{L}{U}s}& -W_R\end{array}\right]\left[\begin{array}{c}\left(-Z_{A1}+Z_{A2}\right)/2\\ {}_{\mathrm{BG}}\end{array}\right]s=\left[\begin{array}{c}{}_{\mathrm{SFG}}s\\ {}_{\mathrm{SRG}}s\end{array}\right]& \left(58\right)\end{array}$

(127) FIG. 11: Block Diagram for State Quantities Estimation

(128) FIG. 11 illustrates a block diagram for use in the second embodiment with estimating state quantities such as a vertical speed of the sprung and the like and estimating vertical speeds of the unsprungs of the four wheels in the above-described manners. The calculations of a vertical speed of the sprung and the like executed in accordance with the block diagram illustrated in FIG. 11 are also achieved by the electronic control unit 28.