DE102017219918A1 - A method for calculating a tire circumference of a tired wheel of a motor vehicle and means for calculating the tire circumference - Google Patents

Abstract

The invention relates to a method for calculating a tire circumference (R _n ) of a tired wheel (2, 3, 4, 5) of a motor vehicle (1), wherein during a calculation step the following steps are carried out: determining a longitudinal acceleration (a _x ) of the motor vehicle (1) by means of an acceleration sensor, a rotational speed (α _n ) of the wheel (2,3,4) and a rotational acceleration (ω _n ) of the wheel (2,3,4,5); Establishing a linear differential equation with on the one hand the longitudinal acceleration (a _x ) and on the other hand the sum of the product of the rotational acceleration (α _n ) and the tire circumference (R _n ) and the product of the rotational speed (ω _n ) and a derivative of the tire circumference (R _n ) after the time (t); Calculate the tire circumference (R _n ) by solving the differential equation. The invention further relates to a device (9) for calculating a tire circumference (R _n ) of a tired wheel (2) of a motor vehicle (1).

Description

The invention relates to a method for calculating a tire circumference of a tired wheel of a motor vehicle and also to a device for calculating the tire circumference.

From the prior art, for example, the publication DE 10 2010 000 867 A1 known. This relates to a method and a vehicle system for determining an updated wheel circumference, radius and / or diameter of at least one wheel of a vehicle on a ground. To increase the accuracy of the updated wheel circumference, radius, and / or diameter, the updated wheel circumference, radius, or diameter is determined from an assumed wheel circumference, radius, or diameter, a measured wheel acceleration signal, and a corrected vehicle acceleration signal.

Furthermore, the document shows DE 10 2009 033 060 A1 a tire contact patch determining device and a corresponding method. From the publication DE 10 2006 058 567 A1 Finally, a method and an arrangement for determining an updated wheel circumference of at least one arranged on a vehicle wheel out.

It is an object of the invention to provide a method for calculating a tire circumference of a tired wheel of a motor vehicle, which has advantages over known methods, in particular realized a higher accuracy.

This is achieved according to the invention by a method having the features of claim 1. It is provided that during a calculation step, the following steps are carried out: determining a longitudinal acceleration of the motor vehicle by means of an acceleration sensor, a rotational speed of the wheel and a rotational acceleration of the wheel; Establishing a linear differential equation with on the one hand the longitudinal acceleration and on the other hand the sum of the product of the rotational acceleration and the tire circumference and the product of the rotational speed and a derivative of the tire circumference with time; and calculating the tire circumference by solving the differential equation.

The tire circumference of the wheel is needed at numerous points for dynamic driving calculations. This includes, for example, a calculation or estimation of a vehicle longitudinal speed, a vehicle lateral speed or a slip angle. Also in the context of an electronic stability program, the tire circumference can be used, for example for electronic longitudinal guidance and / or transverse guidance of the motor vehicle. The tire circumference is stored in a control unit of the motor vehicle.

Because the tire circumference may change during travel due to a change in the vehicle speed and / or due to a change in environmental conditions, the actual tire circumference does not coincide with the tire circumference stored in the control unit. For this reason, the tire circumference should be calculated or estimated, in particular based on the tire circumference stored in the control unit. For this purpose, there are various approaches, which, however, are disadvantageous in terms of their accuracy.

According to the invention, different variables relating to the motor vehicle and the wheel will now be detected. Thus, with regard to the motor vehicle, its longitudinal acceleration is used, which is measured by means of the acceleration sensor. The acceleration sensor is preferably a gravitationally compensated acceleration sensor that has high accuracy in determining the longitudinal acceleration.

In addition, the rotational speed of the wheel and its spin are detected. For example, it is provided to detect the rotational speed of the wheel by means of a speed sensor and to calculate the rotational acceleration by a derivative of the rotational speed with time. Of course, the spin can also be determined in other ways.

In any case, the rotational speed of the wheel is to be understood as meaning its rotational speed about an axis of rotation about which the wheel is rotatably mounted in or on a wheel bearing. The rotational acceleration analogously describes the rotational acceleration with respect to this axis of rotation. In other words, the longitudinal acceleration is a global quantity for the motor vehicle, whereas the rotational speed and the spin are local variables for the wheel.

After determining the variables mentioned, the linear differential equation is set up. For this purpose, the longitudinal acceleration, the rotational speed, the spin and the tire circumference and its derivative are used over time. For the derivation of the tire circumference after time, for example, an estimate or, alternatively, a value of zero can be used if the tire circumference does not yet have an older value.

verwendet, wobei a_x die Längsbeschleunigung des Kraftfahrzeugs, R_n der Reifenumfang, α_n die Drehbeschleunigung und ω_n die Drehgeschwindigkeit bezeichnet. Der Term dR_n/dt bezeichnet die Ableitung des Reifenumfangs nach der Zeit. Das Subskript n bezeichnet ein bestimmtes Rad des Kraftfahrzeugs, wobei n rein beispielsweise FL (vorne links), FR (vorne rechts), RL (hinten links) oder RR (hinten rechts) sein kann. Specifically, the relationship becomes for the linear differential equation $$a_x=R_n{\alpha }_n+\frac{d{R}_n}{dt}{\omega }_n$$

used, where a _x the longitudinal acceleration of the motor vehicle, R _n the tire circumference, α _n the spin and ω _n denotes the rotational speed. The term dR _{n / dt} refers to the derivation of the tire circumference after the time. Subscript n denotes a particular wheel of the motor vehicle, where n is purely for example FL (Left in the front), FR (front right), RL (back left) or RR (back right) can be.

Subsequently, the tire circumference is determined by solving the differential equation. Basically, any method for solving differential equations can be used, preferably the solution of the differential equation is determined by means of a Kalman filter or an RLS algorithm (RLS: Recursive Least Squares). This approach allows calculating the tire circumference of the wheel of the motor vehicle with extremely high accuracy, because the sizes used for the calculation can all be determined with high accuracy.

A further development of the invention provides that the calculation of the tire circumference is carried out iteratively by repeating the calculation step one or more times. The calculation step includes both determining the quantities, setting up the differential equation and solving them to calculate the tire circumference. It has already been mentioned above that when the differential equation is first set up, there may not yet be any values for determining the derivative of the tire circumference after the time.

For this reason, the calculation step is repeated one time or several times in time immediately one after the other, and the tire circumference calculated in the previous calculation step is used to determine the derivative of the tire circumference with respect to time. Preferably, the calculation is repeated until the change of the tire circumference with respect to the tire circumference calculated in the previous calculation step is smaller than a limit value. In this case, it can be considered that a sufficient number of calculation steps have been performed to achieve a certain accuracy. By repeating the calculation step, the accuracy of the determined tire circumference can be significantly increased.

A particularly preferred further embodiment of the invention provides that the tire circumference is a product of a reference tire circumference stored in a control unit and a correction factor and, as a derivative of the tire circumference, a product of the reference tire circumference and a derivative of the correction factor with respect to time. It was explained at the beginning that the tire circumference is stored in the control unit. This stored tire circumference is referred to in this description as reference tire circumference.

wobei K_n den Korrekturfaktor und R_BUS den Referenzreifenumfang beschreibt. Der Term dK_n/dt ist die Ableitung des Korrekturfaktors nach der Zeit. Diese Vorgehensweise ermöglicht eine einfache und effiziente Berechnung des Reifenumfangs.Finally, the goal of the method is to determine the correction factor, so that the actual tire circumference can be simply determined from the reference tire circumference and the correction factor during a driving operation of the motor vehicle. In this respect, also for reasons of space, not the tire circumference is stored for one or more wheels, but always only a corresponding correction factor. With the given quantities, the relationship is obtained for the differential equation $$a_x=K_n{R}_{BUS}{\alpha }_n+\frac{d{K}_n}{dt}{R}_{BUS}{\omega }_n.$$

in which K _n the correction factor and R _BUS describes the reference tire circumference. The term dK _{n / dt} is the derivative of the correction factor over time. This procedure allows a simple and efficient calculation of the tire circumference.

A further embodiment of the invention provides that the tire circumference is calculated from the differential equation by means of a Kalman filter or an RLS algorithm. This has already been pointed out above. Both procedures make it possible to calculate the tire circumference from the differential equation with comparatively low computational expenditure and at the same time high accuracy, above all because only a small number of computational steps is necessary.

A particularly preferred embodiment of the invention provides that the calculation of the tire circumference is carried out during a straight-ahead travel of the motor vehicle. To check whether the straight ahead is present, for example, a yaw rate of the motor vehicle is determined. If the determined yaw rate is smaller than a yaw rate limit, the calculation of the tire circumference is performed. If the yaw rate exceeds the yaw rate limit during computation, the computation is aborted to avoid corrupting the result. Restricting the calculation of the tire circumference to the straight-ahead allows neglecting otherwise relevant terms, so that for the Calculating the tire circumference necessary calculation effort significantly reduced.

In a further embodiment of the invention can be provided that the wheel is used as a reference wheel and is determined from the tire circumference of the tire circumference of at least one other wheel. It is therefore initially intended to determine the tire circumference of the reference wheel and then to use this as the basis for determining the tire circumference of the at least one further wheel. This means that setting up the differential equation is only necessary for the reference wheel and not for the other wheel, resulting in a reduction of the computational effort. Of course, however, it can also be provided that the differential equation is set up and released for the further wheel in order to determine the tire circumference of the further wheel.

A particularly preferred embodiment of the invention provides that a distance traveled by the reference wheel and a covered distance of the other wheel are determined by integrating the rotational speed of the respective wheel until the distance traveled by the reference wheel corresponds to a specific value. In other words, the rotational speeds of the reference wheel and the other wheel are determined and integrated over time, so that for each of the wheels results in each covered distance. The integration is terminated when the distance covered corresponds to the determined value. After integrating, the distance traveled therefore lies in each case for the reference wheel and the further wheel, this distance corresponding to the specific value for the reference wheel.

This approach is a particularly simple way to close from the tire circumference of the reference wheel on the tire circumference of the other wheel. It is particularly preferably provided that the integration of the rotational speed for the wheels is carried out only during the straight-ahead driving of the motor vehicle, that is, when the yaw rate of the motor vehicle is smaller than the yaw rate limit. In this case, disturbing influences on the calculation of the distance covered in each case are avoided.

gilt, wobei S_r die zurückgelegte Wegstrecke des Referenzgrads, S_r die zurückgelegte Wegstrecke des weiteren Rads, R_n den Reifenumfang des Referenzrads und R_r den Reifenumfang des weiteren Rads bezeichnet.A particularly preferred development of the invention provides that a tire circumference of the further wheel is determined from the traveled distance of the reference wheel, the traveled distance of the further wheel and the tire circumference of the reference wheel. From the assumption that the motor vehicle has traveled a certain distance, it follows that the relationship $${\text{S}}_{\text{n}}{\text{R}}_{\text{n}}={\text{S}}_{\text{r}}{\text{R}}_{\text{r}}$$

applies, where S _r the distance covered by the reference degree, S _r the traveled distance of the other wheel, R _n the tire circumference of the reference wheel and R _r denotes the tire circumference of the other wheel.

Finally, within the scope of a preferred further embodiment of the invention, it can be provided that a reference wheel factor for the further wheel is determined from the traveled distance of the reference wheel and the traveled distance of the further wheel by means of division or linear regression, and the tire circumference of the further wheel is determined from the reference wheel factor and the tire circumference of the reference wheel is determined. The reference wheel factor here describes the relationship between the tire circumference of the reference wheel and the tire circumference of the other wheel.

The reference wheel factor is stored analogously to the correction factor in the control unit and can subsequently be used for determining the tire circumference of the further wheel, namely by being multiplied by the tire circumference of the reference wheel. The determination of the reference wheel factor can be effected, for example, by means of division or by means of linear regression, the former being particularly advantageous with regard to the computing time. However, when using linear regression, higher accuracy can be achieved.

The invention further relates to a device for calculating a tire circumference of a tired wheel of a motor vehicle, in particular for carrying out the method according to the statements in the context of this description, wherein the device is adapted to perform the following steps during a calculation step: determining a longitudinal acceleration of a motor vehicle by means an acceleration sensor, a rotational speed of the wheel and a rotational acceleration of the wheel; Establishing a linear differential equation with on the one hand the longitudinal acceleration and on the other hand the sum of the product of the rotational acceleration and the tire circumference and the product of the rotational speed and a derivative of the tire circumference with time; Calculate the tire circumference by solving the differential equation.

The advantages of such an approach or such an embodiment of the device has already been pointed out. Both the device and the method for its operation can be further developed according to the statements in the context of this description, so that reference is made to this extent.

• 1 eine schematische Darstellung eines Kraftfahrzeugs,
• 2 eine schematische Darstellung eines Rad des Kraftfahrzeugs in einem Radkoordinatensystem, sowie
• 3 eine schematische Darstellung einer Einrichtung zur Berechnung eines Reifenumfangs des Rads.

The invention will be explained in more detail with reference to the embodiments illustrated in the drawings, without any limitation of the invention. Showing:

• 1 a schematic representation of a motor vehicle,
• 2 a schematic representation of a wheel of the motor vehicle in a wheel coordinate system, and
• 3 a schematic representation of a device for calculating a tire circumference of the wheel.

The 1 shows a schematic representation of a motor vehicle 1 during cornering and a curve center M. The motor vehicle 1 has four wheels 2 . 3 . 4 and 5 on, with the wheels 2 and 3 a front axle 6 and the wheels 4 and 5 a rear axle 7 of the motor vehicle 1 as well as the wheels 3 and 5 a first lane and the wheels 2 and 4 associated with a second lane. In other words, the wheel 2 front left, the wheel 3 front right, the wheel 4 rear left and the wheel 5 back right.

Also indicated is a focus 8th of the motor vehicle, in which at the same time a motor vehicle-related coordinate system has its origin. Regarding the center of gravity 8th the motor vehicle has a longitudinal speed V _x and a cross speed V _y on. Lever arms of the motor vehicle 1 , ie the distance of the center of gravity 8th to the front axle 6 and the rear axle 7 are through I _f for the front axle 6 and I _r for the rear axle 7 indicated. Gauges of the front axle 6 and the rear axle 7 are through b _f for the front axle 6 and b _r marked for the rear axle.

Each of the wheels 2 . 3 . 4 and 5 can be a longitudinal acceleration a _{i, x} and a lateral acceleration a _{n, y} be assigned, where n is the respective wheel 2 . 3 . 4 respectively 5 designated. For the wheel 2 n = FL, for the wheel 3 n = FR, for the wheel 4 n = RL and for the wheel 5 n = RR. Furthermore, for the wheels 2 . 3 . 4 and 5 in each case the steering angle δ _n where n is as above.

When driving the motor vehicle 1 around the center of the curve M results for the center of gravity curve radius R _SP , for the wheel 2 a curve radius R _FL and for the bike 4 a curve radius R _RL , It is further evident that each of the wheels 2 . 3 . 4 and 5 each two separate coordinate systems are zugordnet, with a first of these wheel coordinate systems only translational with respect to the center of gravity 8th whereas a second one of the wheel coordinate systems is shifted by the steering angle with respect to the first wheel coordinate system δ _n is turned. The distance of the origins of the two wheel coordinate systems from the center of gravity 8th is indicated by the values in parentheses.

sowie $${\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]}_{X\text{'}\text{'}Y\text{'}\text{'}}=\left[\begin{array}{cc}\text{cos}{\delta }_n& -\text{sin}{\delta }_n\\ \text{sin}{\delta }_n& \text{cos}{\delta }_n\end{array}\right]\left[\left[\begin{array}{c}{V}_x\\ V_Y\end{array}\right]+\left[\begin{array}{c}-b_f/2\\ l_f\end{array}\right]{\omega }_z\right],$$

für die beiden Radkoordinatensysteme, die durch Subskripte gekennzeichnet sind. Aufgelöst folgt hieraus: $${\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]}_{X\text{'}\text{'}Y\text{'}\text{'}}=\left[\begin{array}{c}\left(\left(V_x-\frac{b_f}{2}{\omega }_z\right)\text{cos}{\delta }_n-\left(V_y+l_f{\omega }_z\right)\text{sin}{\delta }_n\right)\\ \left(\left(V_x-\frac{b_f}{2}{\omega }_z\right)\text{sin}{\delta }_n+\left(V_y+l_f{\omega }_z\right)\text{cos}{\delta }_n\right)\end{array}\right].$$

The 2 shows a detailed representation of the wheel 2 , where clearly the two wheel coordinate systems can be recognized. The first wheel coordinate system is by the axis designations X ' and Y ' whereas the second wheel coordinate system is characterized by the axis designations X " and Y " Marked are. Using the terms defined above α _i for the spin and ω _i for a rotational speed of the wheels 2 . 3 . 4 and 5 the following relationships apply $${\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]}_{X\text{'}Y\text{'}}=\left[\begin{array}{c}{V}_x\\ V_Y\end{array}\right]+\left[\begin{array}{c}-b_f/2\\ l_f\end{array}\right]{\omega }_z$$

such as $${\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]}_{X\text{'}\text{'}Y\text{'}\text{'}}=\left[\begin{array}{cc}\text{cos}{\delta }_n& -\text{sin}{\delta }_n\\ \text{sin}{\delta }_n& \text{cos}{\delta }_n\end{array}\right]\left[\left[\begin{array}{c}{V}_x\\ V_Y\end{array}\right]+\left[\begin{array}{c}-b_f/2\\ l_f\end{array}\right]{\omega }_z\right].$$

for the two wheel coordinate systems, which are identified by subscripts. Dissolved follows from this: $${\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]}_{X\text{'}\text{'}Y\text{'}\text{'}}=\left[\begin{array}{c}\left(\left(V_x-\frac{b_f}{2}{\omega }_z\right)\text{cos}{\delta }_n-\left(V_y+l_f{\omega }_z\right)\text{sin}{\delta }_n\right)\\ \left(\left(V_x-\frac{b_f}{2}{\omega }_z\right)\text{sin}{\delta }_n+\left(V_y+l_f{\omega }_z\right)\text{cos}{\delta }_n\right)\end{array}\right],$$

If this relationship is derived over time without taking the steering angle gradient into account: $${\left[\begin{array}{c}\frac{d}{dt}{V}_x\\ \frac{d}{dt}{V}_y\end{array}\right]}_{X\text{'}\text{'}Y\text{'}\text{'}}=\left[\begin{array}{c}\left(\frac{d}{dt}\left(V_x-\frac{b_f}{2}{\omega }_z\right)\text{cos}{\delta }_n-\frac{d}{dt}\left(V_y+l_f{\omega }_z\right)\text{sin}{\delta }_n\right)\\ \left(\frac{d}{dt}\left(V_x-\frac{b_f}{2}{\omega }_z\right)\text{sin}{\delta }_n+\frac{d}{dt}\left(V_y+l_f{\omega }_z\right)\text{cos}{\delta }_n\right)\end{array}\right],$$

When using a gravitationally compensated lateral acceleration sensor: $$\left[\begin{array}{c}\frac{d}{dt}{V}_x\\ \frac{d}{dt}{V}_y\end{array}\right]=\left[\begin{array}{c}{a}_x+{\omega }_z{V}_y\\ a_y+{\omega }_z{V}_x\end{array}\right],$$

From this follows for the above relationship: $${\left[\begin{array}{c}\frac{d}{dt}{V}_x\\ \frac{d}{dt}{V}_y\end{array}\right]}_{X\text{'}\text{'}Y\text{'}\text{'}}=\left[\begin{array}{c}{a}_x-\frac{d{\omega }_z}{dt}\frac{b_f}{2}-\frac{d{\omega }_z}{dt}{l}_f{\delta }_n\\ a_x{\delta }_n-\frac{d{\omega }_z}{dt}\frac{b_f}{2}{\delta }_n+\frac{d{\omega }_z}{dt}{l}_f\end{array}\right],$$

For each of the wheels: $$\frac{d{V}_{x.n}}{dt}=R_n{\alpha }_n+\frac{d{R}_n}{dt}{\omega }_n$$

die bei kleiner Gierrate ω_z durch Ignorieren eines Effekts der Gierrate und einer Spurbreite vereinfacht werden kann zu: $$a_x=R_n{\alpha }_n+\frac{d{R}_n}{dt}{\omega }_n.$$

This ultimately results in the relationship $$a_x-\frac{d{\omega }_z}{dt}\frac{b_f}{2}-\frac{d{\omega }_z}{dt}{l}_f{\delta }_n=R_n{\alpha }_n+\frac{d{R}_n}{dt}{\omega }_n.$$

the at low yaw rate ω _z by ignoring a yaw rate effect and a track width can be simplified to: $$a_x=R_n{\alpha }_n+\frac{d{R}_n}{dt}{\omega }_n,$$

Using a reference tire circumference R _BUS and a correction factor K _n this equation can be expressed as: $$a_x=K_n{R}_{BUS}{\alpha }_n+\frac{d{K}_n}{dt}{R}_{BUS}{\omega }_n,$$

In summary for all wheels applies accordingly: $$\left[\begin{array}{c}{a}_x\\ a_x\\ a_x\\ a_x\end{array}\right]=\left[\begin{array}{c}{K}_{FL}{R}_{BUS}{\alpha }_{FL}+\frac{d{K}_{FL}}{dt}{R}_{BUS}{\omega }_{FL}\\ K_{FR}{R}_{BUS}{\alpha }_{FR}+\frac{d{K}_{FR}}{dt}{R}_{BUS}{\omega }_{FR}\\ K_{RL}{R}_{BUS}{\alpha }_{RL}+\frac{d{K}_{RL}}{dt}{R}_{BUS}{\omega }_{RL}\\ K_{RR}{R}_{BUS}{\alpha }_{RR}+\frac{d{K}_{RR}}{dt}{R}_{BUS}{\omega }_{RR}\end{array}\right],$$

The 3 shows a device 9 for determining the tire circumference of the wheel 2 , which is used as a reference wheel by way of example. An arithmetic unit 10 For this purpose, the required values are supplied, in particular the longitudinal acceleration a _x on the one hand and the sum of the product of a reference tire circumference R _BUS and the spin of the wheel 2 and the product of the reference tire circumference R _BUS , the rotational speed of the wheel 2 and the derivative of the correction factor over time.

The summands are in one unit 11 merged and then the arithmetic unit 10 fed. Furthermore, in one unit 12 checked if the longitudinal acceleration a _x is sufficiently large, in particular at least corresponds to a longitudinal acceleration minimum value. Furthermore, in one unit 13 checked for a yaw rate of the motor vehicle 1 is sufficiently small.

The results of in the units 12 and 13 Employed comparisons are made as part of a unit 14 subjected to a and comparison and the result also the arithmetic unit 10 fed. For example, it is provided that both conditions must be met. Otherwise, the calculation of the tire circumference is canceled or not initiated at all. As the output of the arithmetic unit 10 results in the correction factor K, which is part of a unit 15 derived over time and the derivative is returned.

The procedure described allows a very exact determination of the tire circumference of the wheel 2 , which is used here as a reference wheel. The tire circumference of the reference wheel can then on the other wheels 3 . 4 and 5 of the motor vehicle 1 be transmitted. This has already been discussed in the context of this description, so that reference is made to the corresponding statements.

QUOTES INCLUDE IN THE DESCRIPTION

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Cited patent literature

• DE 102010000867 A1 [0002]
• DE 102009033060 A1 [0003]
• DE 102006058567 A1 [0003]

Claims (10)

Method for calculating a tire circumference (R _n ) of a tired wheel (2, 3, 4, 5) of a motor vehicle (1), wherein the following steps are performed during a calculation step: - determining a longitudinal acceleration (a _x ) of the motor vehicle (1) by means of an acceleration sensor, a rotational speed (α _n ) of the wheel (2, 3, 4) and a rotational acceleration (ω _n ) of the wheel (2, 3, 4, 5), establishing a linear differential equation with, on the one hand, the longitudinal acceleration (a _x ) and on the other hand the sum of the product of the rotational acceleration (α _n ) and the tire circumference (R _n ) and the product of the rotational speed (ω _n ) and a derivative of the tire circumference (R _n ) after the time (t), - calculating of the tire circumference (R _n ) by solving the differential equation. Method according to Claim 1 , characterized in that the calculation of the tire circumference (R _n ) is carried out iteratively by repeating the calculation step one or more times. Method according to one of the preceding claims, characterized in that the tire circumference (R _n ) is a product of a reference tire circumference (R _BUS ) stored in a control unit and a correction factor (K _n ) and a derivative of the tire circumference (R _n ) Reference _{tire circumference} (R _BUS ) and a derivative of the correction factor (K _n ) after the time (t) is used. Method according to one of the preceding claims, characterized in that the tire circumference (R _n ) is calculated from the differential equation by means of a Kalman filter or an RLS algorithm. Method according to one of the preceding claims, characterized in that the calculation of the tire circumference (R _n ) during a straight-ahead travel of the motor vehicle (1) is performed. Method according to one of the preceding claims, characterized in that the wheel (2,3,4,5) is used as a reference wheel and from the tire circumference (R _n ) of at least one further wheel (2,3,4,5) is determined. Method according to one of the preceding claims, characterized in that a distance traveled by the differential wheel (2) and a traveled distance of the other wheel (3,4,5) by integration of the rotational speed (ω _n ) of the respective wheel (2,3,4 , 5) are determined until the traveled distance of the reference wheel (2) corresponds to a certain value. Method according to one of the preceding claims, characterized in that from the traveled distance of the reference wheel (2), the traveled distance of the further wheel (3,4,5) and the tire circumference (R _n ) of the reference wheel (2) a tire circumference (R _n ) of the other wheel (3,4,5) is determined. Method according to one of the preceding claims, characterized in that from the distance traveled by the reference wheel (2) and the distance covered by the further wheel (3,4,5) by means of division or linear regression a reference wheel factor (K _n ) determined for the other wheel and the tire circumference (R _n ) of the further wheel (3, 4, 5) is calculated from the reference wheel factor (K _n ) and the tire circumference (R _n ) of the reference wheel (2). Device (9) for calculating a tire circumference (R _n ) of a tired wheel (2) of a motor vehicle (1), in particular for carrying out the method according to one or more of the preceding claims, wherein the device is designed to carry out the following steps during a calculation step to perform: - Determining a longitudinal acceleration (a _x ) of the motor vehicle (1) by means of an acceleration sensor, a rotational speed (ω _n ) of the wheel (2) and a rotational acceleration (α _n ) of the wheel (2), - Establishing a linear differential equation on the one hand the longitudinal acceleration (a _x ) and on the other hand the sum of the product of the rotational acceleration (α _N ) and the tire circumference (R _i ) and the product of the rotational speed (ω _n ) and a derivative of the tire circumference (R _n ) by time ( t), calculating the tire circumference (R _n ) by solving the differential equation.

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