Method for estimating the external radius of a tyre fitted to a wheel of a motor vehicle

1. A method for estimating the external radius R e of a tire fitted to a wheel of a motor vehicle, said wheel comprising a radial acceleration sensor, said method comprising:

an acquisition step of acquisition, by the radial acceleration sensor, of a signal S during a predetermined time window W when the vehicle is in motion under non-steady-state conditions,

a detection step of detecting at least three local extrema of the signal S which are respectively associated with phase values and with detection instants,

a determination step of determining, for the relevant time window W, a variation in frequency F′ of rotation of the wheel of the vehicle as a function of said phase values and of said detection instants,

a determination step of determining, for at least one detection instant, a discrepancy between the local extremum associated with said at least one detection instant and a reference signal obtained by eliminating the fluctuations in the signal S, so that said reference signal is indicative of the central acceleration of the wheel during said time window W,

a determination step of determining a value for the longitudinal acceleration V al of the vehicle for the relevant time window W as a function of said at least one discrepancy, and

an estimation step of estimating said external radius R e as a function of said longitudinal acceleration value A L and of said variation in frequency F′.

2. The estimation method as claimed in claim 1 , wherein the step of determining the variation in frequency F′ comprises determining a phase time signal φ by quadratic interpolation of the respective phase values of three local extrema, said variation in frequency F′ being determined by evaluating the second derivative of said signal φ.

3. The method as claimed in claim 2 , wherein the three local extrema considered within the time window W are consecutive.

4. The method as claimed in claim 1 , wherein the signal S acquired is sampled at a predetermined frequency, and wherein said reference signal is obtained, during the step of determining the discrepancies, by linear regression of said samples of the signal S.

5. The method as claimed in claim 1 , wherein a plurality of detection instants are considered during the step of determining the discrepancy, so as to obtain a plurality of discrepancies respectively associated with said detection instants, said longitudinal acceleration value V al being calculated using the formula:

V al =√{square root over (Δ M 2 −g 2 )}

where ΔM is a quantity indicative of a mean of the respective absolute values of said discrepancies, and g is the acceleration due to gravity.

6. The method as claimed in claim 5 , wherein all the detection instants determined during the detection step are considered during the step of determining the discrepancies.

7. The method as claimed in claim 5 , wherein the quantity ΔM is equal to the ratio between the arithmetic mean of said absolute values and an error E G in the gain of the radial acceleration sensor, said gain error E G being determined prior to the acquisition step during a phase of steady-state running of the vehicle.

8. The method as claimed in claim 1 , wherein the external radius R e is calculated using the formula:

R

e

=

V

al

2

×

π

×

F

′

.

9. A wheel unit comprising a radial acceleration sensor, said wheel unit comprising means configured for implementing the steps of the estimation method as claimed in claim 1 .

10. A motor vehicle comprising a wheel unit as claimed in claim 9 .