DE102018123092A1 - Method for determining a lateral speed and a yaw rate for a self-movement of a motor vehicle - Google Patents

Abstract

The invention relates to a method for determining a lateral speed (V) and a yaw rate (θ̇) for a self-movement of a motor vehicle. For this purpose, a steering angle (δ) of the front axle, a steering angle of the rear axle (δ), a rotational speed for the front axle (RPS) and for the rear axle (RPS), a lateral measured acceleration (a) and a measured yaw rate (θ̇) are recorded . Predicted values for the angle-based parameters, a predicted lateral speed and a predicted yaw rate are calculated from these variables using a prediction model (PM). A fusion model (FM) calculates fused values for the angle-based parameters, for the fused lateral velocity and for the fused yaw rate. The merged values calculated in the fusion model (FM) can either be returned as start values for the prediction model (PM) and / or the fused values of the fusion model (FM) can be used as result values for determining the own movement of the motor vehicle.

Description

The present invention relates to a method for determining a lateral speed and a yaw rate for self-movement of a motor vehicle with a front axle and a rear axle. This invention further relates to a sensor system for a motor vehicle with a sensor device for determining a lateral speed and a yaw rate for a self-movement of the motor vehicle.

So far, no solutions for odometry calculation with high accuracy and stability based on simple conventional basic sensors are known. Existing alternative solutions are mostly based on very expensive or complex sensors which are arranged on a vehicle. Such sensors are, for example, differential GPS (dGPS) or lidar sensors.

The publication WO 2014/146821 A1 relates to a method for determining a current circumference of a wheel of a motor vehicle. A yaw rate sensor of the motor vehicle is detected by means of a yaw rate sensor and the current extent of at least one wheel is determined as a function of the yaw rate and at least one geometry parameter of the vehicle. To determine the circumference, a steering angle of the motor vehicle is recorded during cornering and a curve radius of the corner traveled is determined as a function of a steering angle and of the at least one geometry parameter of the vehicle.

The disclosure DE 10 2006 020 490 A1 relates to a method and a device for determining the circumference of vehicle wheels. The exact circumference of a first wheel of the vehicle is determined as a function of a yaw rate of the vehicle, a first rotational speed of the first wheel, a second rotational speed of the second wheel and a track width between the first wheel and the second wheel.

The publication US 8,326,480 B2 describes a method and a device for monitoring a stator of a tire. For this purpose, an analysis value is used, which is determined from the rotational speeds of the wheels. The analysis value describes in particular an absolute rolling circumference of a tire. In particular, a dynamic tire radius is determined. This dynamic tire radius is determined by evaluating the number of revolutions of the wheels and a signal from at least one further sensor which is designed to determine the speed of the vehicle against a surface.

The object of the invention is to provide a method which enables the calculation of a lateral speed and a yaw rate for a self-movement of the motor vehicle with simple basic sensors. Measured values of an acceleration sensor and a yaw rate sensor should be taken into account for calculating the lateral speed and the yaw rate.

This object is achieved in accordance with the independent patent claims. Useful further training results from the subclaims.

The invention provides a method for determining a lateral speed and a yaw rate for a self-movement of a motor vehicle with a front axle and a rear axle. This process is characterized by the following process steps. In a first step a), a steering angle of the front axle, a steering angle of the rear axle, a rotational speed for the front axle and for the rear axle, a lateral measured acceleration and a measured yaw rate are recorded and / or measured. The measurement of the two steering angles for the front axle and the rear axle is preferably carried out by using a steering angle sensor. The respective rotational speed is preferably measured with a speed sensor. The measured yaw rate is preferably determined using a gyroscope. In step a), the two steering angles, the two rotational speeds for the front and rear axles, the measured acceleration and the measured yaw rate are thus preferably detected or measured by means of a corresponding sensor device. The yaw rate is often referred to as the yaw rate.

In a step b), predicted values for predicted angle-based parameters, a predicted lateral speed and a predicted yaw rate are calculated using a prediction model, the prediction model for the calculation in step b) the two steering angles for the front axle and rear axle and predefined starting values for the angle-based ones Parameters, for the lateral speed and for the yaw rate. The prediction model thus determines, in particular, predicted values for the lateral speed, the yaw rate and the angle-based parameters from the starting values for the steering angle, the angle-based parameters, the lateral speed and the yaw rate. Using the prediction model, predicted values for the respective variables can be determined on the basis of the starting values. In particular, further starting values for additional parameters can be estimated or otherwise measured. For example, a starting value for a longitudinal speed can be estimated. This estimate of the longitudinal velocity can also be taken into account when calculating the predicted values in step b). The prediction model can be used to generate more precise values, in this case predicted values, from the starting values.

The prediction model is used in particular to calculate parameters relating to the self-movement of a motor vehicle. The prediction model can use elements of a single-track model, among other things. Within the prediction model, values for a radius of the motor vehicle, a lateral speed, a slip angle in the center of gravity of the motor vehicle and for slip angle can be determined, for example. However, in particular the method according to the prediction model has not yet been completed, but is preferably continued with the fusion model. A merger model will therefore be introduced later in this application. The fusion model is preferably divided into two different Kalman filters, an “ordinary” Kalman filter and an unscented Kalman filter. The Unscented Kalman filter is used in particular as a further prediction model within the fusion model. The Unscented Kalman filter can primarily take into account non-linear systems of equations or non-linear relationships.

The "ordinary" Kalman filter - hereinafter simply called the Kalman filter - can incorporate measured parameters into the fusion model. The Kalman filter has systems of equations that can take measured parameters or quantities into account. This means that the fusion model can be used to determine new starting values for the parameters of the self-motion. These start values can be fed back to the prediction model for a next cycle. This would mean that the prediction model and the fusion model can be run again with the new starting values. The start values can also be output as result values. Thus, the prediction model and the fusion model can be viewed as a cycle, cycle or loop. The fusion model can thus include measured parameters in the method and update the parameters determined in the prediction model. In this way, the prediction model can be coupled with measured variables.

If, for example, the prediction model is executed again with result values from the fusion model, an improvement in the accuracy can be achieved. In particular, changes in the movement of the motor vehicle can be recognized and taken into account by coupling the prediction model with the fusion model. A criterion can preferably be defined as to whether the cycle comprising the prediction model and the fusion model is run through again. This criterion can, for example, be a difference between current start values and previous start values from the cycle immediately before. Other criteria, such as a fixed number of cycles that have been run through, can also be used to determine whether the cycle from the prediction model and the fusion model is executed again or whether the starting values are output as result values.

In a step c), fused values for fused angle-based parameters, a fused lateral velocity and a fused yaw rate are calculated on the basis of the predicted values from step b) by means of a fusion model for fusing predicted values and measured values. The fusion model has an Unscented Kalman filter and a Kalman filter. The Kalman filter takes into account the lateral measured acceleration and the measured yaw rate when calculating the fused values. The Unscented Kalman filter in particular calculates a set of sigma points. For the sigma points, a weight coefficient or a weighting matrix is generally determined with the Unscented Kalman filter. The Unscented Kalman filter is used in particular for nonlinear systems of equations. The Unscented Kalman filter takes into account the additional uncertainty of a linearized function due to errors in the linearization process. The Unscented Kalman filter represents in particular a further development of an Extended Kalman filter, that is to say an extended Kalman filter. The values predicted in step b) are predicted again in particular by means of the Unscented Kalman filter. For this purpose, in particular the predicted values calculated in step b) are fed to the Unscented Kalman filter as input values. After the predicted values generated in step b) have been processed into new values by the Unscented Kalman filter, these new values can be transferred to the Kalman filter. In particular, the Kalman filter is designed to further process the values generated by the Unscented Kalman filter into the merged values. For this purpose, the values generated by the Unscented Kalman filter can be fed as input values to the Kalman filter, which can generate the fused values from these input values, taking into account measured sensor values. The measured values are preferably the measured yaw rate and the measured lateral acceleration.

In a step d), the calculated merged values from step c) are supplied as predetermined starting values for the prediction model in step b) and / or the fused values calculated in step c) are used as the result values Determine the own movement of the motor vehicle issued. Process step d) thus provides several options. The merged values calculated in step c) can be used again for the prediction model in step b). This means in particular that the fused values calculated in step c) are taken into account as starting values for step b). Method steps b) and c) can thus be carried out again, in which case the starting values in step b) represent the merged values from step c).

However, it is also possible for some of the fused values to be returned to method step b) and for some of the calculated fused values to be output as result values in step c). For example, the longitudinal speed can be output as a result and the remaining variables can be taken into account as start values for step b). Step d) also provides for the possibility that the merged values calculated in step c) are output as result values for determining the self-movement of the motor vehicle. In addition, method step d) provides for the possibility that method steps b) to d) can be carried out cyclically. This is provided in particular when a desired accuracy regarding the lateral speed and the yaw rate has been achieved. In addition, it can be provided that several process cycles are to be run through if the lateral measured acceleration and the measured yaw rate change greatly over time. In this case, repeating the process steps b) to d) a number of times can bring about greater accuracy.

A further variant of this invention provides that a starting value for a longitudinal speed is predetermined, recorded and / or determined for calculating the predicted values in step b), the longitudinal speed being perpendicular to the lateral speed. The longitudinal speed is determined in particular on the basis of the rotational speeds for the front axle and for the rear axle. It is possible to form a single averaged rotational speed from the two rotational speeds. In the simplest case, the longitudinal speed could simply be neglected. In order to increase the accuracy of the method, however, a starting value for the longitudinal speed is usually determined. This is done especially taking into account both rotational speeds for the front axle and for the rear axle. Both speed components, namely the longitudinal speed and the lateral speed, can thus be taken into account for determining the yaw rate.

A further variant of this invention provides that start values for the two angle-based parameters, the lateral speed and the yaw rate for the calculation of the predicted values are predefined, recorded and / or determined in step b). In particular, this variant of the invention provides that the starting values of method step b) can not only be predetermined, but can instead be detected and / or determined. For example, simple approximation solutions or other estimates can be used. The better the predetermined starting values are selected in method step b), the faster and more efficiently the predicted values can tend to be calculated. For example, the angle-based parameters can be determined on the basis of a mass and a stiffness. For the angle-based parameter relating to the front axle, a relation could be formed from a mass for the front axle versus a stiffness relating to the front axle.

A further variant of this invention provides that the starting value for the longitudinal speed and / or a predicted value for the longitudinal speed is calculated on the basis of an effective scope relating to the front axle and the rear axle, the effective scope being determined as a function of the respective rotational speed becomes. A wheel circumference can change significantly, especially at speeds above 80 km / h. This can be caused, for example, by changing the tire pressure. At higher motor vehicle speeds, air in the tire can heat up more, which can lead to an increase in the tire inflation pressure. This can lead to a significant change in the wheel circumference. This variant of the invention takes into account the fact that the circumference regarding the front axle and the rear axle changes at certain rotational speeds. The scope describes in particular a wheel circumference. However, the circumference can be assigned to the front axle or the rear axle. An effective range is determined in particular as a function of the respective rotational speed. This is preferably done by taking into account several section-wise linear functions. The respective coefficients of these linear functions are preferably determined on the basis of a predetermined reference data set. The effect that a wheel circumference changes at higher speeds can thus also be taken into account. This can lead to a significant increase in accuracy for odometric calculations.

A further variant of this invention provides that method steps a) to d) are carried out several times cyclically, periodically new values for the steering angle, the rotational speeds, the lateral measured acceleration are measured and these measured values are taken into account for the prediction model and / or fusion model. Thus, this variant of the invention not only provides that the method steps are carried out several times cyclically, but also that periodically new values for the steering angle, the rotational speeds and the lateral measured acceleration are measured. These measured values are taken into account for the prediction model and / or function model. On the one hand, this can increase the precision of the method and, on the other hand, changing measured values relating to the lateral acceleration, the rotational speeds and the steering angle can be taken into account continuously. This ensures that the fusion model does not develop separately from sensor data. A possible "drifting apart" of the models (prediction model and fusion model) of measured sensor data can thus be recognized or prevented in good time. In addition, new values for the measured yaw rate for the prediction model and / or fusion model can also be periodically taken into account.

Another variant of this invention provides that the unscented Kalman filter of the fusion model averages the predicted values from step b). For this purpose, weight coefficients or corresponding weighting matrices are preferably determined as part of the unscented Kalman filter, which transform the predicted values from step b) into weighted values of the unscented Kalman filter. The weight coefficients can also be summarized in the form of a weight matrix. The predicted values from step b) can be summarized in a matrix. Using the weighting matrix, this matrix consisting of predicted values can be converted into a new matrix. This new matrix then preferably has weighted values. These weighted values can be used in particular to calculate the merged values.

Another variant of this invention provides that the Kalman filter of the fusion model calculates new starting values for the two angle-based parameters, the lateral speed and the yaw rate, from the weighted, averaged, predicted values. The Kalman filter takes into account the measured lateral acceleration and the measured yaw rate for this calculation. Thus, this variant provides in particular that the Kalman filter of the fusion model uses the weighted averaged predicted values provided by the Unscented Kalman filter as input values. The result values of the Unscented Kalman filter preferably flow into the Kalman filter as starting values. The Kalman filter describes in particular the interaction of the corresponding physical equations of motion and the corresponding sensor data. In this example, the measured lateral acceleration and the measured yaw rate are taken into account as sensor data. Depending on the design of the Kalman filter, the respective steering angle and respective rotational speeds can also be taken into account. As a rule, additional sensor data are not provided, since this invention intends to do without cost-intensive sensors. The Unscented Kalman filter can represent non-linear systems and the Kalman filter can in particular provide a feedback of the fusion model with the measured lateral acceleration and the measured yaw rate.

Another variant of this invention provides that the values for the predicted angle-based parameters, the predicted lateral speed and the predicted yaw rate are filtered using a low-pass filter. The filtering by means of the low-pass filter serves in particular to avoid sudden changes or outliers regarding the predicted values mentioned. In this way, unexpected or unrealistic peaks or deviations regarding the calculated predicted values can be effectively avoided. In particular, low-pass filters with a size 5 buffer are used. In addition, other values can be low-pass filtered. This applies to the respective movement angle, a slip angle in the center of gravity, a radius and the predicted values mentioned.

Another variant of this invention provides that the starting values relating to the two angle-based parameters are determined based on a predetermined data set, the predetermined data set linking a slip angle for the front axle and rear axle with a product of the starting values for the longitudinal speed and the yaw rate . A slip angle cannot always be detected with an appropriate sensor system. This applies in particular if a corresponding sensor is not available. This variant of the invention nevertheless makes it possible to determine the slip angle. A predefined data record is used for this. This data set contains, in particular, reference measurements which were carried out with a vehicle equipped with appropriate sensors. Among other things, the slip angle was measured in these reference measurements. In addition, measured values for the longitudinal speed and the yaw rate were also recorded. A preferred representation of this data set consists in a diagram in which the respective slip angle on the x-axis and a product of the longitudinal speed and on the y-axis Yaw rate is shown. There may be two such diagrams for a vehicle, one for the front axle and one for the rear axle. In particular, it can be provided that the corresponding slip angle can be determined directly from the predetermined data set using the longitudinal speed and the yaw rate. The slip angle can thus be determined despite a corresponding missing sensor.

$$K_R=\frac{m_R}{c_R};$$

Another variant of this invention provides that in order to determine the starting values for the two angle-based parameters, a slope of the specified data set is determined. As was shown in the previous variant, the specified data record is preferably shown in the form of a diagram. The respective measuring points usually show a linear trend. Based on this linear tendency, a slope of the given data set can be determined. This slope can be linked to equation 1 or equation 2. $$K_F=\frac{m_F}{c_F};$$

$$K_R=\frac{m_R}{c_R};$$

Here m _{F is} the mass relating to the front axle. c _F is the stiffness regarding the front axle. The parameters m _R and c _R relate accordingly to the rear axle. The quotient in equation 1 or 2 corresponds to the slope of the specified data set or the inverse slope.

The slope of the specified data set can be determined, for example, using a linear regression compensation calculation. This can be done easily with many program tools that include a curve fitting tool. Thus, the starting values for the two angle-based parameters or the respective slip angle can be determined by the slope of the specified data set.

$$A_R={\delta }_R+{\alpha }_R;$$

δ_F beziehungsweise δ_R sind entsprechend den jeweiligen Lenkwinkeln. Die Schräglaufwinkel α_F und α_R können durch die vorgenannten Varianten der Erfindung bestimmt werden. Eine Zusammenfassung dieser beiden Winkel zu einem Bewegungswinkel erleichtert die weitere Berechnung, da anstelle zweier Werte nur noch ein Wert abgespeichert und verarbeitet werden muss. Dies kann die Geschwindigkeit der odometrischen Berechnungen erhöhen.Another variant of this invention provides that two movement angles for the front axle and rear axle are formed from a sum of the two slip angles and the measured steering angles. This is preferably done using equations 3 and 4. $$A_F={\delta }_F+{\alpha }_F;$$

$$A_R={\delta }_R+{\alpha }_R;$$

δ _F respectively δ _R are according to the respective steering angles. The slip angle α _F and α _R can be determined by the aforementioned variants of the invention. Combining these two angles into one movement angle facilitates the further calculation, since instead of two values, only one value has to be saved and processed. This can increase the speed of the odometric calculations.

$$K_{R_p}=1.25\times EG;$$

Another variant of this invention provides that the predicted angle-based parameters are calculated as a function of a case distinction, the case of the case distinction comparing the value of the measured lateral acceleration with a threshold value for the lateral acceleration. This means in particular that the starting values for the two angle-based parameters are determined by means of a case distinction. This case distinction should in particular take into account different directions of rotation of the front and rear axles. If the measured lateral acceleration exceeds the threshold value for the lateral acceleration, it is particularly provided that the predicted angle-based parameters are calculated using equations 5 and 6, respectively. $$K_{F_p}=2.25\times EG;$$

$$K_{R_p}=1.25\times EG;$$

$$K_{R_p}=-0.01-\frac{5\times EG}{6};$$

In den Gleichungen 5 bis 8 ist ein Parameter EG enthalten. Der Parameter EG wird mittels der dargestellten Fallunterscheidung zu den prädizierten winkelbasierenden Parametern umgeformt. Auf den Parameter EG wird später eingegangen.However, if the measured lateral acceleration is lower than the threshold value of the lateral acceleration, it is particularly provided that the predicted angle-based parameters are determined using equations 7 or 8. $$K_{F_p}=-0.01+\frac{EG}{6};$$

$$K_{R_p}=-0.01-\frac{5\times EG}{6};$$

A parameter EG is contained in equations 5 to 8. The parameter EG is transformed into the predicted angle-based parameters using the case differentiation shown. The parameter EG will be discussed later.

Another variant of this invention provides that a slip angle in the center of gravity of the motor vehicle as a function of the movement angles, a distance between the front axle to the rear axle and a distance of the front axle to the center of gravity of the motor vehicle is calculated. The calculation of the slip angle in the center of gravity of the motor vehicle facilitates the later calculation of the predicted lateral speed. The slip angle β is calculated in particular using equation 9. $$\beta ={\text{tan}}^{-1}\left[\text{tan}\left(A_F\right)-\frac{l_F}{l}\left[\text{tan}\left(A_F\right)-\text{tan}\left(A_R\right)\right]\right];$$

beschreibt ein Längenverhältnis. Da der Schräglaufwinkel β im weiteren Verlauf für weitere Berechnungen benötigt wird, kann eine Vorabberechnung des Schräglaufwinkels β die Effizienz des Berechnungsverfahrens erhöhen und somit rasche odometrische Berechnungen ermöglichen. A _F respectively A _R are the respective movement angles, the quotient $\frac{l_F}{l}$

describes an aspect ratio. Because the slip angle β in the further course of further calculations is required, a pre-calculation of the slip angle β increase the efficiency of the calculation process and thus enable quick odometric calculations.

Zu beachten ist, dass Gleichung 10 nicht den Radius R direkt sondern den inversen Radius R^-1 in der Mitte der Vorderachse des Kraftfahrzeugs berechnet. Diese Darstellung ist zweckmäßig, da im weiteren Verlauf der inverse Rotationsradius direkt verarbeitet werden kann. Bezüglich der Berechnung des Rotationsradius gelten dieselben Vorteile wie bei der Berechnung des Schräglaufwinkels β.Another variant of this invention provides that a rotation radius of the motor vehicle is calculated as a function of the movement angles and as a function of the distance between the front axle and the rear axle. The radius of rotation is determined in particular by equation 10. $$R^{-1}=\left[\frac{\text{tan}\left(A_F\right)-\text{tan}\left(A_R\right)}{l}\right]\times \text{cos}\left(A_F\right);$$

It should be noted that equation 10 does not calculate the radius R directly but the inverse radius R ^-1 in the middle of the front axle of the motor vehicle. This representation is useful because the inverse rotation radius can be processed directly in the further course. With regard to the calculation of the rotation radius, the same advantages apply as for the calculation of the slip angle β.

Another variant of this invention provides that the measured lateral acceleration and the measured yaw rate are low-pass filtered. When measuring the lateral acceleration and the yaw rate, systematic and statistical errors can lead to deviations in the measured values. In the worst case, so-called outliers can occur, which in the worst case flow into the calculation process via the Kalman filter. Such statistical outliers could then lead to unrealistic results and are often undesirable. Low-pass filtering of the measured lateral acceleration and the measured yaw rate can prevent individual statistical outliers from falsifying the odometric calculations when measuring the lateral acceleration or the yaw rate. Low-pass filtering with a size 5 buffer is also preferably used here.

The present invention also provides a sensor system for a motor vehicle with a sensor device for detecting a measured lateral acceleration, a measured yaw rate, a steering angle of a front axle, a steering angle of a rear axle and in each case a rotational speed for the front axle and rear axle. In addition, the sensor system has an evaluation unit, the evaluation unit being designed to process the variables detected by the sensor device in accordance with a method according to the preceding variants. The evaluation unit can in particular contain the prediction model and the two different Kalman filters. The quantities measured by the sensor device can be fed to the evaluation device. The evaluation unit can process these supplied measured variables in accordance with the prediction model, the unscented Kalman filter and the Kalman filter. The respective Kalman filter and the prediction model can be used several times cyclically. In particular, it can be provided that new measured values, which are recorded by the sensor device, are regularly incorporated into the cyclic process as input variables. The advantages mentioned in the previous variants also apply mutatis mutandis to this device claim.

A further variant of this invention provides a sensor system, the sensor device comprising a gyroscope for measuring the measured yaw rate, a steering angle sensor for measuring the steering angle, an acceleration sensor for measuring the measured lateral acceleration and a speed sensor for measuring the rotational speed in each case for the front axle and for has the rear axle. The term orbit frequency can be used instead for the term orbit speed. A revolution speed or revolution frequency primarily describes how many revolutions a wheel makes within a predetermined time. The unit for the revolution speed or revolution frequency is in particular revolutions per minute or revolutions per second. The sensor system preferably does not have a lidar sensor. In contrast to the acceleration sensor or steering angle sensor, a lidar sensor is a cost-intensive sensor. Within the scope of this invention, attempts are made to carry out effective odometric calculations using inexpensive basic sensors. The sensor system therefore preferably has a limited number of different sensors.

Another variant of this invention provides a sensor system, the sensor device having a low-pass filter for filtering the measured lateral acceleration and the measured yaw rate. As was explained in a previous variant of the invention, the low-pass filter is used in particular to filter out statistical outliers or so-called peaks. In this way, odometric calculations can be stabilized. The low-pass filter can in particular also low-filter the calculated predicted or merged values.

A further variant of this invention provides a computer program product with program code means which are stored on a computer-readable medium in order to carry out the method according to one of the preceding variants if the computer program product is processed on a processor of an electronic evaluation unit. The evaluation unit can in particular be implemented in a microchip. The microchip can itself be part of a printed circuit board.

Another variant of this invention provides a vehicle assistance system with a computer program product. The computer program product contains in particular the electronic evaluation unit, which can calculate the lateral speed and the yaw rate for a self-movement of the motor vehicle. The vehicle assistance system can thus receive current values for the lateral speed and the yaw rate and, under certain circumstances, for further parameters. Using these calculated values, the computer program product can enable effective control of the vehicle assistance system.

Another variant of this invention provides a motor vehicle with a vehicle assistance system. With the above-mentioned variants of the invention, the motor vehicle can use the vehicle assistance system to effectively calculate its position or its own movement without having to resort to expensive sensors.

$${\alpha }_R=K_{R_0}\times \sqrt{V_x{}_0^2+V_y{}_0^2}\times {\dot{\theta }}_0;$$

Die Gleichungen 11 und 12 beinhalten Startwerte für die winkelbasierenden Parameter K_{F 0} , K_{R 0} , einen Startwert für die longitudinale Geschwindigkeit V_{x 0} , einen Startwert für die laterale Geschwindigkeit V_{y 0} sowie einen Startwert für die Gierrate θ̇₀. Diese Startwerte können zum Beispiel von einem vorangegangenen Berechnungszyklus als Eingangswerte übernommen worden sein. Bei einem erstmaligen Starten dieser Berechnung können zum Beispiel auch Schätzwerte vorgegeben werden. Insbesondere können für die Startwerte in den Gleichungen 11 und 12 Messwerte der Sensoreinrichtung übernommen werden. So kann beispielsweise ein Startwert für die Gierrate durch einen Messwert des Gyroskops vorgegeben sein. Entsprechendes gilt für die longitudinale beziehungsweise laterale Geschwindigkeit. Die laterale Geschwindigkeit kann beispielsweise mittels des Beschleunigungssensors indirekt gemessen werden. Mittels einer Integration über die Zeit des Sensorsignals des Beschleunigungssensors kann eine gemessene laterale Beschleunigung ermittelt werden. Die Startwerte für die winkelbasierenden Parameter K_{F 0} beziehungsweise K_{R 0} können anhand des vorgegebenen Datensatzes ermittelt werden. Im weiteren Verlauf werden die gemessenen Bewegungswinkel δ_F und δ_R mit den Schräglaufwinkeln aus den Gleichungen 11 und 12 zu den Bewegungswinkeln A_F beziehungsweise A_R addiert. A_F und A_R sind durch die Gleichungen 3 beziehungsweise 4 gegeben. Die Bewegungswinkel A_F und A_R werden bevorzugt mittels eines Tiefpassfilters gefiltert.A possible calculation method is now explained below. The prediction model particularly provides for the respective slip angle using equations 3 and 4 α _F and α _R to calculate. $${\alpha }_F=K_{F_0}\times \sqrt{V_x{}_0^{\mathrm{2nd}}+V_y{}_0^{\mathrm{2nd}}}\times {\dot{\theta }}_0;$$

$${\alpha }_R=K_{R_0}\times \sqrt{V_x{}_0^{\mathrm{2nd}}+V_y{}_0^{\mathrm{2nd}}}\times {\dot{\theta }}_0;$$

Equations 11 and 12 contain start values for the angle-based parameters K _{F 0} , K _{R 0} , a starting value for the longitudinal velocity V _{x 0} , a starting value for the lateral speed V _{y 0} and a starting value for the yaw rate θ̇ ₀ . These start values can, for example, have been adopted as input values from a previous calculation cycle. When this calculation is started for the first time, for example, estimated values can also be specified. In particular, measured values of the sensor device can be adopted for the start values in equations 11 and 12. For example, a starting value for the yaw rate can be predetermined by a measured value of the gyroscope. The same applies to the longitudinal or lateral speed. The lateral speed can be measured indirectly, for example, using the acceleration sensor. A measured lateral acceleration can be determined by means of an integration over the time of the sensor signal of the acceleration sensor. The starting values for the angle-based parameters K _{F 0} respectively K _{R 0} can be determined using the specified data record. In the further course, the measured movement angles δ _F and δ _R with the slip angles from equations 11 and 12 to the movement angles A _F respectively A _R added. A _F and A _R are by equations 3 respectively 4th given. The movement angle A _F and A _R are preferably filtered using a low-pass filter.

Equation 9 is used in this example to determine the slip angle β calculated. This slip angle β is also preferably filtered using the low-pass filter. The inverse rotation radius R ^-1 is preferably calculated using equation 10. In particular, it is provided that the values relating to the inverse rotation radius R ^-1 are filtered by means of the low-pass filter. A predicted value related to longitudinal speed V _{x p} is calculated in particular using equation 13. $$V_{x_p}=\left(a1\cdot RP{S}_R+a\mathrm{2nd}\cdot RP{S}_F\right)\times W{\mathrm{C.}}_{cOrr};$$

The predicted longitudinal velocity V _{x p} is calculated in equation 13 by means of a weighted sum, which has the respective rotational speeds as summands. Equation 13 also takes into account a possible change in a wheel circumference. The changed wheel circumference WC _corr is determined in particular by means of a further linear function. This further linear function is particularly dependent on the rotational speeds. The two rotational speeds can be weighted differently by means of the coefficients a1 and a2. This is supposed to be sudden Deviations in the rotational speeds for the rear axle should be avoided as far as possible. In particular, it is provided that the coefficient a1 is 90 percent (a1 = 0.9) and the coefficient a2 is 10 percent (a2 = 0.1).

In Gleichung 14 taucht der Schräglaufwinkel β des Schwerpunkts auf. Hier macht sich eine vorhergehende Berechnung des Schräglaufwinkels β sowie dessen Filterung positiv bemerkbar. Die in Gleichung 14 ermittelten Werte betreffend die prädizierte laterale Geschwindigkeit werden bevorzugt ebenfalls tiefpassgefiltert. Ein prädizierter Wert für die Gierrate kann anhand der Gleichung 15 bestimmt werden. $${\dot{\theta }}_p=R^{-1}\times \sqrt{V_{x_p}^2+V_{y_p}^1};$$

Die prädizierten Werte für die gemessene Gierrate werden ebenfalls bevorzugt tiefpassgefiltert.A predicted value for the lateral velocity V _{y p} is determined, for example, using equation 14. $$V_{y_p}=V_{x_p}\text{tan}\left(\beta \right)+l_F\times {\dot{\theta }}_0;$$

Equation 14 shows the slip angle β of focus. A previous calculation of the slip angle is made here β and its filtering is noticeable. The values relating to the predicted lateral velocity determined in equation 14 are preferably also low-pass filtered. A predicted value for the yaw rate can be determined using equation 15. $${\dot{\theta }}_p=R^{-1}\times \sqrt{V_{x_p}^{\mathrm{2nd}}+V_{y_p}^1};$$

The predicted values for the measured yaw rate are also preferably low-pass filtered.

After predicted values for the yaw rate, the lateral speed and the longitudinal speed have been calculated, a value relating to an angle gradient EG, which is also called a flowing angle gradient, can be calculated. This can be done using equation 16, for example. $$EG=\frac{\frac{l\times {\dot{\theta }}_p}{\sqrt{V_{x_p}^{\mathrm{2nd}}+V_{y_p}^{\mathrm{2nd}}}}-\left({\delta }_F-{\delta }_R\right)}{{\dot{\theta }}_p\times \sqrt{V_{x_p}^{\mathrm{2nd}}+V_{y_p}^{\mathrm{2nd}}}};$$

In the following, this angle gradient EG becomes predicted values regarding the angle-based parameters by the already mentioned case distinction (equations 5 to 8) K _{F p} and K _{R p} converted. If the measured lateral acceleration is greater than the predetermined threshold value, equations 5 and 6 are applied. If the measured lateral acceleration is less than the predetermined threshold value, equations 7 and 8 are used in particular.

Further features of the invention result from the claims, the figures and the description of the figures. The features and combinations of features mentioned above in the description and the features and combinations of features mentioned below in the description of the figures and / or shown alone in the figures can be used not only in the respectively specified combination but also in other combinations without departing from the scope of the invention . Embodiments of the invention are thus also to be regarded as encompassed and disclosed, which are not explicitly shown and explained in the figures, but can be derived from the explanations explained and can be generated by separate combinations of features. Versions and combinations of features are also to be regarded as disclosed, which therefore do not have all the features of an originally formulated independent claim. In addition, versions and combinations of features, in particular those explained above, are to be regarded as disclosed which go beyond or differ from the combinations of features set out in the references of the claims.

• 1 eine Skizze betreffend ein Einspurmodell; und
• 2 ein schematisches Ablaufdiagramm betreffend das Vorhersagemodell und das Fusionsmodell in Zusammenwirkung mit gemessenen Sensorwerten.

The present invention will now be explained in more detail with reference to the accompanying drawings. In it show:

• 1 a sketch relating to a single-track model; and
• 2nd a schematic flow diagram relating to the prediction model and the fusion model in cooperation with measured sensor values.

1 shows a sketch for a single track model. In it are a rear wheel schematically WR as well as a front wheel WF shown. The focal points of these two wheels are with a main axis HA connected. On this main axis HA is a focus CG arranged a motor vehicle. The rear wheel WR as well as the front wheel WF each have an axis that runs along the orientation of the respective wheel. For the front wheel WF is a longitudinal axis WAF , for the rear wheel WR is a longitudinal axis WAS shown. If the speed vector V _F regarding the front wheel WF not along the long axis WAF runs, there is a slip angle | α _F | > 0. A steering angle δ _F together with the slip angle α _F gives a movement angle A _F . The arrows relating to the respective angles show the sign of the respective angle. If the arrow points counter-clockwise, the sign is positive, such as the steering angle δ _F in 1 . At α _R for example, the angle is negative. α _R runs from the longitudinal axis WAS to an imaginary (in 1 indicated by dashed lines) Extension of the speed vector V _R . The sign convention chosen here does not have to be adopted, the only thing that is important is that a sign convention once defined is adhered to.

The angle of movement A _F describes in particular a deviation of the speed direction from the main axis HA . For the corresponding angles and sizes of the rear axle, the above statements apply analogously. The single-track model also has a speed vector V relating to the entire motor vehicle. Due to movement of the motor vehicle at an angle to the main axis HA lies according to 1 a slip angle β in front. In the example of 1 is a direction of rotation W indicated. This causes the front wheel WF tends to according to the value θ̇ _f l _F and the rear wheel WR moved according to the value θ̇ _f l _R. F _R such as F _F represent the respective lateral frictional forces which act on the respective wheels.

2nd shows a representation, which should illustrate the process steps more clearly. The respective speeds flow in a speed model SM RPS _F , RPS _R to calculate the longitudinal speed V _x on. The longitudinal speed V _x or their predicted value V _{x p} are calculated in particular using equation 13. The longitudinal speed determined in this way V _x becomes the input parameter of a predictive model PM fed. In addition, flow into the forecast model PM measured values regarding the steering angle δ _F and δ _R on. The prediction model PM is especially designed to perform calculations according to equations 3 to 16. Among other things, a starting value for the yaw rate θ G _{0 is} provided in these equations. In the very first cycle of this process, in which the fusion model FM has not yet been used, estimates can be used for the respective starting values. Instead of estimated values, measured values from the sensor device can also be used.

$$X{1}_{4\times 9}=Prediction\_Model\left(X_{4X9}\right);$$

$$x{1}_{4X1}={\left[Zeros\right]}_{4X1};$$

$$x{1}_{4\times 1}=x{1}_{4\times 1}+{\left[W_m\left(i\right)\right]}_{1\times 1}\times {\left[X1\left(i\right)\right]}_{4\times 1};$$

$$X{2}_{4\times 9}=X{1}_{4\times 9}-{\left[x1\left|x1\right|\mathrm{..}|x1\right]}_{4\times 9};$$

$${\left[W_c\right]}_{9\times 9}=W_{c_{1\times 9}}\times I_{9\times 9};$$

$$P{1}_{4\times 4}=X{2}_{4\times 9}\times {\left[W_c\right]}_{9\times 9}\times X{2}_{9\times 4}^T+Q_{4\times 4};$$

The prediction model PM can now use equations 3 to 16 to calculate predicted values for the yaw rate θ̇ _p , the angle-based parameters and for the lateral speed. These predicted values θ̇ _p , K _{F p} , K _{R p} and V _{y p} become the fusion model FM to hand over. The fusion model FM has an Unscented Kalman filter and a Kalman filter. The fusion model FM is designed to merge values from the predicted values regarding the yaw rate θ̇ _f , the angle-based parameters K _{F f} , K _{R f} as well as the lateral speed V _{y f} to calculate. For this purpose, measured values relating to the yaw rate θ̇ _obs and measured values relating to the lateral speed flow V _y into the fusion model FM on. The measured lateral speed V _{y, obs} is in particular through a time integration of a measured acceleration a _{y, obs} determined. The measured yaw rate θ̇ _obs can be obtained in particular from the measurement data of a gyroscope. The Unscented Kalman filter of the fusion model FM is especially trained to calculate sigma points, weighting factors and a new covariance matrix P1. The Unscented Kalman filter uses the following equations, for example: $$X_{\mathrm{4th}\times 9}=SiGmas\left(x_{\mathrm{4th}\times 1},P_{\mathrm{4th}\times \mathrm{4th}},{\mathrm{C.}}_{1\times 1}\right);$$

$$X{1}_{\mathrm{4th}\times 9}=PredictiOn\_MOdel\left(X_{\mathrm{4th}X9}\right);$$

$$x{1}_{\mathrm{4th}X1}={\left[\mathrm{Z.}erOs\right]}_{\mathrm{4th}X1};$$

$$x{1}_{\mathrm{4th}\times 1}=x{1}_{\mathrm{4th}\times 1}+{\left[W_m\left(i\right)\right]}_{1\times 1}\times {\left[X1\left(i\right)\right]}_{\mathrm{4th}\times 1};$$

$$X{\mathrm{2nd}}_{\mathrm{4th}\times 9}=X{1}_{\mathrm{4th}\times 9}-{\left[x1\left|x1\right|\mathrm{..}|x1\right]}_{\mathrm{4th}\times 9};$$

$${\left[W_c\right]}_{9\times 9}=W_{c_{1\times 9}}\times {\mathrm{I.}}_{9\times 9};$$

$$P{1}_{\mathrm{4th}\times \mathrm{4th}}=X{\mathrm{2nd}}_{\mathrm{4th}\times 9}\times {\left[W_c\right]}_{9\times 9}\times X{\mathrm{2nd}}_{9\times \mathrm{4th}}^T+Q_{\mathrm{4th}\times \mathrm{4th}};$$

$$H=\left[\begin{array}{llll}1\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 1\hfill \end{array}\right];$$

$$Z{1}_{2\times 1}=H_{2\times 4}\times x{1}_{4\times 1};$$

$$K=\frac{P1\times H^T}{H\times P1\times H^T+RS};$$

$$x=x1+K\times \left(Z-Z1\right);$$

$$P=P1-K\times H\times P1;$$

The vector x ₁ and the new covariance matrix P1, which were calculated by the Unscented Kalman filter, are fed to the Kalman filter as input parameters. The Kalman filter is particularly designed to use equations 24 to 29 to calculate a new state vector x and a new covariance matrix P. $$\mathrm{Z.}=\left[\begin{array}{c}{\dot{\theta }}_{Obs}\\ a_{y,Obs}\times \Delta T\end{array}\right];$$

$$H=\left[\begin{array}{llll}1\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 1\hfill \end{array}\right];$$

$$\mathrm{Z.}{1}_{\mathrm{2nd}\times 1}=H_{\mathrm{2nd}\times \mathrm{4th}}\times x{1}_{\mathrm{4th}\times 1};$$

$$K=\frac{P1\times H^T}{H\times P1\times H^T+RS};$$

$$x=x1+K\times \left(\mathrm{Z.}-\mathrm{Z.}1\right);$$

$$P=P1-K\times H\times P1;$$

x1 and X1 are different variables regarding the state vector x, which contains the values for the angle-based parameters, the yaw rate and for the lateral speed. During the calculations of the Unscented Kalman filter, the length of the vector x can change, which leads to the different indices. ΔT is a time difference. In equation 21, the state vector is converted into a new matrix X2 _{4 × 9} .

The predicted values for the yaw rate, for the angle-based parameters and for the lateral speed can in particular be combined to form a state vector x. This state vector x is particularly designated x _p if it has the predicted values. These predicted values or the state vector x _p are transferred to the Unscented Kalman filter as an input data record.

The Unscented Kalman filter calculates sigma points (equation 17) and weighting factors [W _m (i)] _{1 × 1} in particular using this input data. A weighting matrix can be calculated from the weighting factors using an inertia tensor I _{9 × 9} (equation 22). The Unscented Kalman filter in particular converts the predicted values in the vector x _p to new values and transfers these new values to the Kalman filter. These new values are represented by the matrix P1.

Equations 17 through 23 relate in particular to the Unscented Kalman filter. The Unscented Kalman filter sometimes contains very complex mathematical transformations and transformations. However, these are not the core of the invention. Equations 17 to 23 presented only show one possible variant of which equations the Unscented Kalman filter can have. To understand this application, it is sufficient to understand that the Unscented Kalman filter uses the predicted values from the prediction model PM weighted and the new covariance matrix P1 was calculated. These values or covariance matrix P1 are transferred to the Kalman filter as input values in the further course.

The Kalman filter in particular has a plurality of matrices or vectors. These are used for the mathematical representation of the Kalman filter. A Z vector contains measurement values of the gyroscope and a measurement value relating to the measured lateral acceleration. Z is thus designed as a measured value vector. The matrix H represents the sensor model. The matrix H can thus be referred to as the sensor model matrix. Equation 27 also has an uncertainty matrix RS regarding additional uncertainties (e.g. measurement errors). The matrix P1 calculated by the Unscented Kalman filter can be converted together with the measured value vector Z, the sensor model matrix H and a covariance matrix regarding the uncertainty into a new matrix, the Kalman gain. This Kalman gain matrix K is used in the further course to calculate a new state vector x which contains new starting values relating to the yaw rate, the angle-based parameters and the lateral speed. In addition, a new matrix for the covariance matrix P can be calculated using the Kalman gain matrix K. The new state vector x and the new covariance matrix P can now use the prediction model PM are supplied as new input values. However, it can also be provided that individual values for the parameters of the state vector x are output as result values. If the calculation process is run through again, either the values calculated by the Kalman filter or new sensor values can be adopted as start values.

Equations 24 through 29 show a possible representation of the Kalman filter. The Kalman filter as such is not the core of this application. For this reason, the Kalman filter, like the Unscented Kalman filter, is not shown in more detail. A skilled professional knows how to deal with the Unscented Kalman filter and the Kalman filter.

Through the calculations of the fusion model FM the predicted values relating to the yaw rate, the angle-based parameter and the lateral speed are transformed into fused values. That means the fusion model FM merged values for the yaw rate θ̇ _f , the angle-based parameters K _{F f} , K _{R f} as well as the lateral speed V _{y f} calculated. The merged values can now be output as result values in order to carry out odometric calculations.

Alternatively, it can be provided that these merged values as input parameters for the prediction model PM to provide. That means the merged values of the fusion model FM become starting values for the prediction model PM . Another calculation cycle can thus be run through. The number of calculation cycles carried out can be made dependent on a desired accuracy. In the next calculation cycle, the fusion model can again FM newly measured values relating to the measured yaw rate θ̇ _obs and newly measured values relating to the lateral speed V _{y, obs} consider.

This in 2nd The method shown was compared with comparative measurements. These measurements were carried out with a reference vehicle. The reference vehicle has corresponding sensors, which can measure a longitudinal speed, a lateral speed and a yaw rate with a sufficiently high accuracy. With a measurement duration of over two hours, different speeds and different maneuvers were carried out on different roads with the reference vehicle. The following statistical deviations were found. For the longitudinal speed V _x a deviation of 1.08 km / h was found. For the lateral speed V _y a statistical deviation of 0.36 km / h was found. A statistical deviation of 0.09 degrees per second was found for the yaw rate. With that, in 2nd The calculation methods shown clearly show that the aforementioned parameters can also be determined with sufficient accuracy using inexpensive basic sensors. This enables vehicle assistance systems to be developed which, in the best case, can do without expensive lidar sensors and still enable precise odometric calculations.

QUOTES INCLUDE IN THE DESCRIPTION

This list of documents listed by the applicant has been generated automatically and is only included for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent literature cited

• WO 2014/146821 A1 [0003]
• DE 102006020490 A1 [0004]
• US 8326480 B2 [0005]

Claims (21)

Method for determining a lateral speed and a yaw rate for a self-movement of a motor vehicle with a front axle and a rear axle characterized by the following method steps: a) detecting and / or measuring a steering angle (δ _F ) of the front axle, a steering angle of the rear axle (δ _R ) , in each case a rotation speed for the front axle (RPS _F ) and for the rear axle (RPS _R ), a lateral measured acceleration (a _{y, obs} ) and a measured yaw rate (θ̇ _obs ), b) calculating predicted values for predicted angle-based parameters ( K _{F p} , K _{R p} ), a predicted lateral velocity (V _{y p} ) and a predicted yaw rate (θ̇ _p ) by means of a prediction model, the prediction model for calculating in step b) the two steering angles (δ _F , δ _R ) for the front axle and rear axle and predefined starting values for the angle-based parameters (K _{F 0} , K _{R 0} ), the lateral velocity (V _y0 ) and the yaw rate (θ̇ ₀ ) are taken into account, c) calculation of fused values for fused angle-based parameters (K _{F f} , K _{R f} ), a merged lateral velocity (V _{y f} ) and a fused yaw rate (θ̇ _f ) based on the predicted values from step b) by means of a fusion model for fusing predicted values and measured values, the fusion model having an Unscented Kalman filter and a Kalman filter, the Kalman filter being the lateral measured acceleration (V _{y, obs} ) and the measured yaw rate (θ̇ _obs ) are taken into account for calculating the fused values, d) supplying the calculated fused values from step c) as predetermined starting values for the prediction model in step b) and / or outputting the merged values calculated in step c) as result values for determining the self-movement of the motor vehicle. Procedure according to Claim 1 , where a starting value for a longitudinal speed (V _{x 0} ) is predefined, recorded and / or determined for calculating the predicted values in step b), the longitudinal speed (V _x ) being perpendicular to the lateral speed (V _y ). Procedure according to Claim 1 , where start values for the two angle-based parameters (K _F0 , K _{R 0} ), the lateral speed (V _{y 0} ) and the yaw rate (θ̇ ₀ ) for calculating the predicted values in step b) are predetermined, recorded and / or determined. Procedure according to Claim 2 , where the starting value for the longitudinal velocity (V _{x 0} ) and / or a predicted value for the longitudinal velocity (V _{x p} ) is calculated based on an effective circumference (WC _corr ) relating to the front axle and the rear axle, the effective circumference (WC _corr ) being determined as a function of the respective rotational speed (RPS _F , RPS _R ). Method according to one of the preceding claims, wherein the method steps a) to d) are carried out several times cyclically, periodically new values for the steering angle (δ _F , δ _R ), the rotational speeds (RPS _F , RPS _R ), the lateral measured acceleration (a _{y, obs} ) are measured and these measured values are taken into account for the prediction model and / or fusion model. Method according to one of the preceding claims, wherein the unscented Kalman filter of the fusion model averages the predicted values from step b). Procedure according to Claim 6 , whereby the Kalman filter of the fusion model generates new starting values (K _F0 , K _{R 0} ) for the two angle-based parameters the lateral speed (V _{y 0} ) and the yaw rate (θ̇ ₀ ), the Kalman filter taking into account the measured lateral acceleration (a _{y, obs} ) and the measured yaw rate (θ̇ _obs ) for this calculation. Method according to one of the preceding claims, wherein the values for the predicted angle-based parameters (K _Fp , K _{R p} ), the predicted lateral velocity (V _{y p} ) and the predicted yaw rate (θ̇ _p ) are filtered using a low-pass filter. Method according to one of the preceding claims, the starting values relating to the two angle-based parameters (K _{F 0} , K _{R 0} ) are determined based on a predetermined data set, the predetermined data set in each case a slip angle (α _F , α _R ) for the front axle and rear axle with a product of the starting values for the longitudinal speed (V _{x 0} ) and the yaw rate (θ̇ ₀ ). Procedure according to Claim 9 , whereby to determine the starting values for the two angle-based parameters (K _{F 0} , K _{R 0} ) a slope of the specified data set is determined. Procedure according to Claim 9 or 10th , wherein two movement angles (A _F , A _R ) for the front axle and rear axle are formed from a sum of the two slip angles (α _F , α _R ) and the measured steering angles (δ _F , δ _R ). Method according to one of the preceding claims, wherein the predicted angle-based parameters (K _Fp , K _{R p} ) are calculated depending on a case distinction, with the case of the case distinction the value of the measured lateral Acceleration (a _{y, obs} ) is compared with a threshold value for the lateral acceleration (a _y , _th ). Procedure according to Claim 11 , where a slip angle (β) in the center of gravity (CG) of the motor vehicle as a function of the movement angles (A _F , A _R ), a distance between the front axle to the rear axle (1) and a distance from the front axle to the center of gravity of the motor vehicle (I _F ) is calculated. Procedure according to Claim 13 , wherein a radius of rotation (R) of the motor vehicle is calculated as a function of the movement angles (A _F , A _R ) and the distance between the front axle and the rear axle (1). Method according to one of the preceding claims, wherein the measured lateral acceleration (a _{y, obs} ) and the measured yaw rate (θ̇ _obs ) are low-pass filtered. Sensor system for a motor vehicle with - a sensor device for detecting a measured lateral acceleration (a _{y, obs} ), a measured yaw rate (θ̇ _obs ), a steering angle (δ _F ) of a front axle, a steering angle of a rear axle (δ _R ) and in each case a rotational speed for the front axle (RPS _F ) and rear axle (RPS _R ) and - an evaluation unit, the evaluation unit being designed to process the quantities detected by the sensor device in accordance with a method according to the preceding claims. Sensor system according to Claim 16 , wherein the sensor device comprises a gyroscope for measuring the measured yaw rate (θ̇ _obs ), a steering angle sensor for measuring the steering angle (δ _F , δ _R ), an acceleration sensor for measuring the measured lateral acceleration (a _{y, obs} ) and a speed sensor for measuring the each have a rotational speed for the front axle (RPS _F ) and for the rear axle (RPS _R ). Sensor system according to one of the Claims 16 or 17th , wherein the sensor device has a low-pass filter for filtering the measured lateral acceleration (a _{y, obs} ) and the measured yaw rate (θ̇ _obs ). Computer program product with program code means which are stored on a computer-readable medium in order to carry out the method according to one of the preceding claims when the computer program product is processed on a processor of an electronic evaluation unit. Vehicle assistance system with a computer program product Claim 19 . Motor vehicle with a vehicle assistance system Claim 20 .

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