Method for determining the position of a radial acceleration sensor of a wheel of a motor vehicle
A method for determining the position of a radial acceleration sensor of a wheel of a motor vehicle, including: acquiring, by the sensor, signals S i which are acquired during a predetermined time window W i when the vehicle is in motion, the windows W i being different from one another; detecting, for each time window W i , local extrema of the signal S i ; determining, for each time window W i , a frequency F i of the rotation of the wheel of the vehicle as a function of the phase values and of the detection instants for the local extrema detected; filtering of the signals S i , so as to obtain, for each time window W i , a filtered value Z i ; and determining the radial distance R c between the radial acceleration sensor and the axis of rotation of the wheel.
1. A method for determining a position of a radial acceleration sensor of a wheel of a motor vehicle, said method comprising:
an acquisition step of acquisition, by the radial acceleration sensor, of signals S i , each signal S i being acquired during predetermined time windows W i when the vehicle is in motion, the windows W i being different from one another,
a detection step of detecting, for each time window W i , at least three local extrema of the signal S i which are respectively associated with phase values and with detection instants,
a determination step of determining, for each time window W i , a frequency F i of a rotation of the wheel of the vehicle as a function of the phase values and of the detection instants for the local extrema detected in said time window W i ,
a filtering step of low-pass filtering of the signals S i , so as to obtain, for each time window W i , a filtered value Z i associated with the frequency F i , and
a determination step of determining a radial distance R c between the radial acceleration sensor and an axis of rotation of the wheel as a function of the filtered values Z i and of the frequencies F i .
2. The method as claimed in claim 1 , wherein the step of determining the frequency F i comprises, for each time window W i considered, determining a phase time signal φ i by quadratic interpolation of the respective phase values of three local extrema, the frequency F i being determined by evaluating a derivative of said signal φ i with respect to time at a predetermined instant t p within said time window W i .
3. The method as claimed in claim 2 , wherein the three local extrema considered within each time window W i are consecutive.
4. The method as claimed in claim 1 , wherein the cut-off frequency of the low-pass filter applied to the signals S i is less than or equal to 10 Hz .
5. The method as claimed in claim 1 , wherein the step of determining the radial distance R c comprises a linear regression of points P i each point P i having Z i and F i 2 as its ordinate and abscissa values respectively, the radial distance R c being estimated according to the formula:
R c =C d /(4× n 2 )
where C d is a quantity representing a gradient of said linear regression.
6. The method as claimed in claim 5 , wherein the quantity C d is equal to the ratio between the gradient of said linear regression and an error E i , in the gain of the radial acceleration sensor, said gain error E i , being determined, for at least one time window W i , during an estimation step, after the detection step and before the step of determining the radial distance R c , and according to the formula:
E i =V i /Q i ,
where V i , represents an amplitude associated with at least one local extremum of the signal S i , acquired during said at least one time window W i , and Q i represents an amplitude that is expected on a basis of measurements theoretically supplied by the radial acceleration sensor for said at least one local extremum, the gain error E i , being calculated only if a steady-speed phase is detected for the signal S i .
7. The method as claimed in claim 6 , wherein the step of determining the frequency F i , comprises, for each time window W i considered, determining a phase time signal φ i by quadratic interpolation of the respective phase values of three local extrema, the frequency F i , being determined by evaluating a derivative of said signal φ i with respect to time at a predetermined instant t p within said time window W i , and wherein, when a phase time signal φ i is determined, the step of estimating a gain error comprises, for each time window W i , making a comparison between a second derivative of the phase time signal φ i and a predetermined value ε, such that if |d 2 φ i /dt 2 |<ε, a steady-speed phase is detected.
8. The method as claimed in claim 6 , wherein the amplitude V i corresponds to the amplitude between two consecutive local extrema of the signal S i in a steady-speed phase, and Q i satisfies:
Q i =2× g×G,
where g is the acceleration due to gravity, and G represents a gain of a filter applied to the signal S i during the detection step so as to reduce measurement noise.
9. A wheel unit comprising a radial acceleration sensor, said wheel unit comprising means configured for implementing the method as claimed in claim 1 so as to determine the position of the radial acceleration sensor.
10. A motor vehicle comprising a wheel unit as claimed in claim 9 .
11. The method as claimed in claim 7 , wherein the amplitude V i corresponds to the amplitude between two consecutive local extrema of the signal S i in a steady-speed phase, and Q i satisfies:
Q i =2× g×G,
where g is the acceleration due to gravity, and G represents a gain of a filter applied to the signal S i during the detection step so as to reduce measurement noise.
12. The method as claimed in claim 1 , wherein the cut-off frequency of the low-pass filter applied to the signals S i is less than 5 Hz.
13. The method as claimed in claim 1 , wherein the cut-off frequency of the low-pass filter applied to the signals S i is 1 Hz.