METHOD OF COMPENSATING FOR SENSOR TOLERANCES

Abstract

A method for compensating sensor tolerances of accelerometers of a vehicle. The method includes following steps: recording of measurement signals of at least three similarly oriented accelerometers, calculation of an acceleration (a.sub.b,z) at a reference position in the spatial direction, which corresponds to the orientation of the accelerometers, low-pass filtering of the measurement signals, determination of tolerance parameters (c.sub.x, c.sub.y, c.sub.z) of each sensor via an optimization method with the aid of the calculated acceleration (a.sub.b,z) at the reference position, and calculation of the adjusted measurement signals from the recorded measurement signals and the tolerance parameters (c.sub.x, c.sub.y, c.sub.z).

Claims

1. A method of compensating for sensor tolerances of accelerometers of a vehicle, said method comprising the following steps: (A) recording measurement signals of at least three similarly oriented accelerometers, (B) calculating an acceleration (a.sub.b,z) at a reference position in a spatial direction corresponding to the orientation of the accelerometers, (C) low-pass filtering the measurement signals, (D) determining tolerance parameters (c.sub.x, c.sub.y, c.sub.z) of each accelerometer via an optimization method with the aid of the calculated acceleration (a.sub.b,z) at the reference position, and (E) calculating adjusted measurement signals from the recorded measurement signals and the tolerance parameters.

2. The method according to claim 1, wherein each of the tolerance parameters (c.sub.x, c.sub.y, c.sub.z) corresponds to one of the tolerances of one of the accelerometers in a spatial direction.

3. The method according to claim 1, wherein the rigid body movement of the vehicle structure is used in order to determine the tolerance parameters (c.sub.x, c.sub.y, c.sub.z).

4. The method according to claim 1, wherein, to calculate the acceleration (a.sub.b,z) at the reference position, a yawing rate (ω.sub.z) at the reference position is measured by a sensor.

5. The method according to claim 1, further comprising using a least-squares-fault method in order to determine the tolerance parameters (c.sub.x, c.sub.y, c.sub.z).

6. A computer program product comprising instructions that, when executed by a computer, cause the computer to perform a method of compensating for sensor tolerances of accelerometers of a vehicle, the method comprising the steps of: (A) recording measurement signals of at least three similarly oriented accelerometers, (B) calculating an acceleration (a.sub.b,z) at a reference position in a spatial direction corresponding to the orientation of the accelerometers, (C) low-pass filtering the measurement signals, (D) determining tolerance parameters (c.sub.x, c.sub.y, c.sub.z) of each accelerometer via an optimization method with the aid of the calculated acceleration (a.sub.b,z) at the reference position, and (E) calculating adjusted measurement signals from the recorded measurement signals and the tolerance parameters.

7. A vehicle comprising the computer program product of claim 6.

Description

BRIEF DESCRIPTION OF THE DRAWING

[0019] FIG. 1 shows a flow chart of the method according to aspects of the invention.

[0020] As explained above in further detail, the measurement signals of the accelerometers are first detected. Subsequently, the acceleration is calculated at a specified and accurately known reference position, and the detected measurement signals are low-pass filtered. The obtained data is used in order to determine tolerance parameters. The tolerance parameters are then used in order to calculate adjusted measurement signals.

DETAILED DESCRIPTION OF THE INVENTION

[0021] An embodiment of the method according to aspects of the invention is described in further detail below. The subject addressed here is the compensation of the sensor tolerances of accelerometers, which are provided in order to record a vertical acceleration of the vehicle. It should be noted that, in principle, the method is also suitable analogously for compensating accelerometers in the longitudinal or transverse direction to the vehicle.

[0022] As already described above, in addition to the vertical component of a vehicle acceleration to be detected, accelerometers (sensors) a.sub.S,z also record components of the transverse acceleration a.sub.S,y and the longitudinal acceleration a.sub.S,x of the vehicle, respectively. As described, this is attributable to measurement tolerances and installation tolerances of the sensor. Thus, taking into account a linearization allowable for small angles, the measured acceleration of a sensor a.sub.S can be expressed as follows:

a.sub.S≈a.sub.S,xc.sub.x+a.sub.S,yc.sub.y+c.sub.z+a.sub.S,z

[0023] The factors c.sub.x and c.sub.y and the offset c.sub.x of the vertical acceleration result from the tolerances (tolerance parameters). The longitudinal and transverse acceleration at the sensor position a.sub.S,x and a.sub.S,y can be calculated from the rigid body movement of the vehicle structure.

a.sub.S,x≈a.sub.b,x−{dot over (ω)}.sub.b,zr.sub.y−ω.sub.z.sup.2r.sub.x

a.sub.S,y≈a.sub.b,y−{dot over (ω)}.sub.b,zr.sub.x−ω.sub.z.sup.2r.sub.y

[0024] Here, a.sub.b, represents the longitudinal acceleration at the reference position, a.sub.b,y represents the transverse acceleration at the reference position, {dot over (ω)}.sub.b,z represents the yawing acceleration, and ω.sub.z represents the yawing rate of the structure. The distances from the reference position to the sensor position are provided as r.sub.x, r.sub.y in the equations. The yawing rate ω.sub.z can be measured by a corresponding sensor, and the yawing acceleration {dot over (ω)}.sub.b,z can be derived from the yawing rate. Disregarding the acceleration portions dependent on the rotation rates, the vertical acceleration at the sensor position a.sub.S,z results according to

[00001]$a_{S,z}\approx \left[\begin{array}{ccc}1& r_{S,y}& -r_{S,x}\end{array}\right]\left(\begin{array}{c}{a}_{b,z}\\ {\dot{\omega }}_{b,x}\\ {\dot{\omega }}_{b,y}\end{array}\right)$

from the vertical acceleration at the reference position a.sub.b,z, the rolling acceleration at the reference position {dot over (ω)}.sub.b,x, the pitching acceleration at the reference position {dot over (ω)}.sub.b,y, and the distances r.sub.S,x, and r.sub.S,y between the sensor position and the reference position.

[0025] By converting the above equation, the rolling, pitching, and vertical acceleration at the reference position can be calculated by adding the measurement results of the vertical accelerations of the three sensors.

[00002]$\left(\begin{array}{c}{a}_{b,z}\\ {\dot{\omega }}_{b,x}\\ {\dot{\omega }}_{b,y}\end{array}\right)={\left(H^{T}H\right)}^{-1}{H}^T\left(\begin{array}{c}{a}_{S1,z}\\ a_{S2,z}\\ a_{S3,z}\end{array}\right)$

[0026] The matrix H must be formulated as follows:

[00003]$H=\left[\begin{array}{ccc}1& r_{S1,y}& -r_{S1,x}\\ 1& r_{S2,y}& -r_{S2,x}\\ 1& r_{S3,y}& -r_{S3,x}\end{array}\right]$

[0027] In stationary driving maneuvers, the rolling acceleration {dot over (ω)}.sub.b,x and pitching acceleration {dot over (ω)}.sub.b,y are equal to zero. Accordingly, the vertical accelerations at the various sensor positions a.sub.Si,z correspond to the vertical acceleration at the reference position a.sub.b,Z. Thus, in stationary driving maneuvers, for the part of the acceleration Δa.sub.S,z that is dependent on the tolerances of the sensors, the following can be formulated.

Δa.sub.S,z=a.sub.S,z −a.sub.b,z=a.sub.S,xc.sub.x+a.sub.S,yc.sub.y+c.sub.z

[0028] In corresponding driving maneuvers, the signal content of the measurement signals of the sensors contains low-frequency portions corresponding to the portions of the stationary driving maneuver (stationary portions) as well as high-frequency portions, which [are] attributable to the rolling and pitching acceleration. Thus, by low-pass filtering, the signal content can be limited to the stationary portions. Thus, the tolerance parameters c.sub.x, c.sub.y, and c.sub.z can be identified from different maneuvers using the least-squares-fault method. For the signal values of m time points, the correlation in matrix notation can be given as follows.

[00004]$\underset{\Delta {\stackrel{.fwdarw.}{a}}_{\left[1,m\right]}}{\underbrace{\left(\begin{array}{c}\Delta a\left[0\right]\\ .Math.\\ \Delta a\left[m\right]\end{array}\right)}}=\underset{R_{\left[1,m\right]}}{\underbrace{\left[\begin{array}{ccc}{a}_{S,x}\left[1\right]& a_{S,y}\left[1\right]& 1\\ .Math.& .Math.& .Math.\\ a_{S,x}\left[m\right]& a_{S,y}\left[m\right]& 1\end{array}\right]}}\underset{\Delta {\stackrel{.fwdarw.}{c}}_{\left[1,m\right]}}{\underbrace{\left(\begin{array}{c}{c}_x\\ c_y\\ c_z\end{array}\right)}}$

[0029] The index [1,m] indicates that the values of the first to the m-th signal sampling are considered in the matrix. If the product of the matrix R is invertable with its transposes, the parameters can be determined according to

[00005]${\stackrel{.fwdarw.}{c}}_{\left[1,m\right]}=\underset{L_{\left[1,m\right]}}{\underbrace{{\left(R_{\left[1,m\right]}^T{R}_{\left[1,m\right]}\right)}^{-1}}}\underset{P_{\left[1,m\right]}}{\underbrace{R_{\left[1,m\right]}^T\Delta a_{\left[1,m\right]}}}$

[0030] The matrix L and vector p can be easily renewed and extended by the appropriate value with a new sampling at the time m+1.

L.sub.[1,m+1]=L.sub.[1,m]+R.sub.[m+1,m+1].sup.TR.sub.[m+1,m+1]

p.sub.[1,m+1]=p.sub.[1,m]+R.sub.[m+1,m+1].sup.TΔ{right arrow over (a)}.sub.[1,m+1]

[0031] Due to external influences, for example temperature changes, changes in the travel situation, or mechanical influences, for example a slight change in the sensor position due to a potentially unwanted contact of the sensor during service, it is advantageous for more recent measurement signals to have a greater importance for the calculation than older ones. To increase the weighting of more recent measured values versus that of older readings, an update factor f.sub.u can be introduced, thereby changing the equations as follows.

L.sub.[m+1]*=(1−f.sub.u)L.sub.[m]*+f.sub.uL.sub.[m+1,m+1 ]

p.sub.[m+1]*=(1−f.sub.u)p.sub.[m]*+f.sub.up.sub.[m+1,m+1 ]

[0032] This results in a recursive correlation for L* and p*, with which the tolerance parameters c* for the weighted sampling can be calculated.

c.sub.[m]*=L.sub.[m]*.sup.−1p.sub.[m]*

[0033] Finally, initial parameters for the calculation must be defined. For this purpose, for example for L.sub.[m]* , the unit matrix I can be selected and specified for p.sub.[0]*=c.sub.[0]*. It is disadvantageous, however, that the measurement of the driving dynamics would initially contain a large deviation until, through a sufficiently large recording of measured values, more realistic values are recorded while passing through various driving maneuvers.

[0034] Another alternative first allows the method to run in the background without allowing the compensation to be directly incorporated into the measurement of the driving dynamics. Here, values can be recorded and incorporated into the system of equations of the compensation, wherein it is checked whether the system of equations can be solved for the measured values. If sufficient measured values have been recorded for which the system of equations can be solved, p.sub.[0]* and L.sub.[m]* can be calculated on the basis of the available values, and the compensation of the measured value recording can be started.