Method to determine tire circumference and corresponding ECU for vehicle

Abstract

The invention relates to a method to determine a tire circumference value of a tire of at least one wheel (RL, RR) of a vehicle (1), during movement of the vehicle (1), the method comprising: a GPS di

Description

The invention relates to a method to determine a tire circumference of a wheel of a vehicle, and an electronic control unit adapted to execute the method during movement of the vehicle. In certain automated automotive systems, like parking systems, the estimation of the current position of the vehicle is crucial. The estimated position is needed to control the vehicle on the planned trajectory towards to final parking position. The vehicle position is estimated using the wheel pulses provided by the wheel speed sensors connected to the AntiBrake Lock System (ABS). This gives an information about the current wheel rotational angle. Knowing the tire circumference, the vehicle’s longitudinal displacement can be determined. The prior art uses GPS and wheel speed sensor data to estimate the tire circumference of the rear wheel. It relies on GPS and wheel speed sensor data to reduce the uncertainties which in turn improves the precision requirement offer example a modern automated parking system. The high noises from GPS data can lead to inaccurate determination of vehicle driven distance and it leads to inaccurate and very slow convergence of the true tire circumference value estimation as observed in said prior art. This results in that the prior art requires more driven distance to learn the accurate tire circumference, shows non convergence during driving maneuver with high accelerations and decelerations and it Is unable to learn at velocities beyond 80kph. Inaccuracies in the online estimated tire circumference has increased the error accumulation in the driven distance and in vehicle position estimations. For these reasons, the known method of estimating tire circumference cannot be used for other applications like deflated tires detection or tire pressure level detection. Finally, the prior art shows no structure to store the t-1 learned estimations and utilize it when needed. Against this background, it is an object of the invention to provide for a method to determine a tire circumference of a wheel of a vehicle, and a corresponding electronic control unit capable of fast and reliably determining a “true” circumference value of a wheel including Its tire. In any case, It Is a further object of the invention to provide for an alternative method and electronic control unit. These objects are achieved by a method according to claim 1 and an electronic control unit according to claim 9. The method according to the invention determines a tire circumference value of a tire of at least one wheel of a vehicle during movement of the vehicle, wherein the method comprises: - a GPS displacement determining step of obtaining GPS data and determining a GPS displacement of the vehicle; - a movement sensor displacement calculating step of obtaining movement sensor data and calculating a movement displacement of the vehicle; wherein the GPS displacement determining step and movement sensor displacement calculating step are executed in predetermined intervals during movement of the vehicle; and - a recursive circumference determination step, which is executed in each of the intervals, of determining a latest circumference value of the tire using (i) a preceding circumference value determined in a preceding interval of the predetermined intervals, (ii) the movement displacement and a corresponding movement sensor measurement noise, and (Hi) the GPS displacement and a corresponding GPS measurement noise, wherein, for determining the latest circumference value in the recursive circumference determination step, the GPS measurement noise is adapted under consideration of the movement displacement. The movement sensor data are obtained by a movement sensor like an angular-displacement-sensor / wheel speed sensor allocated to said wheel. The circumference values (the latest and the previous) as well as the movement displacement are preferably mean values. Preferably, the vehicle is a car like a SUV, a truck, a bus, or a motor bike. Compared to the case that no adaptation of the GPS measurement noise takes place, the implementation of the recursive circumference determination step provides for fast and reliable convergence of the estimated tire circumference value towards the actual true tire circumference value. In particular, the said convergence requires less driven distances and takes place during driving maneuvers with high accelerations and decelerations as well as higher velocities of the vehicle. In the method, preferably, the predetermined intervals are defined by n being an update count value of counting updates of the GPS data, wherein the predetermined intervals are preferably defined by n >= 2, 3, 4, 5, 6, 7, 8, 9 or 10. The value n Is preferably 3, 4, 5, 6, 7, 8, 9 or 10 which allows to cope with overestimations and underestimation of the GPS data. The method is executed preferably, wherein the circumference value of the tire is determined for a tire of a rear-left-wheel and a tire of a rear-right-wheel of the vehicle, in the movement sensor displacement calculating step, the movement displacement of the vehicle is calculated using (i) the preceding circumference value of the tire of the rear-right-wheel together with an output of a rear-right-wheel angular displacement sensor measuring an angular displacement of the rear-right-wheel, and (ii) the preceding circumference value of the tire of the rear-left-wheel together with an output of a rear-left-wheel angular displacement sensor measuring an angular displacement of the rear-left-wheel. Since the circumference values of the rear wheels are determined, the values can preferably be used in an odometry of a parking system with respect to a rear axle of the vehicle. The method is executed preferably, wherein the recursive circumference determination step comprises a Kalman filter to determine the latest circumference value, the Kalman filter using a measurement noise covariance matrix (R) defining, as the GPS measurement noise, a GPS variance of the GPS displacement and, as the movement sensor measurement noise, an angular displacement variance of the displacement of the rear-right-wheel and an angular displacement variance of the displacement of the rear-left-wheel, and, for determining the latest circumference value in the recursive circumference determination step, the GPS variance is adapted using the movement displacement of the vehicle. Preferably, said Kalman filter is an Extended Kalman filter (EKF), which includes linearizing of a non-linear measurement model. Moreover, a prediction step of the Extended Kalman filter preferably accounts for control inputs (Bz). Preferably, in the movement sensor displacement step, the movement displacement is calculated on the basis of an expression of: I-------------------------------------------------------------;----------------------------------------------------; M = --------~----------, where = estimated nearest maximum likelihood circumference mean value of the rear-right-wheel, = synchronized right wheel angular displacement for n GPS update counts, estjmated nearest maximum likelihood circumference mean value of the rear-left-wheel, = synchronized left wheel angular displacement for n GPS update counts, and AS = calculated movement displacement. The method is executed, preferably, wherein the GPS variance is adapted using the movement displacement of the vehicle, on the basis of a polynomial curve ora Look-up-Table. For example, the mentioned adaptation is done using a polynomial characteristic curve based on a velocity mean value and the calculated displacement based on the nearest maximum likelihood mean values. Or, in the alternative, by using a Look-up-table (LUT). The calculated movement displacement AS, mentioned above, is preferably used as an input along with other variables for constructing the polynomial characteristic curve or the look-up-table which determines the GPS noise variance. After executing the recursive circumference determination step, the method preferably further comprises: a gradient calculating step of calculating a circumference gradient value for the tire of the rear-right wheel, using the latest and preceding circumference values of the tire of the rearright wheel, and a circumference gradient value for the tire of the rear-left wheel, using the latest and preceding circumference values of the tire of the rear-left wheel, wherein, for a predetermined first movement distance of the vehicle, the circumference gradient values are preferably accumulated and compared against a first gradient threshold, and, if the circumference gradient values are within the first gradient threshold, gn(j nbt are updated by the latest circumference value of the tire of the rear-right-wheel and the latest circumference value of the tire of the rear-left-wheel. The predetermined first movement distance is measured, preferably, by GPS data and checked against a first fixed distance threshold. The circumference gradient values are preferably accumulated for the predetermined movement distance by using a respective first circumference gradient variable for each wheel. When ~8and >: are updated, the first circumference gradi ent variables are reset. If the accumulated circumference gradient values reflected by the first circumference gradient variable are not within the first gradient threshold, no update of ;and s takes place. These steps advantageously support for the faster convergence of the vehicle tire circumference estimation towards the actual true tire circumference value. The first predetermined distance is, for example 500 meters. Further the method is preferably executed such that, for a predetermined second movement distance of the vehicle, which is longer than the first movement distance, the circumference gradient values are preferably accumulated and compared against a second gradient threshold, and, if the circumference gradient values are within the second gradient threshold, the latest circumference value of the tire of the rear-right-wheel and the latest circumference value of the tire of the rear-left-wheel are stored as true circumference values of the rear tires. The predetermined second movement distance is measured, preferably, by GPS data and checked against a second fixed distance threshold, to determine the true circumference value. The circumference gradient values are preferably accumulated for the predetermined second movement distance by using a respective second circumference gradient variable for each wheel, to determine the true circumference value. The true circumference values are stored preferably in a non-volatile memory. The invention relates to an electronic control unit for a vehicle, in particular a car like a SUV, a truck, a bus, or a motor bike, storing a computer program, wherein, when executing the computer program, the electronic control unit executes the method according to the invention and, preferably, its preferable steps. The stored true circumference values may be used for certain applications, like an automated parking system, a tire deflation detection or a pressure loss level indication, wherein corresponding results may be presented by a HMI. In the following, a preferred embodiment of the method according to the invention is described, wherein the method is performed by an ECU of a car. The description above holds for the description of the embodiment mutatis mutandis and vice versa. Figure 1 shows schematically a vehicle from above and a corresponding ECU (Electronic Control Unit) which is connected to angular-displacement-sensors / wheel speed sensors each allocated to one of four wheels of the vehicle, a GPS unit / GPS receiver, an IMU unit (Inertial Measurement Unit) and a HMI unit (Human Machine Interface); Figure 2 shows a process flow of a method to determine a tire circumference of a wheel of the vehicle according to the invention, which is executed by the ECU; Figure 3A shows displacement data of GPS data updates of 1 second duration and 3B shows displacement data of n = 3 GPS data updates used in the method according to the invention; Figure 4 shows a test result of a circumference determination of rear left tire of the vehicle using the method according to the invention. Figure 1 schematically shows a vehicle 1, namely car 1, from above. The vehicle 1 comprises four wheels, i.e. a front left wheel FL, a front right wheel FR, a rear left wheel RL, and a rear right wheel RR, an electronic control unit (ECU) 3 including a non-volatile memory 31, a global positioning system (GPS) unit 4, an inertial measurement unit (IMU) 6 and a human machine interface (HMI) 5. Each of the wheels FL, FR, RL, RR carries a corresponding tire. Each of wheels FL, FR, RL, RR is equipped with a corresponding angular-displacement sensor (wheel speed sensor) 2, which Is adapted to measure an angular displacement of the correspondingly allocated wheel FL, FR, RL, RR. Further, the ECU 3 is connected to the inertial measurement unit IMU for measuring a vehicle heading angle and, as will be mentioned in the following, a vehicle yaw , as well as to a GPS unit 4 to obtain GPS data to measure a displacement of the vehicle 1. The vehicle heading angle M, in the alternative, can be calculated based on a steering model. The ECU 3 Is adapted to execute a method to determine a tire circumference value of a wheel of a vehicle, according to the invention. The ECU 3 has a computer hardware structure and is capable of executing stored computer programs. The method is implemented by such a computer program stored in the ECU 3. When a user starts the vehicle 1, the ECU 3 executes the computer program so as to execute the method according to the invention during movement of the vehicle 1. The described method is executed for the two rear tires of the shown two rear wheels RL, RR of the vehicle 1, i.e. the tires of the rear-left wheel RL and the rear-right wheel RR, so as to determine a circumference value for each of said wheels. Nevertheless, the invention is not limited to the mentioned two tires, and the method to determine the tire circumference value according to the invention can be executed for at least one of the four wheels, or for said two tires, or three tires or all four tires of all the four wheels FL, FR, RL, RR. The determined tire circumference values of the wheels RL, RR, which are considered as the “true” circumferences of said wheels, are stored by the ECU 3, for example, in the non-volatile memory 31, and are usable for certain functions of the vehicle, like an automatic parking system or a tire deflation warning system. Figure 2 shows a process flow of the method according to the invention, which is executed by the ECU 3. The method recursively determines and estimates, respectively, the circumference values of the rear tires by preferably using an Extended Kalman filter. Step SO When the vehicle 1 is started, the ECU 3 executes the step SO, which is an initialization step. In this step, the following initializations are made: - Initialization of states preferably from the non-volatile memory 31, wherein — Rear Rig hr Wheel longitudinal displacement: ASRf. ™ Rear Lef t Wheel longitudinal displacement ~ Rear Right wheel Circumference = Rear Left Wheel Circumference - Initialization of state covariance , ; - Initialization of nearest maximum likelihood mean value and 3. The initial values of the mentioned parameter are retrieved by the ECU 3, for example, from electronic stability control (ESC) parameters. Further, variables used when executing the method are initialized. These variables comprise synchronized variables, circumference gradients, driven distance variables (a first driven distance variable and a second driven distance variable), update-counts and other global variables. The process proceeds to the next step. Step S1 In this step, the ECU 3 gets a synchronized rear-right wheel rotation angle and a synchronized rear-left wheel rotation angle from the correspondingly allocated angular-displacement sensor (wheel speed sensor) 2. The process then proceeds to the next step. Step S2 The method executes, in this step, a state prediction of the state vector sil'in accordance with the Extended Kalman filter, The prediction model used is a constant model which means that the used state transition matrix A is an identity matrix [1 0 0 0' 0 10 0 0 0 1 0 0 C 0 1. But the state prediction accounts for the control inputs Su and the process covariance , where and u = ~ (u = Acceleration / Deceleration), and 0 0 a 0 •0 a (1 0 0 .. •> . 0 a 0 Simultaneously and in parallel to S1 and S2, the ECU 3 receives GPS data from the GPS unit 4. An update interval of receiving new GPS data from the GPS unit 4 takes around 1 second (1 hertz). Then, in C1, the method specifies whether an update count value of updating the GPS data has reached a predetermined value n. If not, the process proceeds to Step S3. Step S3 In this step, the obtained learned / estimated (predicted) circumference values are set to false or discarded, and are not stored. The process then returns to step S1. The loop S1, S2, C1 (No), S3 is executed until the update count value, i.e. a number of GPS updates, has reached the predetermined value n. Preferably, the predetermined value n is set to 3, but the invention is not limited to this value and may be different. The used GPS unit 4 is preferably a peak GPS receiver unit and the value of n=3 results leads to beneficial results to cope with overestimations and underestimations of GPS displacement data which would be observed in case of n=1 (or approximately 1-second GPS updates). This is supported by comparing Figures 3A and 3B, where 3A shows the 1 second duration GPS displacement data and 3B the GPS displacement data for n=3. Consequently, said loop is executed as long as n<3. One loop takes around 10 milliseconds. The ECU 3 stores the received GPS data and the synchronized rear-right wheel rotation angle and the synchronized rear-left wheel rotation angle in a ring buffer. Each GPS update takes approximately around 1 second (1 hertz), so that all the three GPS updates take around 3 seconds. The ECU 3 keeps accumulating the synchronized rear-right wheel rotation angle and the synchronized rear-left wheel rotation angle for the three GPS updates, i.e. until n=3. When n reaches n=3, C1 specifies (Yes) that the update count value of updating the GPS data has reached n=3, and proceeds to Step S4. Step S4 In this step, the ECU 3 sets a measurement vector = where ASaifc = far 3 SES cwse. ASsssi = GPS mw fcr 3 GPScycfe. = jj-ieasutw cefe:cfejw / ram iMt / for the Extended Kalman filter on the basis of the measured data stored in the ring buffer. This includes the execution of a GPS displacement determining step of obtaining the stored GPS data from the ring buffer and determining the GPS displacement of the vehicle 1. Figure 3B shows displacements ASg^ in meters on the Y-axis for a number of three GPS update cycles (n=3), as an example. The three GPS updates take as mentioned around 3 seconds. Moreover, a part of a movement sensor displacement calculating step is executed, wherein the synchronized rear-right wheel angular displacement and the synchronized rear-left wheel angular displacement are obtained from the rotation angles accumulated for the three GPS updates, stored in the ring buffer. The measured vehicle yaw is obtained by the ECU 3 from the IMU 6. The process proceeds then to the next step. Step S5 In this step, a further part of the movement sensor displacement calculating step is executed, wherein a movement displacement AS of the vehicle 1 is calculated, using the following formula AS- \W / \2TT) 2 where Estimated nearest maximum likelihood circumference mean value of the rear right tire. Estimated nearest maximum likelihood circumference mean value of the rear left tire. If it is the first calculation after vehicle start, the estimated nearest maximum likelihood circumference mean values correspond to the initialized values of step SO. The process proceeds then to the next step. Step S6 Essential for the invention, the calculated movement displacement AS of the vehicle 1 is used to set the measurement noise matrix % of the Extended Kalman filter. 6 0 ” e 0 0 Q 0 Q 0 0 Ml- where a is a wheel noise scale factor. In particular, the corresponding to wheel displacement error, gets adapted using the movement displacement AS of the vehicle 1. For example, the mentioned adaptation is done using a polynomial characteristic curve based on a velocity mean value and the calculated displacement based on the nearest maximum likelihood mean values. Or, in the alternative, by using a Look-up-table (LUT). The process proceeds then to the next step. Step S7 In this step, the measurement model M*} is constructed and described as: Measurement Model &(*) At 1 ----------j 2;^ The non-linear measurement model is linearized using 1st order Tailor expansion and partial differentiations to form the Jacobian matrix ♦ 33¾ 3¾ 3% 3¾ 3¾ 3,¾ £ 3¾ 3¾ 3¾ 3¾ 3¾ 33¾ 33¾ fl 0 2 s 0: 0.5 0,5 0 1 I The process proceeds then to the next step. Step S8 In this step, the state update of the Extended Kalman filter takes place, wherein the predicted state gets corrected in a known manner to obtain an updated state and covariance, by: 1¾ Kalman Gain / ¾ = —~ Predicted meas- } urements Innovation / residual )¾ = .¾ ” Updated state - 2¾ + Update Covariance The updated state $ includes the mean values of ). The process proceeds then to the next step. Step S9 In this step, the ECU 3 updates the first driven distance variable and the second driven distance variable by a vehicle displacement which is obtained by the GPS unit 4. The ECU calculates additionally a circumference gradient value for each rear wheel by where Right wheel Circumference gradient, and Left wheel Circumference gradient. The ECU 3 uses the obtained circumference gradient values of the two rear wheels to update (accumulate) a first circumference gradient variable and a second circumference gradient variable. The two circumference gradient variables may be provided for each of the rear wheels (in total two first circumference gradient variables and two second circumference gradient variables) or for both the rear wheels. In the latter case, each of the two circumference gradient variables concern a mean value of both calculated circumference gradient values. Then, in C2, using the first driven distance variable, the ECU 3 specifies whether (i) the vehicle 1 has driven a fixed distance interval of fixed consecutive distance intervals using a first fixed distance threshold. The fixed distance interval and the first fixed distance threshold, respectively, may be 500 meter, for example. In addition, using the (updated) first circumference gradient variable(s), the ECU specifies (ii) whether the accumulated right wheel circumference gradient value and the left wheel circumference gradient value (or their mean value) are within a defined first gradient threshold. If the ECU 3 confirms that the vehicle has driven the fixed distance interval and that the (updated) first circumference gradient variable(s) show(s) the circumference gradient values of both wheels to be within the defined first gradient threshold, the process proceeds to step S11. If not, the process proceeds to step S10. Step S10 In this step, the ECU 3 discards the calculated gradient values and maintains the used nearest maximum likelihood mean values and Step S11 In this step, the ECU 3 updates the nearest maximum likelihood mean values nMLCx#[ and nMLCslby the calculated mean values of step S8 and stores them. Mathematically seen, the nearest maximum likelihood estimate takes the below form under consideration of a Gaussian distribution. .......------------ J The following equations show how the values are being optimized dur ing the process and arrives at the best fit mean estimation. After taking the log of Maximum likelihood function, it results in the below form = Log (£0 = Log (jUjs ~ a$.)) The optimization happens by taking the log of maximum likelihood function resulting in equations: --- — (- -- (£02 = == (- (£(^ = = - (log (£-{g = - (log (£:« - Moreover, in S11, the ECU 3 resets the first driven distance variable and the first circumference gradient variable(s). Then, in C3, the ECU specifies, using the second driven distance variable, whether (i) the vehicle 1 has driven another fixed distance interval of another fixed consecutive distance intervals using a second fixed distance threshold. The another fixed distance interval and the second fixed distance threshold, respectively, are longer than the first fixed distance threshold, and may be 2000 meter, for example. In addition, using the (updated) second circumference gradient variable(s), the ECU 3 specifies (ii) whether the accumulated right wheel circumference gradient value and the left wheel circumference gradient value (or their mean value) are within a defined second gradient threshold. If the ECU 3 confirms that the vehicle has driven the another fixed distance interval and that the (updated) second circumference gradient variable(s) show(s) the circumference gradient values of both wheels to be within the defined second gradient threshold, the process proceeds to step S12. If not, the process proceeds to step S1. StepS12 In this step, the ECU sets the obtained data to true, so that the determined (calculated learned / estimated / corrected) mean values of step S8 of the circumference of the rear-right-wheel RR and the circumference of the rear-left wheel RL are written into the nonvolatile memory 31 of the ECU and are considered as the determined "true” circumference values. The values stored in the non-volatile memory 31 are available whenever needed for applications or functions of the vehicle 1. The process proceeds then to Step S1. Actually the whole process runs as long as the vehicle 1 is operated. In general, one cycle of the process from S1 to S1, independent of C1, takes around 10 milliseconds and every 3 GPS updates (approximately every 3 seconds), the steps S4, S5 et sqq. are executed. Figure 4 shows test results of the method according to the invention. The test was conducted on a test track. The circumferences of the wheels amounted to 2.035 meters. The shown results belong to the rear-left wheel. The Y-axis shows the determined circumference and the X-axis the number of GPS data updates. The graph L1 is the determined (estimated) circumference value obtained by the method according to the invention, and the graph L2 is a ground truth tire circumference value of rear left tire calculated using DGPS data (Differential GPS). The Differential GPS device is used as the ground truth to calculate the real tire circumference such that the true tire circumference of summer tires is 2.045m and winter tires are 2.035m. It is evident from Figure 4 that the tire circumference has been learned and converged by the method according to the invention very early compared to the convergence of the case that the measurement noise matrix was static and not adapted. Front wheel circumference The method according to the invention may be used to determine the “true” circumference values for the front wheels as well. In the alternative, preferably, the determined “true” circumference values can be used to derive circumference values of the front wheels as follows: First, it is observed, if the wheels are free rolling. The wheels of the driven axle would rotate faster when the torque gets applied on a camshaft of the vehicle 1. Because of these conditions, the driving situation is checked when the wheel speed on the rear wheels can be compared to the speed of the front wheels. The algorithm executed by the ECU may be summarized as: IF left rear wheel angular velocity in radians per second >PI IF right rear wheel angular velocity in radians per second >PI IF throttle Position percent <Throttle-Position-Threshold (for example 5.0) IF steering wheel angle in radians <PI / Wheel-Angle-Threshold (for example 8.0) IF axle torque in nm <Axle-torque-positive-threshold (for example 120.0) IF axle torque in nm >Axle-torque-negative-threshold (for example -120.0) Front wheels free rolling will be true. ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF IF Front wheels free rolling is true Increment wheel free rolling debounce counter by 1. ELSE Set to 0. ENDIF Sum Wheels Ratio: IF wheels free rolling debounce cycle threshold is less than equal to wheel free rolling debounce counter Increment the sum left wheel ratio by the left front and left rear wheel angular velocity ratio. Increment the sum right wheel ratio by the right front and right rear wheel angular velocity ratio. Increment the counter for the number of left ratio samples. Increment the counter for the number of right ratio samples. ENDIF Ratio left = sum left wheel ratio / left ratio samples counter. Ratio right = sum right wheel ratio / right ratio samples counter. Front left wheel Circumference value = Ratio left * Estimated rear left tire circumference value (rear left wheel "true” circumference value). Front right wheel Circumference = Ratio right * Estimated rear right tire circumference (rear right wheel “true” circumference value). Moreover, the determined “true” circumference values stored in the non-volatile memory 31 can be used for various applications and functions, respectively. For example, the values may be used for an automatic parking system, tire deflation detection, or pressure loss level detection. In particular, executing the method for the rear wheels, is beneficial in case the Odome-try, which the parking system uses, provides motion estimation (vehicle pose data), with respect to a center of the rear axle of the vehicle 1. Tire Deflation Detection: During ignition off, the learned / estimated determined “true” circumference values and its associated covariance of each individual tires are stored in the non-volatile memory 31. During the next ignition, if any of the tires gets deflated or punctured, can be detected by driving the vehicle for around 200 meters and by comparing the newly learned circumference value of step S8 of each individual wheel and its circumference value stored in the nonvolatile memory. The non-deflated tires will learn and arrive at almost the same circumference stored in the non-volatile memory 31. But the deflated tire circumference will learn and arrive at a circumference value which is less than the current learned tire circumference of other tires as well as arrive at a value which is way below than its own determined “true” circumference value retrieved from the non-volatile memory 31. If the difference (determined “true” circumference value stored in memory 31 - current learned circumference value of step S8) exceeds a deflation threshold value of, for example, 0.03 meters, then it’s an indication that the tire is deflated. The tire deflation indication may be shown in the HMI unit 5 as a warning icon to indicate it to the driver. Tire Pressure loss level Indication: The method always learns during using / driving the vehicle 1 and stores the determined “true” circumference values and its associated noise covariance values in the non-volatile memory 31. After prolonged usage of the tires the change in circumference will be accurately determined / estimated and stored in the non-volatile memory 31. Under consideration that a 5-psi difference creates a 0.127 / 0.4064th-meters difference in tire circumference in a normal condition, the tire pressure loss level indication can be performed. The percentage of pressure loss of each individual tires during standstill can be calculated based on the difference seen in the circumference values of step S8 when the vehicle 1 is driven for, for example, 200 meters compared to the previously learned true tire circumference value stored in the non-volatile memory 31.

Claims

1. Method to determine a tire circumference value of a tire of at least one wheel (RL, RR) of a vehicle (1), during movement of the vehicle (1), the method comprising:- a GPS displacement determining step (S4) of obtaining GPS data and determining a GPS displacement of the vehicle;- a movement sensor displacement calculating step (S4, S5) of obtaining movement sensor data and calculating a movement displacement of the vehicle; whereinthe GPS displacement determining step (S4) and movement sensor displacement calculating step (S4, S5) are executed in predetermined intervals during movement of the vehicle (1); and- a recursive circumference determination step (S8), which is executed in each of the intervals, of determining a latest circumference value of the tire using(i) a preceding circumference value determined in a preceding interval of the predetermined intervals,(ii) the movement displacement and a corresponding movement sensor measurement noise, and(iii) the GPS displacement and a corresponding GPS measurement noise, wherein, for determining the latest circumference value in the recursive circumference determination step, the GPS measurement noise is adapted under consideration of the movement displacement.

2. Method according to claim 1, wherein the predetermined intervals are defined by n being an update count value of counting updates of the GPS data, wherein the predetermined intervals are preferably defined by n >= 2, 3, 4, 5, 6, 7, 8, 9 or 10.

3. Method according to claim 1 or 2, whereinthe circumference value of the tire is determined for a tire of a rear-left-wheel (RL) and a tire of a rear-right-wheel (RR) of the vehicle (1),in the movement sensor displacement calculating step (S4, S5), the movement displacement of the vehicle (1) is calculated using(i) the preceding circumference value of the tire of the rear-right-wheel (RR) together with an output of a rear-right-wheel angular displacement sensor (2) measuring an angular displacement of the rear-right-wheel (RR), and(ii) the preceding circumference value of the tire of the rear-left-wheel (RL) together with an output of a rear-left-wheel angular displacement sensor (2) measuring an angular displacement of the rear-left-wheel (RL).

4. Method according to claim 1,2 or 3, whereinthe recursive circumference determination step (S8) comprises a Kalman filter to determine the latest circumference value, the Kalman filter using a measurement noise covariance matrix (R) defining, as the GPS measurement noise, a GPS variance of the GPS displacement and, as the movement sensor measurement noise, an angular displacement variance of the displacement of the rear-right-wheel (RR) and an angular displacement variance of the displacement of the rear-left-wheel (RL), and,for determining the latest circumference value in the recursive circumference determination step (S8), the GPS variance is adapted using the movement displacement of the vehicle (1).

5. Method according the claim 1, 2, 3 or 4, wherein, in the movement sensor displacement step (S4, S5), the movement displacement is calculated on the basis of an expression of:= estimated nearest maximum likelihood circumference mean value of the rear-right-wheel (RR),= synchronized right wheel angular displacement for n GPS update counts, X $« estimated nearest maximum likelihood circumference mean value of therear-left-wheel (RL),M’s = synchronized left wheel angular displacement for n GPS update counts, and= calculated movement displacement.

6. Method according to claim 4 or 5, wherein the GPS variance is adapted using the movement displacement of the vehicle (1), on the basis of a polynomial curve or a Look-up-Table.

7. Method according to claim 5 or 6, wherein,after executing the recursive circumference determination step (S8), the method further comprises:a gradient calculating step (S9) of calculating a circumference gradient value for the tire of the rear-right wheel (RR), using the latest and preceding circumference values of the tire of the rear-right wheel (RR), and a circumference gradient value for the tire of the rear-left wheel (RL), using the latest and preceding circumference values of the tire of the rear-left wheel (RL),wherein, for a predetermined first movement distance of the vehicle (1), the circumference gradient values are accumulated and compared against a first gradient threshold, and, if a sum of accumulated circumference gradient values (RR, RL) are within the first gradient threshold,anc| jare updated by the latest circumference value of the tire of the rear-right-wheel and the latest circumference value of the tire of the rear-left-wheel.

8. Method according to one of claims 1 to 7, wherein,for a predetermined second movement distance of the vehicle (1), which is longer than the first movement distance, the circumference gradient values are accumulated and compared against a second gradient threshold, and, if a sum of accumulated circumference gradient values are within the second gradient threshold, the latest circumference value of the tire of the rear-right-wheel and the latest circumference value of the tire of the rear-left-wheel are stored as true circumference values of the rear tires.

9. Electronic control unit (3) for a vehicle (1), storing a computer program, wherein, when executing the computer program, the electronic control unit (3) executes a method according to any of the preceding claims 1 to 8.

10. Vehicle (1) comprising the electronic control unit (3) according to claim 9.21

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