Method to determine the roll angle of a motorcycle

Abstract

A method to determine a roll angle (λ.sub.E) of a vehicle, wherein the roll angle (λ.sub.E) is calculated as a combination of at least a first roll angle variable (λ.sub.1) and a second roll angle variable (λ.sub.2), wherein the first roll angle variable (λ.sub.1) is determined from an acquired rolling rate ({dot over (λ)}.sub.m) of the vehicle using a first method, wherein the second roll angle variable (λ.sub.2) is determined from one or more further vehicle movement dynamics characteristic variables using a second method.

Claims

1. A method to determine a roll angle (λ.sub.E) of a vehicle, comprising: determining, by a processor of the vehicle, a first roll angle variable (λ.sub.1) from an acquired rolling rate {dot over (λ)}.sub.m ({dot over (λ)}.sup.M) of the vehicle using a first method; determining, by the processor of the vehicle, a second roll angle variable (λ.sub.2) from one or more further vehicle movement dynamics characteristic variables using a second method; calculating, by a processor of the vehicle, the roll angle (λ.sub.E) as a combination of at least the first roll angle variable (λ.sub.1) and the second roll angle variable (λ.sub.2) by: calculating a first combination, by combining the first roll angle variable of the first method high-passed filtered with a first cutoff frequency and the second roll angle variable of the second method low-passed filtered with the first cutoff frequency, calculating a second combination, by combining the first roll angle variable of the first method high-passed Filtered with a second cutoff frequency and the second roll angle variable of the second method low-passed filtered with the second cutoff frequency, and calculating a third combination as the roll angle (λ.sub.E) by combining the result of the first combination low-passed filtered with a third cutoff frequency and the result of the second combination high-passed filtered with the third cutoff frequency, wherein the first, the second and the third cutoff-frequencies are different; and controlling, by the processor of the vehicle, an operation of the vehicle using the roll angle (λ.sub.E).

2. The method according to claim 1, wherein the combination comprises multiple levels, wherein each level comprises at least one filtering step and at least one combination step.

3. The method according to claim 1, wherein the first roll angle variable (λ.sub.1) has different characteristics than the second roll angle variable (λ.sub.2).

4. The method according to claim 1, wherein the second roll angle variable (λ.sub.2) is determined from: a yaw rate of the vehicle and a vehicle velocity; and/or a lateral acceleration and vertical acceleration of the vehicle.

5. The method according claim 1, further comprising eliminating, based on inertial measurement, cross effects occurring between angular rates due to inclinations of a measurement system, wherein the cross effects are erroneous angular rates.

6. The method according to claim 1, wherein one of the roll angle variable determination methods applies a resettable integrator in combination with a resettable high-pass filter to eliminate roll-rate offset effects.

7. The method according to claim 6, wherein the first method applies an integrator for determining the first roll angle variable (λ.sub.1), wherein the integrator and direct subsequent high-pass filters are reset when the output of the integrator reaches a predefined threshold.

8. The method according to claim 1, wherein the processor uses a compensation method to increase a precision of the calculation of the first roll angle variable (λ.sub.1) and the second roll angle variable (λ.sub.2) based on a vertical centrifugal acceleration.

9. The method according to claim 1, wherein the processor uses a compensation method to increase a precision of the calculation of the first roll angle variable (λ.sub.1) and the second roll angle variable (λ.sub.2) based on lateral acceleration and roll rate.

10. The method according to claim 1, wherein the first roll angle variable is for rapidly changing roll angle values, and the second roll angle variable is for steady roll angle values, wherein the combination takes place in a frequency domain.

11. The method according to claim 1, wherein an amplitude of high frequencies of the roll angle variable of the first method is weighted higher than an amplitude of high frequencies of the roll angle variable of the second method, wherein an amplitude of low frequencies of the roll angle variable of the second method is weighted higher than an amplitude of low frequencies of the roll angle variable of the first method, wherein an amplitude of mid frequencies are weighted similarly.

12. The method according to claim 1 wherein the third cutoff frequency lies between the first cutoff frequency and the second cutoff frequency.

13. A method to determine a roll angle (λ.sub.E) of a vehicle, comprising: determining, by a processor of the vehicle, a first roll angle variable (λ.sub.1) from an acquired rolling rate ({dot over (λ)}.sup.M) of the vehicle using a first method; determining, by the processor of the vehicle, a second roll angle variable (λ.sub.2) from one or more further vehicle movement dynamics characteristic variables using a second method; calculating, by a processor of the vehicle, the roll angle (λ.sub.E) as a combination of at least the first roll angle variable (λ.sub.1) and the second roll angle variable (λ.sub.2) and controlling, by the processor of the vehicle, an operation of the vehicle using the roll angle (λ.sub.E), wherein the combination comprises multiple levels, wherein each level comprises at least one filtering step and at least one combination step, and wherein the number of levels is x, wherein the y-st level comprises 2.sup.x−y+1 filtering steps and 2.sup.x−y combination steps, wherein the output of level y is the input of level y+1, and wherein in the y-st level 2.sup.x−y cutoff frequencies are applied.

14. A device to determine a roll angle (λ.sub.E) of a vehicle, comprising: a processor of the vehicle configured to: determine a first roll angle variable (λ.sub.1) from an acquired rolling rate ({dot over (λ)}.sup.M) of the vehicle using a first method; determine a second roll angle variable (λ.sub.2) from one or more further vehicle movement dynamics characteristic variables using a second method; calculate the roll angle (λ.sub.E) as a combination of at least the first roll angle variable (λ.sub.1) and the second roll angle variable (λ.sub.2) by: calculating a first combination, by combining the first roll angle variable of the first method high-passed filtered with a first cutoff frequency and the second roll angle variable of the second method low-passed filtered with the first cutoff frequency, calculating a second combination, by combining the first roll angle variable of the first method high-passed filtered with a second cutoff frequency and the second roll angle variable of the second method low-passed filtered with the second cutoff frequency, and calculating a third combination as the roll angle (λ.sub.E), by combining the result of the first combination low-passed filtered with a third cutoff frequency and the result of the second combination high-passed filtered with the third cutoff frequency, wherein the first, the second and the third cutoff-frequencies are different; and control an operation of the vehicle using the roll angle (λ.sub.E).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further preferred exemplary embodiments of aspects of the invention emerge from the subclaims and from the subsequent description on the basis of figures, of which

(2) FIG. 1 is a schematic illustration of a motorcycle in a sloping position,

(3) FIG. 2 is a schematic illustration of a first exemplary embodiment of a method according to an aspect of the invention,

(4) FIG. 3 is a schematic illustration of a second exemplary embodiment of a method according to an aspect of the invention,

(5) FIG. 4 is a schematic illustration of a third exemplary embodiment of a method according to an aspect of the invention,

(6) FIG. 5 is a schematic illustration of an exemplary method for determining a roll angle,

(7) FIG. 6 is a schematic illustration of a fourth exemplary embodiment of a method according to an aspect of the invention,

(8) FIG. 7 is a schematic illustration of an exemplary method for adaptive calculation of a roll angle for use in the fourth exemplary embodiment illustrated in FIG. 7,

(9) FIG. 8 is a schematic illustration of an exemplary method for adaptive calculation of a roll angle,

(10) FIG. 9 is a schematic illustration of measured acceleration, particularly for a nonzero pitch angle, and

(11) FIG. 10 is a schematic illustration of an exemplary method of a combination.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(12) The core of the device or of the method for determining the roll angle (angle of inclination) of a vehicle, in particular a motorcycle, during driving is the combination of at least two individual calculation results (for steady-state travel and non-steady-state travel), in particular by means of a specific filter.

(13) FIG. 1 is a schematic illustration of a number of variables which are relevant to the method according to an aspect of the invention. A motorcycle 2 travels in a sloping position on roadway 1. A tire 3 of the motorcycle 2 is illustrated in sectional form. Line 4 represents the direction of the perpendicular to the roadway, and line 5 represents the axis of symmetry of the motorcycle 5. At the center of gravity SP of the motorcycle 2, the coordinate system which is fixed to the motorcycle is indicated by the vertical axis z.sup.M, which is fixed to the motorcycle and which runs parallel to the axis of symmetry of the motorcycle 5, and the transverse axis y.sup.M, which is perpendicular thereto and is fixed to the motorcycle. Line 6 represents the connecting line, projected into the y/z plane, between the center of gravity SP of the motorcycle 2 and the wheel contact point or wheel contact line RAP. The total roll angle λ.sub.ges corresponds to the angle between the perpendicular 4 to the roadway and the plane 5 of symmetry of the vehicle, and the physically active roll angle λ.sub.th corresponds to the angle between the perpendicular 4 to the roadway and the line 6. By way of example, one or more sensors 7, for example a rolling rate sensor for determining the rolling rate {dot over (λ)}.sup.M which is fixed to the motorcycle and/or a yaw rate sensor for determining the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle, is/are arranged laterally on the motorcycle 2. Alternatively or additionally, one or more sensors or a sensor cluster 8 can be arranged on the motorcycle 2, in particular in the region of the center of gravity SP, these being, for example, a yaw rate sensor for determining the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle and/or acceleration sensor or sensors for determining the vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle and/or the lateral acceleration ÿ.sup.M which is fixed to the motorcycle. The position of the rolling rate sensor and the position of the yaw rate sensor on the motorcycle 2 are advantageously not relevant.

(14) In customary tires, the total roll angle λ.sub.ges is approximately 10% to 20% above the physically active roll angle λ.sub.th. The difference between the total roll angle λ.sub.ges and the physically active roll angle λ.sub.th is also referred to as the additional roll angle λ.sub.ZS. The following therefore applies:
λ.sub.ges=λ.sub.ZS+λ.sub.th  (1)

(15) In customary tires, the additional roll angle λ.sub.ZS which is conditioned by the width of the tire is, as has already been mentioned above, of the order of magnitude of approximately 10% to 20% of the physically active roll angle λ.sub.th. Since λ.sub.ZS is small compared to λ.sub.th, the total roll angle λ.sub.ges is often approximated by the physically active roll angle λ.sub.th:
λ.sub.ges≈λ.sub.th

(16) For small pitch angles, the rolling rate {dot over (λ)}.sup.M which is fixed to the motorcycle and the rolling rate {dot over (λ)}.sup.roadway which is fixed to the roadway are similar to one another. Integration of the rolling rate {dot over (λ)}.sup.M gives rise to the (total) roll angle λ.sub.ges (this corresponds to the first roll angle variable λ.sub.1 in the exemplary embodiments in FIGS. 2, 3 and 4).

(17) A first exemplary embodiment of a method according to an aspect of the invention is illustrated schematically in FIG. 2. The integration 10 over time of the rolling rate {dot over (λ)}.sup.M which is fixed to the motorcycle is here a first calculation result (first roll angle variable λ.sub.1). For example, the calculation result λ.sub.1 is filtered with the high pass filter 11, which has, for example, a cut-off frequency f.sub.Trenn of 0.05 Hz. In the illustrated first exemplary embodiment, the second calculation result (second roll angle variable λ.sub.2) is obtained as a function 13 of the product 12 of the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle and the velocity v of the motorcycle. For example, the calculation result λ.sub.2 is filtered with the low pass filter 14, which has, for example, the same cut-off frequency f.sub.Trenn as the high pass filter 11, for example 0.05 Hz. In order to determine the roll angle λ.sub.E of the motorcycle, the calculation result λ.sub.1 of the integration 10 over time of the rolling rate λ.sup.M which is fixed to the motorcycle and the calculation result λ.sub.2 is added to a function 13 of the product 12 of the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle and the velocity v (block 15).

(18) The calculation of the first roll angle variable λ.sub.1 by integration 10 of the rolling rate {dot over (λ)}.sup.M which is fixed to the motorcycle applies both to steady-state and to non-steady-state travel. However, the calculation by integration 10 of the measurement error of the rolling rate λ.sup.M is not long-term stable, i.e. the result is valid only for a brief time. Depending on the design and accuracy of the rolling rate sensor used, the increase in the measurement error (referred to as drift) is between 1 degree/minute and 1 degree/second.

(19) In order to avoid overflow errors during the integration 10, it is possible, according to an exemplary embodiment which is not illustrated, to transfer the functions of integration 10 and high pass filter 11 into an equivalent low pass filter with additional gain.

(20) The calculation of the second roll angle variable λ.sub.2 from the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle and the vehicle velocity v applies only to steady-state cornering. Function 13 is dependent on the tire geometry and the dynamic tire behavior of the motorcycle.

(21) The filters 11, 14 used are usually first-order PT.sub.1 elements. The cut-off frequency f.sub.Trenn is, for example, in the range from approximately 0.01 Hz to approximately 0.10 Hz.

(22) The following explanation serves to substantiate the relationship between the yaw rate {dot over (ψ)}.sup.M, vehicle velocity v and roll angle λ:

(23) For steady-state cornering the following applies: the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle is provided by the yaw rate {dot over (ψ)}.sup.roadway which is fixed to the roadway and multiplied by the cosine of the total roll angle λ.sub.ges, and by the pitch angle velocity {dot over (ν)}.sub.roadway, wherein, however, the pitch angle velocity {dot over (ν)}.sub.roadway is zero for steady-state travel ({dot over (ν)}.sub.roadway=0), with the result that the second term sin λ.sub.g.Math.{dot over (ν)}.sub.roadway in equation (2) is eliminated:
{dot over (ψ)}.sup.M=cos λ.sub.ges.Math.{dot over (ψ)}.sup.roadway−sin λ.sub.ges.Math.{dot over (ν)}.sub.roadway=cos λ.sub.ges.Math.{dot over (ψ)}.sup.roadway  (2)

(24) For steady-state cornering, the following relationships also apply between the lateral acceleration {dot over (y)}.sup.h in the horizontalized coordinate system (coordinate system which is rotated about the x axis with respect to the coordinate system which is fixed to the motorcycle, with the result that the horizontalized lateral acceleration {dot over (y)}.sup.h extends parallel to the roadway), the vehicle velocity v, the yaw rate {dot over (ψ)}.sub.roadway which is fixed to the roadway, the tangent of the effective roll angle λ.sub.th and the gravitational acceleration g:

(25) $\begin{array}{cc}{\stackrel{\mathrm{.Math.}}{y}}^h=v.Math.{\psi }^{\mathrm{roadway}}& \left(3\right)\\ \tan {\lambda }_{\mathrm{th}}=\frac{v.Math.{\stackrel{.}{\psi }}^{\mathrm{roadway}}}{g}& \left(4\right)\end{array}$

(26) Insertion of (2) into (4) provides:

(27) $\begin{array}{cc}\tan {\lambda }_{\mathrm{th}}=\frac{v.Math.{\stackrel{.}{\psi }}^{\mathrm{roadway}}}{g}=\frac{v.Math.{\stackrel{.}{\psi }}^M}{\cos {\lambda }_{\mathrm{ges}}.Math.g}& \left(5\right)\\ \sin {\lambda }_{\mathrm{th}}.Math.\frac{\cos {\lambda }_{\mathrm{ges}}}{\cos {\lambda }_{\mathrm{th}}}=\frac{v.Math.{\psi }^M}{g}& \left(6a\right)\end{array}$

(28) Assuming that λ.sub.ges=λ.sub.th, this can also be simplified to yield:

(29) $\begin{array}{cc}\sin {\lambda }_{\mathrm{th}}\approx \frac{v.Math.{\stackrel{.}{\psi }}^M}{g}& \left(6b\right)\end{array}$

(30) Therefore, the roll angle λ.sub.th is a function f of the product {dot over (ψ)}.sub.M.Math.v of the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle and the velocity v of the motorcycle:

(31) $\begin{array}{cc}f\left({\lambda }_{\mathrm{th}}\right)=\frac{{\stackrel{.}{\psi }}^M.Math.v}{g}& \left(7\right)\end{array}$

(32) The functional relationship f (λ.sub.th) or the above equation (7) cannot be solved in a closed fashion. For this reason, a numerically acquired characteristic curve is used (block 13) in order to determine the roll angle λ.sub.th (according to the exemplary embodiment illustrated in FIG. 2 the roll angle variable λ.sub.2) from the product (block 12) of the yaw rate {dot over (ψ)}.sub.M which is fixed to the motorcycle and the velocity v.

(33) FIG. 3 is a schematic illustration of a second exemplary embodiment of a method according to an aspect of the invention. In this exemplary embodiment also, the integration 10 over time of the rolling rate {dot over (λ)}.sup.M which is fixed to the motorcycle is the first calculation result (the first roll angle variable λ.sub.1), and here too the first roll angle variable λ.sub.1 is filtered, for example, with a high pass filter 11, with, for example, a cut-off frequency f.sub.Trenn of 0.05 Hz. The explanation and alternative ways of calculating the first roll angle variable λ.sub.1 which are given further above within the scope of the first exemplary embodiment apply here correspondingly. In contrast to the first exemplary embodiment, in the second exemplary embodiment the second calculation result (the second roll angle variable λ.sub.2′) is determined essentially from the acceleration, fixed to the motorcycle, in the z direction {umlaut over (z)}.sup.M (block 16). In order to take into account the width of the tire, the second roll angle variable λ.sub.2′ in block 17 can be multiplied by an empirical factor c. In the second exemplary embodiment of the method according to an aspect of the invention, the second calculation result λ.sub.2′ is also filtered with a low pass filter 14′ with, for example, the same cut-off frequency f.sub.Trenn as that of the high pass filter 11, this being for example 0.05 Hz. In order to determine the roll angle λ.sub.E of the motorcycle, the calculation result λ.sub.1 of the integration 10 over time of the rolling rate {dot over (λ)}.sub.M which is fixed to the motorcycle and the calculation result λ.sub.2′ are added to the determination of a roll angle variable from an acceleration, fixed to the motorcycle, in the z direction {umlaut over (z)}.sup.M (block 15′).

(34) The filters 11, 14′ used are customarily first-order PT.sub.1 elements. The cut-off frequency f.sub.Trenn is, for example, in the range from approximately 0.01 Hz to approximately 0.10 Hz.

(35) The calculation of the second roll angle variable λ.sub.2′ from an acceleration which is fixed to the motorcycle in the z direction {umlaut over (z)}.sup.M applies only to steady-state cornering. Furthermore, if the factor c is not taken into account (c=1), it is based on the assumption of ideally narrow tires. Furthermore, the acceleration, fixed to the motorcycle, in the z direction {umlaut over (z)}.sup.M is not subject to a sign, with the result that a further information item, for example the acceleration, fixed to the motorcycle, in the y direction ÿ.sub.M, can be used to define the correct sign of the roll angle λ.

(36) The following explanation serves to substantiate the relationship between the acceleration, fixed to the motorcycle, in the z direction {umlaut over (z)}.sup.M and the roll angle λ:

(37) For steady-state cornering the physically active roll angle λ.sub.th is provided by the arc cosine of the quotient of the gravitational acceleration g with respect to the vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle:

(38) $\begin{array}{cc}{\lambda }_{\mathrm{th}}=\arccos \frac{g}{{\stackrel{\mathrm{.Math.}}{z}}^M}& \left(8\right)\end{array}$

(39) In order to define the correct sign, the lateral acceleration ÿ.sup.M which is fixed to the motorcycle can be used:

(40) $\begin{array}{cc}{\lambda }_{\mathrm{th}}=\arccos \left(.Math.\frac{g}{{\stackrel{\mathrm{.Math.}}{z}}^M}.Math.\right).Math.\left(-1\right).Math.\mathrm{sign}\left({\stackrel{\mathrm{.Math.}}{y}}^M\right)& \left(9\right)\end{array}$

(41) Here, sign(X) is the sign function which has the value “1” if X is greater than zero, which is “0” if X is equal to zero, and which is “−1” if X is less than zero.

(42) As already mentioned above, the total roll angle λ.sub.ges can be approximated by the physically active roll angle λ.sub.th:
λ.sub.ges≈λ.sub.th

(43) For example, the second roll angle variable λ.sub.2′ is determined according to the equation (9) (block 16).

(44) A third exemplary embodiment of a method according to an aspect of the invention is illustrated schematically in FIG. 4. In this exemplary embodiment, the integration 10 over time of the rolling rate {dot over (λ)}.sup.M which is fixed to the motorcycle is also the first calculation result (the first roll angle variable λ.sub.1), and for example the first roll angle variable λ.sub.1 is also filtered here with a high pass filter 11 with, for example, a cut-off frequency f.sub.Trenn of 0.05 Hz. The explanation and alternatives for the calculation of the first roll angle variable λ.sub.1 which are given above within the scope of the first exemplary embodiment apply here correspondingly. In contrast to the first exemplary embodiment, in the third exemplary embodiment the second calculation result (the second roll angle variable λ.sub.2″) is determined from two acceleration values which are fixed to the motorcycle, in particular an acceleration, fixed to the motorcycle, in the z direction {umlaut over (z)}.sup.M and an acceleration, fixed to the motorcycle, in the y direction ÿ.sup.M (block 20). The second calculation result λ.sub.2″ is filtered with a low pass filter 14″ with, for example, the same cut-off frequency f.sub.Trenn as that of the high pass filter 11, this being, for example 0.05 Hz. In order to determine the roll angle λ.sub.E of the motorcycle, the calculation result λ.sub.1 of the integration 10 over time of the rolling rate {dot over (λ)}.sub.M which is fixed to the motorcycle and the calculation result λ.sub.2″ is added to the determination of a roll angle variable from two acceleration values which are fixed to the motorcycle, for example a vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle and a lateral acceleration ÿ.sup.M which is fixed to the motorcycle (block 15″).

(45) The filters 11, 14″ used are customarily first-order PT.sub.1 elements. The cut-off frequency f.sub.Trenn is, for example, in the range from approximately 0.01 Hz to approximately 0.10 Hz.

(46) The calculation of the second roll angle variable λ.sub.2″ from an acceleration, fixed to the motorcycle, in the z direction {umlaut over (z)}.sup.M and an acceleration, fixed to the motorcycle, in the y direction ÿ.sup.M applies only to steady-state cornering. The calculation includes the geometry of the tire and the dynamic tire behavior of the motorcycle.

(47) The following explanation serves to substantiate the relationship between the acceleration, fixed to the motorcycle, in the z direction {umlaut over (z)}.sup.M, the acceleration, fixed to the motorcycle, in the y direction ÿ.sup.M and the roll angle λ:

(48) As already mentioned above, the following relationship applies:
λ.sub.ges=λ.sub.ZS+λ.sub.th  (10)

(49) According to equation (8), for steady-state cornering the physically active roll angle λ.sub.th is provided by the arc cosine of the quotient of the gravitational acceleration g with respect to the vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle:

(50) $\begin{array}{cc}{\lambda }_{\mathrm{th}}=\arccos \left(\frac{g}{{\stackrel{\mathrm{.Math.}}{z}}^M}\right)& \left(11\right)\end{array}$

(51) Furthermore, for steady-state cornering the additional roll angle λ.sub.ZS is given by the arc tangent of the quotient of the lateral acceleration ÿ.sup.M which is fixed to the motorcycle with respect to the vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle:

(52) $\begin{array}{cc}{\lambda }_{\mathrm{ZS}}=\arctan \left(\frac{{\stackrel{\mathrm{.Math.}}{y}}^M}{-{\stackrel{\mathrm{.Math.}}{z}}^M}\right)& \left(12\right)\end{array}$

(53) Insertion of equations (11) and (12) into (10) provides:

(54) $\begin{array}{cc}{\lambda }_{\mathrm{ges}}=\arccos \left(\frac{g}{{\stackrel{\mathrm{.Math.}}{z}}^M}\right)+\arctan \left(\frac{{\stackrel{\mathrm{.Math.}}{y}}^M}{-{\stackrel{\mathrm{.Math.}}{z}}^M}\right)& \left(13\right)\end{array}$

(55) For example, the total roll angle λ.sub.ges is approximated as a multiple k of the additional roll angle λ.sub.ZS which is conditioned by the width of the tire. It is therefore calculated according to the following relationship (block 20):

(56) 0$\begin{array}{cc}{\lambda }_{\mathrm{ges}}=k.Math.\arctan \left(\frac{{\stackrel{\mathrm{.Math.}}{y}}^M}{-{\stackrel{\mathrm{.Math.}}{z}}^M}\right)& \left(14\right)\end{array}$

(57) Here, the factor k is dependent on the geometry of the tire and the dynamic tire behavior of the motorcycle. An exemplary value is k=9.7.

(58) An advantage of the method according to an aspect of the invention is that the roll angle λ.sub.E of the motorcycle is without time delay, apart from the time delays caused by the sensors. The roll angle λ.sub.E can be determined both under steady-state and non-steady-state travel conditions. Furthermore, the accuracy of the roll angle which is determined by a combination of two calculation methods is higher than is possible with an individual measuring method.

(59) The integration of the rolling rate over time is in itself not suitable as a method for acquiring a roll angle. Owing to the measuring error which increases with time, this method cannot be applied directly with a standard sensor system.

(60) A further advantage is that the manufacturing costs of a device for implementing the method according to an aspect of the invention are significantly lower than a highly accurate inertial sensor system, whilst having the same level of accuracy.

(61) Compared to the first exemplary embodiment (FIG. 2) with a determination of the roll angle from two rotational speed signals (rolling rate {dot over (λ)}.sup.M and yaw rate {dot over (ψ)}.sub.M), the manufacturing costs of the device for determining the roll angle according to the second and third exemplary embodiments from the rolling rate {dot over (λ)}.sub.M, and one acceleration valve {umlaut over (z)}.sup.M or two acceleration values {umlaut over (z)}.sup.M, ÿ.sup.M, are considerably reduced. Use of a sensor cluster, which is already known, for example, from the use in electronic stability programs (ESP) in passenger cars, is appropriate. Such a sensor cluster customarily provides a rotational speed signal and one or two acceleration signals. Such a sensor cluster can, if appropriate, be installed rotated through 90 degrees.

(62) If the results of the integration 10 over time of the rolling rate {dot over (λ)}.sub.M which is fixed to the motorcycle and the function 13 of the product 12 of the yaw rate if {dot over (ψ)}.sub.M which is fixed to the motorcycle and the velocity v of the motorcycle (first exemplary embodiment) are combined, it is advantageous that the position of the sensor system on the motorcycle is not relevant since the rotational speeds on the entire vehicle are the same.

(63) An aspect of the invention also relates to a method for determining the roll angle of a motor cycle during travel from the product of the yaw rate {dot over (ψ)}.sub.M which is fixed to the motorcycle and the velocity of the motorcycle. FIG. 5 is a schematic illustration of a corresponding exemplary embodiment. The product is formed from a yaw rate which is fixed to the motorcycle and the velocity v of the motorcycle (block 23). A roll angle variable is determined from the product by means of a functional relationship, which is predefined for example in the form of a characteristic curve (block 24). After the calculation result has been filtered with a low pass filter 25, the roll angle λ.sub.E of the motorcycle is obtained.

(64) The filter 25 is usually a first-order PT.sub.1 element. The cut-off frequency is, for example, in the region of approximately 1 Hz.

(65) According to an exemplary embodiment, not illustrated, a combination of a plurality of filters is used in order to reduce the signal peaks during rapid slalom travel: a low pass filter (cut-off frequency of approximately 0.05 Hz), a high pass filter (cut-off frequency of approximately 0.05 Hz, gain factor of 0.5), addition of the two signals and possibly further filtering with a low pass filter (cut-off frequency of approximately 1 Hz) in order to smooth the signals. According to the above explanations (equations (2) to (7)), the roll angle λ is a function f of the product {dot over (ψ)}.sub.M.Math.v of the yaw rate {dot over (ψ)}.sub.M which is fixed to the motorcycle and the velocity v of the motorcycle (see equation (7)). A numerically acquired characteristic curve is used (block 24) to determine the roll angle λ from the product (block 23) of the yaw rate {dot over (ψ)}.sub.M which is fixed to the motor cycle and the velocity v.

(66) The manufacturing costs of the device for implementing the method (determination of the roll angle from the product of the yaw rate which is fixed to the motorcycle and the velocity) are considerably lower compared to those for a highly accurate inertial sensor system while the accuracy is the same. The position of the sensor system on the motorcycle is not relevant since the rotational speed is the same over the entire vehicle.

(67) Methods for determining a roll angle on the basis of acceleration measurement ({umlaut over (z)}.sup.M or {umlaut over (z)}.sup.M, ÿ.sup.M) and a measurement of the rolling rate {dot over (λ)}.sub.M are described above. The fault tolerance of these methods can be increased by filtering the rolling rate {dot over (λ)}.sub.M with a first-order high pass filter, for example with a cut-off frequency of approximately 0.01 Hz.

(68) An aspect of the invention also relates to a method for checking the plausibility of the measured value of a roll angle-determining algorithm. In order to check the plausibility of the method, the roll angle can be determined for the steady-state travel condition, i.e. the second roll angle variable, redundantly using different methods. For example, a roll angle variable λ.sub.2 and, respectively, λ.sub.2″ can be determined from the yaw rate {dot over (ψ)}.sub.M which is fixed to the motorcycle and the velocity v as well as from the vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle and the lateral acceleration ÿ.sup.M which is fixed to the motorcycle.

(69) Any selection of two or more roll angle-determining methods is conceivable. The trustworthiness of the roll angle λ.sub.E which is determined by means of the roll angle variable or variables can be estimated by comparing the results.

(70) Furthermore, under certain circumstances a sensor fault can be detected by the plausibility checking/the comparison. If there is a considerable difference between the roll angle variables λ.sub.2, λ.sub.2′, λ.sub.2″ which are determined in a variety of ways it is possible to infer a malfunction of one of the acceleration sensors or rotational speed sensors.

(71) If the acceleration sensors which are present measure constant values over a specific time period, the rolling rate {dot over (λ)}.sub.M must be zero in this time period. An offset of the rolling rate sensor can therefore be determined and compensated.

(72) Between any two travel conditions with a roll angle of zero degrees, the integral of the rolling rate {dot over (λ)}.sub.M is zero degrees. Given a known offset of the rolling rate sensor, the linearity fault of the rolling rate sensor can be determined by means of this condition.

(73) Systems which are critical in terms of safety require information about the reliability of the roll angle signal. This reliability can be determined on the basis of the described method for the purpose of plausibility checking.

(74) A traveling motorcycle must always be in a position of equilibrium. This is necessary both for straight-ahead travel and for cornering. The position of equilibrium of the motorcycle is dependent on a large number of different factors, for example the vehicle velocity v, the coefficient of friction between the tire and roadway, the wheel speeds ω.sub.I (i=1 or 2 for the front wheel or rear wheel), the engine speed, the steering angle, the vehicle load, the inclination of the roadway, etc. These factors influence the equilibrium values for the rolling rate {dot over (λ)}.sub.M, the yaw rate {dot over (ψ)}.sub.M and the three components of the vehicle acceleration {umlaut over (x)}.sup.M, ÿ.sup.M and {umlaut over (z)}.sup.M.

(75) FIG. 6 is a schematic illustration of a fourth exemplary embodiment of a method according to an aspect of the invention. The algorithm according to the example for the calculation 26 of the roll angle λ.sub.E is based on the measurements of the values for the yaw rate {dot over (ψ)}.sub.M, the rolling rate {dot over (λ)}.sub.M, the acceleration, fixed to the motorcycle, in the {umlaut over (z)}.sup.M direction and the acceleration, fixed to the motorcycle, in the y direction ÿ.sup.M with corresponding sensors. In order to ensure a high level of accuracy, the algorithm must change adaptively as a function of the travel situation. In order to make this possible, it is necessary also to use the information from a plurality of vehicle systems (vehicle sensors), to estimate the current travel situation and to adapt the algorithm for the calculation 26 of the roll angle λ.sub.E in accordance with the travel situation. For this purpose, in block 27 the current travel situation is estimated on the basis of one or more of the following variables: engine speed, engine torque, steering angle, vehicle velocity v, vehicle acceleration, wheel speeds ω.sub.i, state of the roadway, wheel slip, vehicle load, inclination of the roadway. This estimation is then included in the calculation 26 of the roll angle λ.sub.E.

(76) It is also necessary to take into account the fact that the theoretical roll angle λ.sub.th and the total roll angle λ.sub.ges differ since the width of the tire is not equal to zero.

(77) FIG. 7 is a schematic illustration of an exemplary method for adaptively calculating a roll angle λ.sub.E. In order to ensure a high degree of accuracy, a combination of various methods is used to calculate the roll angle λ.sub.E. At the same time, measurements of the rolling rate {dot over (λ)}.sub.M, of the yaw rate {dot over (ψ)}.sub.M and of the accelerations in the z and y direction {umlaut over (z)}.sup.M, ÿ.sup.M are carried out, for example with a sensor cluster. The integral 30 of the rolling rate {dot over (λ)}.sub.M is formed, and the result λ.sub.1 is filtered with a high pass filter 31. Furthermore, in block 32 the arc tangent of the quotient of the acceleration in the y direction ÿ.sup.M is calculated with respect to the acceleration in the z direction {umlaut over (z)}.sup.M, and the result λ.sub.2.sup.1 is filtered with a low pass filter 33. Likewise, in block 34 the arc tangent of the quotient of the product of the yaw rate {dot over (ψ)}.sub.M times the vehicle acceleration v is calculated to form the acceleration in the z direction {umlaut over (z)}.sup.M, and the result λ.sub.2.sup.2 is filtered with a low pass filter 35. The three results are multiplied by corresponding weighting parameters P1, P2 and P3 (blocks 36) and summed (block 37).

(78) Properties of the system (for example filter properties) such as, for example, the cut-off frequencies of the individual filters 31, 33, 35 and/or the weighting parameters P1, P2, P3 are changed as a function of the current travel situation 27 which is detected by means of at least one of the abovementioned variables, for example the vehicle velocity v, wheel slip, wheel speeds ω.sub.i, engine speeds, steering angle, vehicle load, inclination of the roadway, rolling rate {dot over (λ)}.sub.M, yaw raw {dot over (ψ)}.sub.M, roll angle acceleration, yaw angle acceleration, and roll angle λ.sub.E (previously calculated, for example). The dependence of the system properties, for example the dependence of the cut-off frequencies of the filters and the dependence of the weighting parameters P1, P2, P3, on these variables are determined empirically or theoretically, stored in a control unit in the form of characteristic curves or characteristic diagrams or calculation rules and taken into account in the calculation of the roll angle. The system can be adapted for any travel situation and the roll angle λ.sub.E of the vehicle can be determined accurately by automatically changing the parameters (on the basis of the stored characteristic curves, characteristic diagrams or calculation algorithms).

(79) FIG. 8 is a schematic illustration of an exemplary method for adaptive determining a roll angle λ.sub.E. In order to ensure high degree of accuracy, a combination of various methods is used to calculate the roll angle λ.sub.E.

(80) The roll angle λ.sub.E is determined based on a first roll angle variable λ.sub.1 and based on a second roll angle variable λ.sub.2.

(81) Subsequently an exemplary method for determining the roll angle λ.sub.E based on the first and the second roll angle variables λ.sub.1, λ.sub.2 will be described. The method takes place in a frequency domain.

(82) A first high-pass filter 83 filters the first roll angle variable λ.sub.1 with a first cutoff frequency, which results in a filtered first roll angle variable λ.sub.11. A second high-pass filter 86 filters the first roll angle variable λ.sub.1 with a second cutoff frequency, which results in a filtered second roll angle variable λ.sub.12.

(83) A first low-pass filter 84 filters the second roll angle variable λ.sub.2 with a first cutoff frequency, which results in a filtered third roll angle variable λ.sub.21. A second low-pass filter 85 filters the second roll angle variable λ.sub.2 with a second cutoff frequency, which results in a filtered fourth roll angle variable λ.sub.22 Arcus sinus function 92 is executed before the low pass filters 84, 85.

(84) A first combination 89 combines the filtered first roll angle variable λ.sub.11 and the filtered third roll angle variable λ.sub.21 which results in a first combined roll angle variable λ.sub.a.

(85) A second combination 90 combines the filtered second roll angle variable λ.sub.12 and the filtered fourth roll angle variable λ.sub.22 which results in a second combined roll angle variable λ.sub.b.

(86) A third high-pass-filter 87 filters the first combined roll angle variable λ.sub.a with a third cutoff frequency. A third low-pass filter 88 filters the second combined roll angle variable λ.sub.b with a third cutoff frequency.

(87) The first cutoff frequency is lower than the third cutoff frequency and the third cutoff frequency is lower than the second cutoff frequency.

(88) A third combination 91 combines the filtered first combined roll angle variable λ.sub.a′ and the filtered second combined roll angle variable λ.sub.b′, which results in the roll angle λ.sub.E.

(89) Particularly the combination takes place in a frequency domain and the amplitudes are added.

(90) Due to an offset error of the roll rate sensor, an integration obtaining the first roll angle variable λ.sub.1 will result in a ramp function, why an overflow will appear at some point in the integrator 93. In order to circumvent such an overflow the integrator 93 will be resetted, as soon as the output value of the integrator 93 reaches a certain positive, respectively negative threshold. Particularly, when resetting, the certain positive, respectively negative threshold may be subtracted, respectively added, to the output value. A jump in the output value due to the reset or an overflow of the integrator 93 may usually be propagated to the first high-pass filter 83 and to the second high-pass filter 86 and be detectable at the output of the first high-pass filter 83 and at the output of the second high-pass filter 86. In order to circumvent the detectable jump in the output of the first high-pass filter 83 and in the output of the second high-pass filter 86, both high-pass filter 83, 86 may be resetted at the same time as the integrator 93. To do so both high-pass filters 83, 86 may be synchronized with the integrator 93. Particularly all previous stored input states of the integrator 93, the first high-pass filter 83 and the second high-pass filter 86 are resetted to zero. Particularly all previous stored output states of the integrator 93, the first high-pass filter 83 and the second high-pass filter 86 are resetted to zero.

(91) Due to synchronized resetting the integrator 93 and the first and the second high-pass filter 83, 86 an overflow, particularly an overflow of the integrator 93, does not affect the output of the first and/or the second high-pass filter 83, 86.

(92) In the exemplary method the low-pass filters comprise an arcsin-function. The arcsin functions are applied on the signals filtered by the low pass filters having very low cut-off frequencies to avoid clipping due to the high noise coming from the low dynamic method, which is shown in FIG. 10. Apart from this the combination method shown in FIG. 10 corresponds to the combination method shown in FIG. 8.

(93) There is a cross effect between angular rates due to inclinations of the measurement system. For example, if a pitch angle α of the motorcycle does not equal zero, the yaw rate sensor measures a portion of the roll rate {dot over (λ)}.sub.roadway which is fixed to the roadway and vice versa the roll rate sensor measures a portion of the yaw rate {dot over (ψ)}.sub.roadway which is fixed to the roadway. This is particularly the case when the motorcycle moves on a circular path. This cross effect can be eliminated based on inertial measurement. Particularly the pitch angle α is not zero, because the sensor cluster is not mounted horizontally on the motorcycle with regard to the roadway 1 and/or because of heavy weight on the motorcycle causing the rear suspension to be pushed down.

(94) Algorithm 81 corrects the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle by eliminating the erroneous roll rate portion {dot over ({tilde over (λ)})}.sup.roadway. The erroneous roll rate portion {dot over ({tilde over (λ)})}.sup.roadway corresponds to this cross effect.

(95) Algorithm 97 (a multiplication) determines the roll angle on the basis of the corrected yaw rate (algorithm 81) and the velocity (corresponding to block 23 of FIG. 5).

(96) Algorithm 82 corrects the roll rate {dot over (λ)}.sup.M which is fixed to the motorcycle by eliminating the erroneous yaw rate portion {dot over ({tilde over (ψ)})}.sup.roadway. The erroneous yaw rate portion {dot over ({tilde over (ψ)})}.sup.roadway corresponds to this cross effect.

(97) In order to eliminate these cross effects the pitch angle α has to be estimated.

(98) Algorithm 81 and algorithm 82 estimate the pitch angle α based on longitudinal acceleration {umlaut over (x)}.sup.M which is fixed to the motorcycle and/or based on vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle and/or based on the overall acceleration of the motorcycle {dot over (ν)} and/or based on the gravity g. Alternatively solely one of these algorithms estimates the pitch angle α and the other algorithm is provided with the estimated pitch angle α.

(99) FIG. 9 exemplary, schematically illustrates at least the relation of longitudinal acceleration {umlaut over (x)}.sup.M which is fixed to the motorcycle, overall acceleration of the motorcycle {dot over (ν)}, the vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle and pitch angle α.

(100) The longitudinal acceleration sensor measures a longitudinal acceleration {umlaut over (x)}.sup.M which is fixed to the motorcycle. The longitudinal acceleration {umlaut over (x)}.sup.M results from a gravity portion {umlaut over (x)}.sub.1 influencing the longitudinal acceleration measurement depending on the pitch angle α and from an overall acceleration portion of the motorcycle {umlaut over (x)}.sub.2 influencing the longitudinal acceleration measurement depending on the pitch angle α:
{umlaut over (x)}.sup.M={umlaut over (x)}.sub.1+{umlaut over (x)}.sub.2  (15)

(101) The vertical acceleration sensor measures a vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle. The vertical acceleration {umlaut over (z)}.sup.M results from a gravity portion {umlaut over (z)}.sub.1 influencing the vertical acceleration measurement depending on the pitch angle α and from an overall acceleration portion of the motorcycle {umlaut over (z)}.sub.2 influencing the vertical acceleration measurement depending on the pitch angle α:
{umlaut over (z)}.sup.M={umlaut over (z)}.sub.1+{umlaut over (z)}.sub.2  (15)

(102) According to the following approach the calculation of pitch angle α can be deduced:

(103) $\begin{array}{cc}\frac{{\stackrel{\mathrm{.Math.}}{x}}^M}{{\stackrel{\mathrm{.Math.}}{z}}^M}=\frac{g*\sin \alpha -\stackrel{.}{v}*\cos \alpha }{g*\cos \alpha +\stackrel{.}{v}*\sin \alpha }& \left(15a\right)\\ {\stackrel{\mathrm{.Math.}}{x}}^M\left(g*\cos \alpha +\stackrel{.}{v}*\sin \alpha \right)={\stackrel{\mathrm{.Math.}}{z}}^M\left(g*\sin \alpha -\stackrel{.}{v}*\cos \alpha \right).Math.\frac{1}{\cos \alpha }& \left(15b\right)\\ {\stackrel{\mathrm{.Math.}}{x}}^{M}g+{\stackrel{\mathrm{.Math.}}{x}}^M\stackrel{.}{v}\tan \alpha ={\stackrel{\mathrm{.Math.}}{z}}^{M}g\tan \alpha -{\stackrel{\mathrm{.Math.}}{z}}^M\stackrel{.}{v}& \left(15c\right)\\ {\stackrel{\mathrm{.Math.}}{x}}^{M}g+{\stackrel{\mathrm{.Math.}}{z}}^M\stackrel{.}{v}=\tan \alpha \left({\stackrel{\mathrm{.Math.}}{z}}^{M}g-{\stackrel{\mathrm{.Math.}}{x}}^M\stackrel{.}{v}\right)& \left(16\right)\\ \alpha ={\tan }^{-1}\left(\frac{{\stackrel{\mathrm{.Math.}}{x}}^{M}g+{\stackrel{\mathrm{.Math.}}{z}}^M\stackrel{.}{v}}{{\stackrel{\mathrm{.Math.}}{z}}^{m}g-{\stackrel{\mathrm{.Math.}}{x}}^M\stackrel{.}{v}}\right)\approx \left(\frac{{\stackrel{\mathrm{.Math.}}{x}}^{M}g+{\stackrel{\mathrm{.Math.}}{z}}^M\stackrel{.}{v}}{{\stackrel{\mathrm{.Math.}}{z}}^{M}g-{\stackrel{\mathrm{.Math.}}{x}}^M\stackrel{.}{v}}\right)& \left(17\right)\end{array}$

(104) Consequently the pitch angle α is obtainable based on longitudinal acceleration {umlaut over (x)}.sup.M which is fixed to the motorcycle and based on vertical acceleration {umlaut over (z)}.sup.M which is fixed to the motorcycle and based on the overall acceleration of the motorcycle {dot over (ν)} and based on the gravity g, particularly according to formula 17. More particularly preferred the arctan function can be neglected.

(105) Algorithm 81 determines corrected yaw rate {dot over (ψ)}.sup.roadway which is fixed to the roadway. The erroneous roll rate portion {dot over ({tilde over (λ)})}.sup.roadway is determined by multiplying the roll rate {dot over (λ)}.sup.M which is fixed to the motorcycle with the pitch angle α. Particularly the erroneous roll rate portion {dot over ({tilde over (λ)})}.sup.roadway is determined by multiplying the roll rate {dot over (λ)}.sup.M with the sinus of the pitch angle α. The corrected yaw rate {dot over (ψ)}.sup.roadway may particularly be determined by subtracting the erroneous roll rate portion {dot over ({tilde over (ψ)})}.sup.roadway from the yaw rate {dot over (ψ)}.sup.M:
{dot over ({tilde over (λ)})}.sup.roadway={dot over (λ)}.sup.M*sin(α)  (18)
{dot over (ψ)}={dot over (ψ)}.sup.M_{dot over ({tilde over (λ)})}.sup.roadway  (19)

(106) Algorithm 82 determines corrected roll rate {dot over (λ)}.sup.roadway which is fixed to the roadway. The erroneous yaw rate portion {dot over ({tilde over (ψ)})}.sup.roadway is determined by multiplying the yaw rate {dot over (ψ)}.sup.M which is fixed to the motorcycle with the pitch angle α. Particularly the erroneous yaw rate portion {dot over ({tilde over (ψ)})}.sup.roadway is determined by multiplying the yaw rate {dot over (ψ)}.sup.M with the sinus of the pitch angle α. Particularly preferred during high dynamic rolling and/or always a corrected erroneous yaw rate portion {dot over ({tilde over ({tilde over (ψ)})})}.sup.roadway is determined by dividing the erroneous yaw rate portion {dot over ({tilde over (ψ)})}.sup.roadway by the squared roll rate ({dot over (λ)}.sup.M).sup.2. The corrected roll rate {dot over (λ)}.sup.roadway can particularly be determined by subtracting the erroneous yaw rate portion {dot over ({tilde over (ψ)})}.sup.roadway or the corrected erroneous yaw rate portion {dot over ({tilde over ({tilde over (ψ)})})}.sup.roadway from the roll rate {dot over (λ)}.sup.M:

(107) $\begin{array}{cc}{\stackrel{\widetilde{.}}{\psi }}^{\mathrm{roadway}}={\stackrel{.}{\psi }}^M.Math.\sin \left(\alpha \right)& \left(20\right)\\ {\stackrel{\stackrel{\widetilde{~}}{.}}{\psi }}^{\mathrm{roadway}}=\frac{{\stackrel{\widetilde{.}}{\psi }}^{\mathrm{roadway}}}{{\left({\stackrel{.}{\lambda }}^M\right)}^2}& \left(21\right)\\ {\stackrel{.}{\lambda }}^{\mathrm{roadway}}={\stackrel{.}{\lambda }}^M-{\stackrel{\widetilde{.}}{\psi }}^{\mathrm{roadway}}& \left(22\right)\\ {\stackrel{.}{\lambda }}^{\mathrm{roadway}}={\stackrel{.}{\lambda }}^M-{\stackrel{\stackrel{\widetilde{~}}{.}}{\psi }}^{\mathrm{roadway}}& \left(23\right)\end{array}$

(108) In the following a compensation method is described for the second method determining the second roll angle variable λ.sub.2 in order to increase the precision of the calculation based on vertical centrifugal acceleration. Thereby algorithm 94 estimates a centrifugal force f.sub.rad. The centrifugal force is proportional to the squared roll rate {dot over (λ)}.sup.M multiplied with a radius r.sub.COG. The center of gravity of the motorcycle moves on the circumference of a circle, of which the radius r.sub.COG is the distance between the tire contact point on the ground and the center of gravity.
f.sub.rad˜{dot over (λ)}.sup.M.sup.2*r.sub.COG  (24)

(109) If the center of gravity of the motorcycle is on the vertical axis of the motorcycle this mentioned force is only measured by the vertical acceleration sensor.

(110) Due to body leaning the center of gravity can shift with regard to the vertical axis of the motorcycle. In this case the centrifugal force f.sub.rad is partly measured by the lateral acceleration sensor, which has to be compensated.
{umlaut over ({tilde over (y)})}=ÿ.sup.M−({umlaut over (z)}.sup.M−f.sub.rad)  (25)

(111) Based on the estimated centrifugal force f.sub.rad, on the lateral acceleration ÿ.sup.M and on the vertical acceleration {umlaut over (z)}.sup.M a centrifugal compensation takes place in algorithm 98 according to e.g. formula 25.

(112) In the following a compensation method is described for the second method determining the second roll angle variable λ.sub.2 in order to increase the precision of the calculation based on the common effect of the lateral acceleration and the roll rate. Algorithm 95 estimates a rapid leaning force f.sub.rap_leaning. The rapid leaning force f.sub.rap_leaning is proportional to the derivative of the roll rate {umlaut over (λ)}.sup.M and the distance between the tire contact point on the ground and the mounting location of the lateral acceleration sensor r.sub.sensor.

(113) Based on the estimated rapid leaning force f.sub.rap_leaning and on the lateral acceleration ÿ.sup.M a rapid leaning compensation takes place in algorithm 98 according to e.g. formula 27. Thereby the common effect of the lateral acceleration and the roll rate is compensated.
f.sub.rap_leaning˜{umlaut over (λ)}.sup.M*T.sub.sensor  (26)
{umlaut over ({tilde over (y)})}.sup.M=ÿ.sup.M−(f.sub.rap_leaning)  (27)

(114) In the following a compensation method is described for the second method determining the second roll angle variable λ.sub.2 in order to increase the precision of the calculation by compensating the difference between the total roll angle λ.sub.ges and the physically active roll angle λ.sub.th. Algorithm 96 estimates a tire profile compensation value. Thereby the gravity g is eliminated in the vertical acceleration {umlaut over (z)}.sup.M. This result is multiplied by the yaw rate ψ.sup.M.

(115) Based on the estimated tire profile compensation value and on the lateral acceleration ÿ.sup.M a tire profile compensation takes place in algorithm 98 according to e.g. formula 28.
{umlaut over ({tilde over (y)})}.sup.M=ÿ.sup.M−({umlaut over (z)}.sup.M−g)*ψ.sup.M  (28)

(116) Algorithm 98 determines the second roll angle variable λ.sub.2 using the second method. Particularly at least one of the previously described compensation methods are applied, wherein the corrected lateral acceleration {umlaut over ({tilde over (y)})}.sup.M can be used for determining the second roll angle variable λ.sub.2.

(117) Particularly the corrected yaw rate {dot over (ψ)}.sup.roadway which is fixed to the roadway and the corrected roll rate {dot over (λ)}.sup.roadway which is fixed to the roadway are applied for determining the first λ.sub.1 and/or the second λ.sub.2 roll angle variable.

(118) Alternatively an aspect of the invention can be described as follows.

(119) Particularly the method to determine the roll angle of a motorcycle is using inertial measurement signals: a. Yaw rate b. Roll rate c. Longitudinal-, lateral- and vertical-acceleration d. Vehicle velocity

(120) Preferably cross effects between angular rates due to the inclinations of the measurement system are eliminated based on the inertial measurement.

(121) Preferably the motorcycle roll angle is calculated as a combination of roll angles calculated by methods providing roll angle values with different properties.

(122) Preferably the combination is calculated by multiple levels of filtering and summing in order to improve noise cancellation and to reduce offset effects.

(123) Preferably one of the roll angle calculation methods is using a special resettable integrator together with a specially prepared high-pass filter to eliminate roll-rate offset effects.

(124) Preferably one of the roll angle calculation methods is using a compensation method to increase the precision of the calculation based on the vertical centrifugal acceleration.

(125) Preferably one of the roll angle calculation methods is using a compensation method to increase the precision of the calculation based on the common effect of the lateral acceleration and the roll rate.