METHOD, DEVICE AND COMPUTER PROGRAM FOR ESTIMATING THE SPEED OF A BICYCLE

Description

[0001] The invention relates to a method, a device and a computer program for estimating the speed of movement of a wheeled vehicle on the ground.

[0002] The field of application of the invention includes, in particular, rolling land motor vehicles, and aircraft with landing gear having wheels rolling on the ground during takeoff or landing.

[0003] The instantaneous speed of a vehicle is a crucial piece of data in inertial navigation. Currently, the speed signal is typically measured by an additional speed sensor (odometer) mounted on the vehicle's wheel. Installing such a sensor is costly and not always feasible in certain applications, particularly in aeronautics and military land navigation.

[0004] US document 2019 / 236859 relates to a method for determining the use of a vehicle from a vibration signal acquired by a sensor attached to the vehicle, by determining a spectral characteristic of the vibration signal, characterizing frequencies of one or more energy peaks.

[0005] US document 2014 / 278206 relates to a method for determining the trajectory of a vehicle, using acceleration measurements and the acquisition of acoustic environmental characteristics of the vehicle, which are acquired by the smartphone and which provide information on the speed of the vehicle.

[0006] The invention seeks to eliminate the need for a direct speed sensor such as an odometer or a position sensor.

[0007] An objective of the invention is to develop a method, a device and a computer program for estimating the speed of movement of a wheeled vehicle on the ground, which are capable of accurately estimating the instantaneous speed of a wheeled vehicle from at least one inertial or vibration sensor (which may be, for example, an accelerometer or gyroscope or microphone), dispensing with a direct speed sensor such as an odometer or a position sensor.

[0008] In the current state of the art, attempts have been made to overcome the problem of the lack of a direct speed sensor by exploiting information present in inertial signals, as for example in the paper "The Future of Automotive Localization Algorithms: Available, reliable, and scalable localization: Anywhere and anytime" by Rickard Karlsson and Fredrik Gustafsson, 2017. According to this paper, the estimation of instantaneous speed from an inertial signal is calculated by selecting, at each instant, the most energetic frequency of a spectrogram. This type of approach can be effectively applied in some simple applications where noise is low, but not in the application domain mentioned above, where the noise-to-signal ratio is often very high.The method described in this document by Rickard Karlsson and Fredrik Gustafsson is not robust to environmental noise such as engine combustion and requires a spectrum in which peaks are easily identifiable, which is not possible in the presence of an internal combustion engine. Furthermore, the spectrum of the inertial or vibrational signal is rich in harmonics, and these undergo considerable energy leakage, making peak identification using Fourier transforms difficult. The vast majority of state-of-the-art inertial navigation systems are unusable in environments with significant environmental noise.

[0009] In certain applications, particularly aeronautical and military ground vehicles, where the number of sensors is very limited, installing a position sensor is very difficult, if not impossible in aeronautics. The presence of an instantaneous velocity signal is crucial for a navigation system to accurately estimate the position of a vehicle. Therefore, it is necessary to measure this instantaneous velocity without adding any physical instrumentation to the vehicle's wheels.

[0010] The invention aims to obtain a method, a device and a computer program for estimating the speed of movement of a wheeled vehicle on the ground, which overcome the disadvantages mentioned above and achieve the objectives mentioned above.

[0011] To this end, a first object of the invention is a method for estimating the speed of a vehicle having at least one wheel in contact with the ground, characterized in that An inertial or vibrational signal is measured from at least one inertial or vibrational sensor on the vehicle. A plurality of spectra of the signal are calculated by at least one computer over a plurality of successive time windows defined with respect to successive instants. The plurality of spectra form at least one spectrogram as a function of successive instants. The spectrogram is filtered by at least one noise attenuation and / or deterministic feature extraction filter to obtain at least one filtered spectrogram of the signal over successive instants. A frequency trajectory, representative of the vehicle's wheel speed in the spectrogram filtered over successive instants, is estimated by the computer. This estimate is based on the fact that the probability of observing the frequency trajectory is based on a calculated amplitude of the filtered spectrogram for each instant.The computer estimates a posterior law for observing the frequency trajectory as being proportional to the product of a prescribed transition probability of the frequency trajectory and the observation probability of the frequency trajectory. The computer estimates the frequency trajectory for successive instants from this posterior law for observing the frequency trajectory. The computer estimates the wheel speed of the vehicle for successive instants from the estimated frequency trajectory.

[0012] The invention thus proposes a noise-robust method for estimating inertial or vibrational signals, utilizing the frequency information present in the measured (inertial or vibrational) signal, and a methodology based on a specifically dedicated probabilistic approach. Unlike the prior art, the invention eliminates environmental noise and extracts a vehicle speed signal without using an odometer, thereby enabling the data to be used in real-world scenarios. The speed is expressed as a function of the amplitude at each point on the time-frequency plane and a transition law that promotes the continuity, direction, and regularity of the trajectory while exploiting the system's kinematics, such as harmonics. An inertial signal is always present when a vehicle navigation system is in operation.In the case of the vibration sensor, the frequency of the vibrations emitted by the vehicle's wheels is proportional to the vehicle's speed (simply multiply by the wheel's circumference).

[0013] According to one embodiment of the invention, a support of frequency values ​​is determined by the computer, the frequency trajectory is estimated by the computer as being for each instant in the support the frequency value which maximizes the a posteriori law of observation of the frequency trajectory up to that instant.

[0014] According to another embodiment of the invention, a support of frequency values ​​is determined by the computer, and the frequency is estimated for each instant by the computer as being a barycenter of the a posteriori law of observation of the frequency, taken in the frequency values ​​of the support and affected by these frequency values.

[0015] According to one embodiment of the invention, a support Ω of frequency values ​​is determined by the computer, the probability of observation is estimated by the computer given a trajectory as depending on the calculated amplitude of the filtered and normalized spectrogram for each instant.

[0016] According to one embodiment of the invention, the probability is estimated by the calculator p Z t | ξ t observation according to the following equation: p Z t | ξ t =f t ( z t ) = | S ( f t , t )|.1 [ f min ( t ), f max ( t )] ( f t where | S ( f t , t )| is the calculated amplitude of the spectrogram S ( f t , t ) filtered for each instant t, f min ( t ) is a minimum frequency trajectory that has been measured, f max ( t) is a maximum frequency trajectory that has been measured, f min ( t ) And f max ( t ) are such that f min ( t ) ≤ ξ t ≤ f max ( t ) , 1 [ f min ( t ), f max ( t )] ( f t ) is a function taking the value 1 for f t between f min ( t ) And f max ( t ) and taking the value 0 for f t below f min ( t ) or above f max ( t ) .

[0017] According to one embodiment of the invention, the probability is estimated by the calculator p Z t | ξ t observation according to the following equation: p Z t ξ t = f t z t = ∏ j j ⋅ f t < F s 2 1 c t S j . f t , t 1 f min t , f max t f t Or j is a positive integer or real number, satisfying j . f t < F s 2 where ft denotes the frequencies of each filtered spectrogram S(ft, t) at time t, and where F s is a threshold frequency, having been predetermined as a function of the filtered spectrogram S(ft , t).

[0018] According to one embodiment of the invention, a support for frequency values ​​is determined by the computer, and the probability is estimated by the computer. p Z t | ξ t trajectory observation ξ t frequency according to the following equations: p Z t ξ t = f t z t = ∏ f ∈ Ω p Z t f ξ t = f t z t f For ξ t = f t E Ω with p Z t [ f t ]| ξ t =f t ( z t [ f t ] = 1) depending on the calculated amplitude of the filtered spectrogram for each instant t, p Z t [ f ]| ξ t =f t ( z t [ f ] = 1) = 0 pour f ≠ f t Or Z t is a binary observation vector having a size N s prescribed for now t ∈ {1, ... , N s } such as Z t [ f ] = 1 if f t = f Otherwise Z t [ f ] = 0 for f ≠ f t .

[0019] According to one embodiment of the invention, p Z t f t ξ t = f t z t f t = 1 = 1 c t S f t t .1 f min t , f max t f t where | S ( f t , t )| is the calculated amplitude of the spectrogram S ( f t , t) filtered for each instant t, c t = max f ∈ f min t , f max t z t f f min ( t ) is a minimum frequency trajectory that has been measured, f max ( t ) is a maximum frequency trajectory that has been measured, f min ( t ) And f max ( t ) are such that f min ( t ) ≤ ξ t ≤ f max ( t ), 1 [ f min ( t ) ,f max ( t )] ( f t ) is a function taking the value 1 for f t between f min ( t ) And f max ( t ) and taking the value 0 for f t below f min ( t ) or above f max ( t ) .

[0020] According to one embodiment of the invention, a support for frequency values ​​is determined by the computer, and the probability is prescribed by the computer. p ξ ( f 1 , ... , f Ns ) of trajectory transition ξ t frequency for now N s starting from the given initial probability p ξ 1 of instant 1, for t ∈ {1, ... , N s } and for each frequency f t ∈ Ω according to the following equation: p ξ f 1 , … , f N s = p ξ 1 f 1 ∏ t = 1 N s − 1 p ξ t + 1 ξ t = f t f t + 1 Or N s is a prescribed integer, greater than or equal to two, of successive prescribed times t, where p ξ t+1 | ξ t = f t ( f t+1) is the transition probability of the frequency ξ t of the frequency trajectory of the present moment t at the frequency ξ t +1 of the frequency trajectory of the next instant t+1.

[0021] According to one embodiment of the invention, the probability p ξ t+1 | ξ t = f t ( f t+1) of frequency transition ξ t of the frequency trajectory of the present moment t at the frequency ξ t +1 of the frequency trajectory of the next instant t+1 follows a conditional Gaussian law centered on the frequency f t of the filtered spectrogram at time t.

[0022] According to one embodiment of the invention, the Gaussian conditional law centered on the frequency f t has a standard deviation σ t = Δ t.γ t where Δt is a calculated temporal resolution of the spectrogram at time t, γ t is a calculated average speed with which the trajectory çt of frequency evolves between time t and the following time t+1.

[0023] According to one embodiment of the invention, the speed of movement of the vehicle wheel is estimated by the computer by multiplying the frequency trajectory by 2nR, where R is the radius of the wheel and is predetermined or estimated.

[0024] According to one embodiment of the invention, the noise attenuation and / or deterministic feature extraction filter comprises a sliding median filter and / or a filter for separating deterministic features from random features.

[0025] A second object of the invention is a device for estimating the speed of a vehicle having at least one wheel rolling on the ground, characterized in that the device comprises: an inertial or vibration sensor of the vehicle for measuring an inertial or vibration signal, a computer configured to calculate a plurality of spectra of the signal over a plurality of successive time windows defined with respect to successive instants, the plurality of spectra forming at least one spectrogram as a function of the successive instants, a noise attenuation and / or deterministic feature extraction filter in the spectrogram, to obtain at least one filtered spectrogram of the signal over the successive instants, the computer being configured to estimate a frequency trajectory, representative of the speed of the vehicle's wheel in the spectrogram filtered over the successive instants, by: estimation, by the computer, of a probability of observing the frequency trajectory from a calculated amplitude of the filtered spectrogram for each instant, estimation, by the computer,of a posterior law of observation of the frequency trajectory as being proportional to the product of a prescribed transition probability of the frequency trajectory and the probability of observation of the frequency trajectory, estimation, by the computer, of the frequency trajectory for successive instants from the posterior law of observation of the frequency trajectory, the computer being configured to estimate the speed of movement of the vehicle's wheel for successive instants from the frequency trajectory.

[0026] A third object of the invention is a computer program, comprising code instructions for implementing the method of estimating the vehicle's speed of movement as described above, when executed in a computer.

[0027] The invention will be better understood upon reading the following description, given solely as a non-limiting example with reference to the figures below of the attached drawings. [ Fig. 1 [ ] represents an example of a flowchart of the process for estimating the speed of a wheeled vehicle on the ground according to embodiments of the invention. ] Fig. 2 ] schematically represents an example of a step in calculating spectrograms of a signal from the process, device, and program for estimating the speed of a wheeled vehicle on the ground according to embodiments of the invention. Fig. 3 ] represents an example of a spectrogram of a time-domain signal in the time-frequency plane of the method, device, and program for estimating the speed of a wheeled vehicle on the ground according to embodiments of the invention. Fig. 4 [ ] schematically represents an example of a device for estimating the speed of a wheeled vehicle on the ground according to embodiments of the invention. ] Fig. 5 ] represents an example of a raw signal that can be measured by the method, device, and program for estimating the speed of a wheeled vehicle on the ground according to embodiments of the invention. Fig. 6 ] represents a spectrogram of the signal of the figure 5 , which can be calculated by the method, device and program for estimating the speed of a wheeled vehicle on the ground according to embodiments of the invention. [ Fig. 7 ] represents an example of a filtered spectrogram of the signal from the figure 5 , which can be calculated by the method, device and program for estimating the speed of a wheeled vehicle on the ground according to embodiments of the invention. [ Fig. 8 ] represents an example of the probability of observing the frequency trajectory, which can be calculated from the signal of the figure 5 by the method, device and program for estimating the speed of movement of a wheeled vehicle on the ground according to embodiments of the invention. Fig. 9 ] represents an example of the frequency trajectory transition probability, which can be calculated from the signal of the figure 5 by the method, device and program for estimating the speed of movement of a wheeled vehicle on the ground according to embodiments of the invention. Fig. 10 ] represents an example of a frequency trajectory, which can be calculated from the signal of the figure 5 by the method, device and program for estimating the speed of movement of a wheeled vehicle on the ground according to embodiments of the invention. Fig. 11 ] schematically represents an example of a device for estimating the speed of movement of a wheeled vehicle on the ground according to embodiments of the invention.

[0028] We describe in more detail below with reference to figures 1 à 10 embodiments and examples of embodiment of the process, device 1 and computer program for estimating an instantaneous speed v of movement of a RO wheel vehicle VE rolling on the ground.

[0029] In the application domain of the invention mentioned above, when vibration signals from complex mechanical systems such as land vehicles or aeronautical systems are used, these signals are significantly affected by noise (ambient, combustion, and aerodynamic noise, etc.), especially for interfering and asynchronous rotating sources. Therefore, identifying the correct trajectory representing the vehicle's velocity v in the time-frequency plane is particularly difficult under conditions of low signal-to-noise ratio: a few peaks related to the instantaneous frequency can be distinguished, and false peaks due to noise can locally replace them. This initial difficulty can be resolved by adding a preprocessing step E4 of the time-frequency representation by filtering out noise to improve the emergence of the wheel signature relative to the background noise.The proposed E4 denoising method not only attenuates background noise but also attenuates quasi-stationary components in the time-frequency plane in the case where the desired component is strongly non-stationary (revving up, revving down) and conversely attenuates non-stationary components in the case where the desired component is quasi-stationary.

[0030] Furthermore, the multi-component nature of the signal and the possibility of asynchronous components in the motor, as in an aircraft engine, means that several harmonics can coexist, overlap, be very close, or even merge within the same frequency band. Thus, simply following the maxima at each instant can lead to deviations from the correct trajectory and therefore provide an erroneous estimate of the velocity v. To overcome this problem, the invention incorporates, in addition to the spectrogram amplitude, further constraints on the optimal trajectory in the estimation procedure, resulting in the estimation of a transition probability. Considering multiple harmonics and the direction of the trajectory of interest, for example, allows for greater weighting of trajectories closer to the desired instantaneous frequency, which is advantageous for the coupling moments between different components.Adding these regularity constraints by estimating a transition probability also helps to avoid jumps and discontinuities in the presence of isolated peaks related to residual noise after the E4 preprocessing step.

[0031] The objective is to find, among all possible trajectories in the spectrograms over time, an optimal trajectory ξ t Or ξ̂ of frequency, satisfying the considered constraints and representative of the velocity v of the RO wheel of the VE vehicle. The optimality of one trajectory relative to another is measured by a cost function or, equivalently, by a probability density function. To do this, the spectrogram information and the constraints are expressed as probabilities. More specifically, the trajectory ξ t Or ξ 1, ..., ξ NS frequency can be modeled by a Markov chain with a transition density p ξ t+1 | ξ t and a given initial probability p ξ 1. The transition density is defined according to the added constraints (continuity, harmonics, direction, etc.). At each time step t, an observation of the spectrogram is provided with a probability p Z t | ξ t which depends on the amplitude of the spectrogram. The trajectory ξ t The frequency of the vehicle's speed v, the vehicle's movement frequency, can be chosen as the one that maximizes the posterior distribution. p ξ 1 , … , ξ N S Z 1 , … , Z N S (or by calculating its average). Uncertainties in this estimate can also be calculated by considering second-order moments. The number of harmonics to be taken into account can be entered by the user on the INT1 physical data input interface. In the figures, the method for estimating the velocity v of a vehicle with one (or more) wheels RO rolling on the ground involves a first step E1 of measuring a time-domain signal X, which is inertial or vibrational, from one (or more) inertial or vibrational CAP sensor(s) on the vehicle. This inertial or vibrational CAP sensor can be located outside the vehicle's engine. The inertial or vibrational CAP sensor can be present on the vehicle's ground-bound wheel RO. Due to the extreme environment, a sensor is often subject to defects or measurement errors.The CAP sensor(s) may be or include one or more accelerometers and / or one or more gyroscopes and / or one or more acoustic sensors and / or one or more microphones. The invention may use inertial sensors that are not located in the motor. Furthermore, if the EV has an inertial measurement unit (IMU) composed of six inertial sensors (three accelerometers and three gyroscopes), the invention may use CAP sensor redundancy formed by several or all of these six inertial sensors to improve the accuracy of the speed information v (the risk of simultaneous measurement error on six sensors being lower). An example of the raw X signal as a function of time on the x-axis is shown in Figure 1. figure 5 .

[0032] In a second step E2 subsequent to the first step E1, one (or more) CAL calculators calculate several SPt spectra of the time-domain signal X over several successive (or sliding) time windows Wt, which are defined with respect to successive instants t, as represented for example in the figure 2 Each time window Wt can, for example, be centered on time t and has a predetermined finite time width relative to time t (for example, successive time windows Wt can have identical time widths). The CAL computer calculates several successive partial time signals Y (or time segments Y), each equal to the signal X multiplied by the successive time windows Wt for successive times t. For example, successive times t belong to the set {1, ..., N s } , Or N s is a predefined number, greater than 1. The times t can be multiples of the same sampling step size, up to a prescribed constant, and are expressed hereafter as an integer number of sampling steps, up to a prescribed constant. The sampling step size and / or sampling frequency can be entered by the user on the INT1 physical data input interface or be pre-recorded in the CAL computer. The sampling step size and / or sampling frequency defines the number of samples acquired per second and the times t.

[0033] The CAL (Calculator) may be or include one or more computers, one or more servers, one or more machines, one or more processors, or one or more microprocessors. The CAL may include one or more physical data input interfaces (INT1) and one or more physical data output interfaces (INT2). These physical data input interfaces (INT1) may be or include one or more computer keyboards, one or more physical data communication ports, one or more touchscreens, or other devices. These physical data output interfaces (INT2) may be or include one or more physical data communication ports, one or more screens, or other devices.The device 1 for estimating the speed v of movement of the vehicle having one or more wheels RO rolling on the ground includes in particular the CAL sensor(s), the CAL computer(s) and the FIL filter(s), as illustrated as an example in the . figure 11 The FIL filter may be included in the CAL control unit or be separate from the CAL control unit. The CAL sensor is configured to perform step E1 mentioned above. The FIL filter is configured to perform step E4 mentioned below. The CAL control unit is configured to perform steps E2, E3, E5, E6 (and optionally E4) and substeps E51, E52, and E53 mentioned below. The CAL control unit and / or the FIL filter and / or the CAP sensor may be programmed by a computer PR program containing code instructions implementing the method for estimating the vehicle's speed v, namely to perform step E1 and / or E2 and / or E3 and / or E4 and / or E5 and / or E6 and substep E51 and / or E52 and / or E53. The CAL calculator includes a non-volatile MEM memory (or non-volatile MEM recording media), in which the computer PR program is stored permanently.Non-volatile MEM memory or non-volatile MEM recording media is readable by a computer and contains instructions stored on it, which, when executed by a processor, cause the processor to execute step E1 and / or E2 and / or E3 and / or E4 and / or E5 and / or E6 and substep E51 and / or E52 and / or E53. The signal X and the data mentioned above and below, used by the process, device 1 and program PR, are stored in the MEM memory.

[0034] The device 1 for estimating the speed v of the RO-wheeled VE can be installed on the VE. This device can serve as an inertial navigation aid and can be integrated into an inertial navigation system, which is included in an inertial measurement unit (IMU) present on the vehicle. The IMU can include three accelerometers in three non-parallel directions, three gyroscopes around three non-parallel directions, the inertial navigation system, and navigation functions.

[0035] According to one embodiment of the invention, the CAL computer calculates, during the second step E2, for each partial time-domain signal Y, the spectrum SPt equal to a Fourier transform (which may be, for example, a Fast Fourier Transform (FFT)), limited to the respective time window Wt, of this partial time-domain signal Y (short-time Fourier transform, also called STFT). The CAL computer thus calculates the Fourier transform over the sliding windows Wt of the time-domain signal X, and therefore the plurality of spectra SPt for the plurality of successive times t. Each spectrum SPt gives an amplitude of the spectrum as a function of the frequency f.

[0036] For each CAP sensor providing a measurement signal X, the series of SPt spectra thus obtained for successive times t forms an SP spectrogram. The SP spectrogram is calculated by the CAL calculator. Each SPt spectrum forms a column of the SP spectrogram, as illustrated as an example in the figure 3 Thus, if multiple CAP sensors provide multiple X signals, the CAL computer calculates a corresponding number of SP spectrograms and a number of S(ft, t) spectrograms. In the case of multiple SP and S(ft, t) spectrograms, these SP and S(ft, t) spectrograms can undergo different processing for the same sensor.

[0037] A time-frequency plane representation, such as for example that of figures 3 And 6 from the signal of the figure 5 , represents in the form of an image: on the time axis in abscissa: the successive instants t, on the ordinate axis: the frequencies ft of the respective spectra SP t for each instant t, in grey levels and on a logarithmic scale on the vertical time axes t: the absolute value of the amplitude of the respective spectrum SP t for each instant t, the absolute value of this amplitude being referred to the ECH scale of grey levels.

[0038] There figure 3 represents, as an example, SPt spectra in the time-frequency plane of an inertial X signal obtained by an inertial CAP sensor formed by a lateral accelerometer recorded on an EV. Examples of recordings of figures 5 à 10 These results were obtained on an electric vehicle (EV) using an inertial CAP sensor. The response of the mechanical system is highly dependent on the operating regime, hence the importance of conditioning the analysis results of the signal X to the speed v at each instant. A time-frequency representation reveals the signatures associated with the mechanical sources. Such a representation provides insight into the evolution of the frequency content over time. Other time-frequency representations, such as the Wigner representation, can also be used.

[0039] In EV vehicles with RO wheels, the RO wheels can emit vibrations that manifest in the time-frequency plane as a series of peaks (trajectory ξ t of frequency). The sources related to the wheels manifest themselves as continuous and smooth trajectories (trajectory ξ t of frequency) without abrupt jumps in speed v. The fundamental frequency (trajectory ξ t of frequency) and its harmonics (other frequency components COMPF) are the most energetic in the time-frequency plane. The frequency of the velocity v of the RO wheel of the VE vehicle is manifested in successive spectra by a regular trajectory varying according to the state of the system (acceleration, deceleration, stop, etc.). Thus, a simple way to estimate the instantaneous frequency of the signal X is to find the positions of the most energetic peaks in the frequency band of the component to be followed (trajectory ξ t of frequency). Taking into account the multiple harmonics of the fundamental of the wheels and adding continuity constraints and information on the direction makes it possible to mitigate continuous trajectories linked to parasitic components such as the combustion of the vehicle's engine.

[0040] In a fourth step E4, following the second step E2, the SP t spectra are filtered by one (or more) FIL filters for noise attenuation and / or deterministic feature extraction, to obtain a filtered spectrogram S(ft, t) of the signal X over successive times t. In the spectrogram S(ft, t), the frequency at time t is denoted by ft. This preprocessing E4 provides a cleaner time-frequency representation. In this step E4, we can differentiate between the two cases where the target component (velocity v) is quasi-stationary or strongly non-stationary. In the case of a quasi-stationary target component (velocity v), the FIL filter can include a deterministic random separation (DRS) filter to separate deterministic (and therefore predictable) features from random (and therefore unpredictable) features, including background noise and non-stationary interfering components.In the case of a highly non-stationary target component (velocity v), the FIL filter can be configured to reduce background noise and time-invariant frequencies (e.g., ventilation noise, electrical components) and may include a sliding median filter for this purpose. An example of a filtered spectrogram S(ft, t) from the signal of the... figure 5 is illustrated at the figure 7 The maximum frequency variation (to ensure signal continuity) of the filtered spectrum S(ft, t) can be determined by the CAL computer or have been pre-recorded in the CAL computer or be prescribed by the user on the INT1 physical data input interface.

[0041] During a fifth stage E5 following the fourth stage E4, a trajectory is estimated by the CAL computer ξ t of frequency, representative of the instantaneous velocity v of the RO wheel of the VE vehicle in the spectrogram S(ft, t) filtered over successive instants t. This step E5 comprises substeps E51, E52, E53 which will be described below. In what follows, the trajectory ξ t frequency is also denoted ξ.

[0042] Indeed, the velocity v of the RO wheel of the VE vehicle translates into a certain frequency component in the time-frequency plane of the spectrogram S(ft, t), this frequency component being able to have a certain frequency (equal in what follows to the trajectory) ξ t frequency) varying over time and a certain amplitude varying over time. This frequency ξ t varying over time t in the spectrogram S(ft, t) therefore forms a trajectory ξ t of the frequency of the velocity v of the RO wheel of the VE vehicle as a function of time t in the spectrogram S(ft, t) (and therefore in the time-frequency plane of the figure 3 This trajectory ξ t frequency is mixed with trajectories of other frequencies of other COMPF frequency components in the spectrogram S(ft, t), as illustrated in the figure 3 According to one embodiment, for the RO wheel rolling on the ground, the instantaneous rotational frequency of the RO wheel (number of revolutions per second) at successive times t is the trajectory ξ t frequency as a function of time t. According to another implementation, for the RO wheel rolling on the ground, the tangential velocity of the RO wheel (number of revolutions per second multiplied by the radius of the RO wheel and multiplied by 2π) at successive times t is the trajectory ξ t frequency as a function of time t.

[0043] Either N s the number (greater than or equal to 2) of successive time segments or instants t in the spectrogram S(ft, t) (x-axis to the figure 2 ), that is to say that the instants t ∈ {1, ... , N s }. Either L s the number (greater than or equal to 2) of frequency bins in the filtered spectrogram S(ft, t). We denote by ft the frequencies of each spectrogram S(ft, t) at time t. We also denote by F = ( f 1, ..., f NS The true trajectory is an unknown frequency to be estimated. The number N s successive instants t can be determined by the CAL computer or have been pre-recorded in the CAL computer or be prescribed by the user on the INT1 physical data input interface.

[0044] According to one embodiment of the invention, during the second step E2, the CAL computer determines a support Ω with values ​​{ f 1< , ... , f Ls< } of frequency, namely Ω= [ f 1< , ... , f Ls< }. The support Ω of values ​​[ f 1< , ... , f Ls< } is the frequency support of the spectrogram S(ft, t) and can contain all frequency values ​​between zero and a maximum frequency, for example, regularly spaced frequencies, which can be multiples of a prescribed frequency step up to a prescribed constant. The number Ls of frequency values ​​in the support Ω is finite and can be determined by the CAL computer, pre-programmed into the CAL computer, or specified by the user on the INT1 physical data input interface. The frequency step can be calculated by the CAL computer based on the sampling frequency and / or the duration of the Wt window.

[0045] We also note by F = ( f 1 , ... , f NS ) the trajectory çt of frequency to be estimated. We therefore have, for successive instants t ranging from 1 to N s, the trajectory ξ t of a frequency equal to a set of frequencies ξ 1, ..., ξ NS that's to say ξ t = ( ξ 1, ..., ξ NS ), which is a random variable modeling the trajectory çt to be estimated. The trajectory çt of frequency can take the frequency values ξ 1, ..., ξ NS in the support Ω = [ f 1< , ..., f Ls< ] of frequency values ​​of the spectrogram S(ft , t).

[0046] The frequency chain ξ 1 , ..., ξ NS successive trajectory ξ t frequency over time t can be described by a transition probability p ξ t+1 | ξ t and a given initial probability p ξ 1.

[0047] According to one embodiment, during the third step E3, which is subsequent to the second step E2 and prior to the fourth step E4, the CAL calculator prescribes a transition probability p ξ trajectory ξ t frequency according to a Markov chain linking the frequency transition probability ξ t of this trajectory at the present moment t at the frequency ξ t +1 of this trajectory at the next instant t+1, starting from the given initial probability p ξ 1. This transition probability p ξ follows a priori law. In what follows, the transition probability p ξ of the trajectory çt of frequency is denoted p ξ ( f 1, ... , f Ns ) . An example of transition probability p ξ calculated from the signal of the figure 5 is illustrated at the figure 9 The transition probability describing the possible changes in velocity over time is specified in advance. Specifically, a large change in frequency has a low probability, and a small change has a high probability. This transition probability defines what is called a Markov chain.

[0048] According to one embodiment of the invention, the CAL calculator calculates the probability during step E3 p ξ ( f 1, ... , f Ns ) of transition of the trajectory çt of frequency for the moment N s starting from the given initial probability p ξ 1 of time 1, for t ∈ {1, ... , N s } and for each frequency f t e Ω (that is, each f 1 , ... , f Ns ∈ Ω) according to the following equation: p ξ f 1 , … , f N s = p ξ 1 f 1 ∏ t = 1 N s − 1 p ξ t + 1 ξ t = f t f t + 1 p ξ 1 ( f 1) is the given initial probability at time t=1. In this equation, p ξ t+1 | ξ t = f t ( f t+1) is the transition probability of the frequency çt of the trajectory from the present moment t to the frequency ξ t +1 of the trajectory of the next instant t+1.

[0049] We therefore have the joint law of the trajectory ξ of frequency, which is given by: ∀ f 1 , … , f N s ∈ Ω N s , p ξ f 1 , … , f N s = p ξ 1 f 1 ∏ t = 1 N s − 1 p ξ t + 1 ξ t = f t f t + 1

[0050] According to one embodiment of the invention, the CAL calculator calculates the probability during step E3 p ξ t+1 | ξ t = f t ( f t+1) transition frequency çt of the trajectory from the present instant t to the frequency ξ t +1 of the trajectory of the next instant t+1 according to a Gaussian conditional law N centered on the frequency f t of the filtered spectrogram (S(ft , t)) at time t, that is p ξ t + 1 ξ t = f t f t ≡ N f t σ t 2 , Or σ t 2 is the variance of the Gaussian conditional distribution N and the frequency f t is the average of the Gaussian conditional law N. This allows us to maintain a certain regularity of the harmonic to follow and to add continuity constraints between consecutive instants t and t+1.

[0051] According to one embodiment of the invention, the CAL calculator calculates the standard deviation during step E3 σ t of the Gaussian conditional law N as being σ t = Δ t.γ t , where Δt is a calculated temporal resolution of the filtered spectrogram (S(ft , t)), γ t is a calculated average speed at which the trajectory çt of frequency evolves between time t and the following time t+1. Thus, by decreasing the variance σ t 2 The smoothing effect will be stronger. Calculating the transition law p ξ t+1 | ξ t = f t ( f t+1) by the CAL computer can also take into account the direction of evolution (for example, ascent, descent, stability) of the trajectory ξ t frequency when this direction is provided at each instant t. For example, the CAL computer can use a transition law p ξ t+1 | ξ t = f t ( f t+1), which is truncated on ξ t +1 ≥ ξ t in the case of a rise in the trajectory çt of frequency and which is truncated on ξ t +1 ≤ ξ t in the case of a descent of the trajectory çt of frequency. In the case where the trajectory ξ t The frequency becomes constant (stopping during descent and ascent), for example at a zero value (stopping the vehicle VE corresponding to a speed v of zero), it is necessary to put γ t to a fairly low value.

[0052] In the first sub-step E51 of the fifth step E5, the CAL calculator estimates a probability p Z t | ξ t trajectory observation ξ t of the velocity frequency v of the vehicle's movement, derived from a calculated amplitude of the spectrogram S(ft, t) filtered for each instant t. In what follows, the probability p Z t | ξ t trajectory observation ξ t The frequency of the speed v of the vehicle's movement is denoted p Z ξ = f 1 , … , f N s z 1 , … , z N s . An example of probability p Z t| ξ t observation calculated from the signal of the figure 5 is illustrated at the figure 8 .

[0053] According to one embodiment of the invention, the CAL calculator calculates during substep E51 the probability p Z t | ξ t observation knowing a trajectory as depending on the calculated amplitude of the spectrogram S(ft , t) filtered and normalized for each instant t.

[0054] According to one embodiment of the invention, the CAL calculator calculates during substep E51 the probability p Z t | ξ t trajectory observation ξ t frequency for te {1, ... , N s} and for each frequency f t ∈ Ω (that is, each f 1 , ... , f Ns ∈ Ω) according to the following equation: p Z ξ = f 1 , … , f N s z 1 , … , z N s = ∏ t = 1 N s p Z t ξ t = f t z t

[0055] The CAL calculator calculates the binary vector Z during substep E51 or Z t observation having a size N s prescribed for the moment t ∈ {1, ..., N s } (and for each frequency f t ∈ Ω, that is to say each f 1 , ... , f Ns ∈ Ω) and being such that each of the coordinates Z t [ f ] of the binary vector Z t observation coordinates Z t [ f ] of the binary vector Z t observation being therefore ( z 1, ... , z Ns )) is equal to: Z t f = 1 si f ¯ t = f = f t , Otherwise Z t [ f ] = 0 for f ≠ f t . Or f ≠ f t .

[0056] In the above, Z = ( Z 1, ... , Z NS ) is the observation.

[0057] The density or probability p Z t | ξ t The observations are then written as follows: ∀ f 1 , … , f N s ∈ Ω N s , ∀ z 1 , … , z N s , p Z ξ = f 1 , … , f N s z 1 , … , z N s = ∏ t = 1 N s p Z t ξ t = f t z t

[0058] The probability of observation p Z t | ξ t is defined from the amplitude | S ( f t , t )| of the spectrogram S ( f t , t) For f t ∈ Ω. Indeed, we can get an idea about the target trajectory ξ t and then confirm if ξ t = f t is very likely to be observed or not depending on the level of the spectrogram amplitude at the point ( f t , t ) compared to other points ( f, t ) , f ∈ Ω.

[0059] The main idea of ​​the method used is to calculate a probability density function from the spectrogram describing the distribution of observations given the target frequency ξ t at each instant t. Indeed, for çt = f t ∈ Ω given, the coefficient of Z t for the frequency f t has a high probability of being equal to 1 at time t, that is to say it is very likely that the true frequency f t is equal to f t .

[0060] According to one embodiment of the invention, the CAL calculator calculates during substep E51 the probability p Z t | ξ t trajectory observation ξ t frequency according to the following equations: p Z t ξ t = f t z t = ∏ f ∈ Ω p Z t f ξ t = f t z t f For ξ t = f t E Ω with p Z t [ f t ]| ξ t=f1 ( z t [ f t ] = 1) depending on the calculated amplitude of the spectrogram (S(ft , t)) filtered for each instant (t),p Z t [ f ]| ξ t=f t ( z t [ f ] = 1) = 0 pour f ≠ f t .

[0061] According to one embodiment of the invention, the CAL calculator calculates during substep E51 the probability p Z t | ξ t observation according to the following equation: p Z t | ξ t=ft ( z t ) = | S ( f t , t )|.1 [ f min ( t ), f max ( t )] ( f t where | S ( f t , t )| is the calculated amplitude of the spectrogram S ( f t , t) filtered for each instant t, f min ( t ) is a minimum frequency trajectory that has been measured, f max ( t ) is a maximum frequency trajectory that has been measured, f min ( t ) And f max ( t ) are such that f min ( t ) ≤ ξ t ≤ f max ( t ), 1 [ f min ( t ) ,f max ( t )] ( f t ) is a function taking the value 1 for f t between f min ( t ) And f max ( t ) and taking the value 0 for f t below f min ( t ) or above f max ( t ) .

[0062] According to one embodiment of the invention, the CAL calculator calculates during substep E51 p Z t f t ξ t = f t z t f t = 1 = 1 c t S f t t .1 f min t , f max t f t where | S ( f t , t )| is the calculated amplitude of the spectrogram S ( f t , t) filtered for each instant t. The CAL calculator calculates the divisor coefficient during substep E51. c t as being the maximum of z t [ f ] for the frequency f located between the minimum trajectory f min ( t ) of frequency and the maximum trajectory f max ( t ) of frequency, that is to say: c t = max f ∈ f min t , f max t z t f .

[0063] The CAL computer measures or determines the minimum trajectory during sub-step E51 f min ( t ) of frequency. The CAL computer measures or determines the maximum trajectory during substep E51 f max ( t ) of frequency. The trajectory çt of frequency of speed v of movement of the vehicle VE is between the minimum trajectory f min ( t ) of frequency and the maximum trajectory f max ( t ) of frequency. Therefore, we have f min ( t ) ≤ ξ t ≤ f max ( t ) .

[0064] The CAL calculator calculates function 1 during substep E51 [ f min ( t ) ,f max ( t )] (ft) as being a single-slot function between f min ( t ) And f max ( t ), that is, the function taking the value 1 for f t between f min (t ) And f max ( t ) and taking the value 0 for f t below f min ( t ) or above f max ( t ) .

[0065] The minimum trajectory f min ( t ) of frequency and the maximum trajectory f max ( t ) of frequency allow us to take into account only the peaks of the components in the vicinity of the trajectory çt of frequency to follow and define a frequency band in which the trajectory çt of frequency is located.

[0066] According to one embodiment of the invention, the minimum trajectory f min ( t ) of frequency is fixed over time t, that is f min ( t ) = f min .

[0067] According to one embodiment of the invention, the maximum trajectory f max ( t ) of frequency is fixed over time t, that is f max ( t ) = f max .

[0068] According to another embodiment of the invention, the minimum trajectory f min ( t ) of frequency is variable over time t.

[0069] According to another embodiment of the invention, the maximum trajectory f max ( t ) of frequency is variable over time t.

[0070] In the case where the trajectory ξ t If the target frequency is spread over a wide frequency band (e.g., a ramp) where other unwanted harmonics may coexist, it is preferable to choose a frequency band that varies over time t. This amounts to defining two trajectories. f min ( t ) And f max ( t ) enveloping the trajectory çt of frequency. For example, the chosen frequency band contains only one complete continuous trajectory ξ t over the entire time period t considered. The continuity constraints that are introduced by the transition law p ξ have the effect of giving more weight to the peaks linked to a regular trajectory curve ξ t frequency. According to one embodiment of the invention, the trajectories f min ( t ) And f max ( t ) can be calculated automatically by the CAL computer. According to one embodiment of the invention, the trajectories f min ( t ) And f max ( t) can be specified by a user to the CAL calculator by randomly selecting points from the spectrogram S(ft, t) that enclose the sequence of peaks to be followed (amplitude maxima) of the spectrogram S(ft, t), and then interpolating these points. Defining the frequency band is optional but significantly improves the method's performance and minimizes computational cost, especially when the observed signal contains a large number of harmonics. Stop intervals can also be identified and this information included in the definition of f min And f max and also in the transition law subsequently. If this information is not available, a simple way to estimate the stopping times from the spectrogram S(ft, t) is to compare the sum of the amplitudes of the spectrogram S(ft, t) at each instant t 0 on all frequencies f at a given threshold ( Si Σ f A ( f, t 0 ) < ε , so stop right now t 0, where ε > 0 is a threshold to be set (for example, the median of all values ​​along the entire time axis). The minimum trajectory f min ( t ) of frequency and / or the maximum trajectory f max ( t The frequency can be entered by the user on the INT1 physical data input interface or may have been pre-recorded in the CAL control unit. If device 1 is integrated into an EV vehicle navigation system, a priori possible data such as, for example f min = 0 and f max can be entered by the user on the INT1 physical data input interface or have been pre-recorded in the CAL computer, for real-time navigation.

[0071] The probability of the observation Z t at every moment t is calculated by the CAL calculator knowing the target frequency ξ t = f t ∈ Ω.

[0072] According to one embodiment of the invention, in the case of a single-component signal with an IF, if the noise-free spectrogram S(ft, t) of the signal is available, then p Z t | ξ t ≠f t ( z t ) = 0 ∀ f t ≠ f t , that is to say the spectrum Z t can only be observed for the frequency f. Otherwise, p Z t | ξ t =f t is important for all frequencies f t where the amplitude of the spectrogram S(ft, t) is maximum at time t. Thus, the function f t → p Z t | ξ t =f t ( z t ) can be multimodal in the case where several peaks (most often related to noise) are present at the moment t In [ f min ( t ) ,f max ( t )] .That is to say, the same observed spectrum can correspond to several plausible frequency solutions. f t . By considering the amplitude of the spectrogram S(ft, t) for several multiples of the target harmonic, we can favor one mode over another. According to one embodiment of the invention, the CAL calculator calculates the probability during substep E51. p Z t | ξ t observation according to the following equation: (the probability is written in this case as the product of several probabilities): p Z t ξ t = f t z t = ∏ j j . f t < F s 2 1 c t S j . f t , t 1 f min t , f max t f t Or y can be any integer or positive real number, satisfying j . f t < F s 2 , and where F s is a threshold frequency, having been predetermined based on the spectrogram S(ft , t).

[0073] In the second sub-step E52 of the fifth step E5, a posterior distribution is estimated by the CAL calculator p ξ | Z trajectory observation ξ t frequency or frequency ξ t This law, enacted after the fact. p ξ | Z observation is proportional to the product of the transition probability p ξ trajectory ξ t frequency and probability p Z t | ξ t trajectory observation ξ t frequency, that is to say p ξ | Z ∝ p ξ · p Z t | ξ t This law, enacted after the fact. p ξ | Z trajectory observation ξ t Frequency is also noted p ξ 1 , … , ξ N S Z 1 , … , Z N S Or p ξ | Z ( f 1, ... , f Ns ).

[0074] According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the CAL calculator calculates the a posteriori law p ξ | Z observation p ξ Z f 1 , … , f N s ∝ p ξ f 1 , … , f N s p Z ξ = f 1 , … , f N s z 1 , … , z N s

[0075] According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the CAL calculator calculates the a posteriori law p ξ | Z observation p ξ Z f 1 , … , f N s ∝ ∏ t = 1 N s − 1 p ξ t + 1 ξ t = f t f t + 1 ∏ t = 1 N s p Z t ξ t = f t z t

[0076] According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the CAL calculator calculates the a posteriori law p ξ | Z observation equal to the product of the transition probability p ξ trajectory ξ t frequency, probability p Z t | ξ t trajectory observation ξ t frequency and a multiplicative factor C calculated by the CAL calculator, that is p ξ | Z = C · p ξ · p Z t | ξt .

[0077] According to one embodiment of the invention, the multiplicative factor C can be taken to be equal to 1.

[0078] According to one embodiment of the invention, in the second substep E52 of the fifth step E5, the CAL calculator calculates the multiplicative factor C equal to C − 1 = ∑ f 1 ∈ Ω ∑ f 2 ∈ Ω … ∑ f N s ∈ Ω p ξ f 1 , … , f N s p Z ξ = f 1 , … , f N s z 1 , … , z N s

[0079] According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the CAL calculator calculates the a posteriori law p ξ | Z observation equal to p ξ Z f 1 , … , f N s = C . p ξ f 1 , … , f N s p Z ξ = f 1 , … , f N s z 1 , … , z N s

[0080] According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the CAL calculator calculates the a posteriori law p ξ | Z observation p ξ Z f 1 , … , f N s = C ⋅ ∏ t = 1 N s − 1 p ξ t + 1 ξ t = f t f t + 1 ∏ t = 1 N s p Z t f t ξ t = f t z t f t = 1

[0081] In the third sub-stage E53 of the fifth stage E5, the CAL computer estimates the trajectory ξ t frequency for successive times t from the posterior distribution p ξ | Z trajectory observation ξ t frequency. The CAL calculator calculates the optimal trajectory as a frequency çt trajectory. ξ ^ = f 1 ^ , f 2 ^ , … , f N s ^ among all possible trajectories in the spectrogram(s) S(ft, t) from the a posteriori law p ξ | Z trajectory observation ξ t frequency, given the observations Z given by the probability p Z t | ξ t observation. An example of a trajectory ξ t frequency calculated from the signal of the figure 5 is illustrated at the figure 10 The frequency trajectory çt or f̂ and / or one or more frequency values ​​of the frequency trajectory çt or f̂ (which may be equal to the instantaneous frequency of the RO wheel) can be provided by the CAL computer on the INT2 data output physical interface, for example by being displayed on a screen. A confidence interval for the calculation, having been calculated by the computer, can be provided by the CAL computer on the INT2 data output physical interface, for example by being displayed on a screen. In the case where device 1 is integrated into a vehicle navigation device, the frequency trajectory çt or f̂ and / or one or more frequency values ​​of the frequency trajectory çt or f̂ can be stored in M ​​memory or in another memory and evaluated in real time in another filter for real-time navigation.

[0082] According to one embodiment of the invention, in the third substep E53 of the fifth step E5, the CAL computer estimates for each instant t the trajectory ξ t frequency as being in the support Ω that of the values f 1< , ... , f Ls< frequency, which maximizes the posterior distribution p ξ | Z trajectory observation ξ t of frequency of velocity v of vehicle movement VE at that instant t. In this case, the CAL computer selects for each instant t the trajectory çt of frequency in the support Ω of the values ​​{ f 1< , ... , f Ls< } of frequency. Therefore, in this case, we have the trajectory ξ t frequency, which is equal to f̂ = argmax p ξ | Z . The calculator includes a maximizing a posterior maximum estimator p ξ | Z ( f 1, ..., f Ns ). The solution to this optimization problem can be easily achieved, for example, by using dynamic programming.

[0083] According to one embodiment of the invention, in the third sub-step E53 of the fifth step E5, the CAL calculator calculates the a posteriori law p ξ | Z observation by convolution (for example two-dimensional) of the probability p Z t | ξ t observation by Gaussian kernels of the transition probability p ξ .

[0084] According to one embodiment of the invention, in the third substep E53 of the fifth step E5, the CAL calculator recursively calculates the posterior law p ξ t | Z 1 ... Z t according to the following equation: p ξ t Z 1 , … Z t ∝ p ξ t Z 1 , … Z t − 1 ∗ N p Z t ξ t Where * is the convolution operator and N is a Gaussian kernel representing the density p ξ t |ξ t-1 These operations are not expensive.

[0085] He then estimates, for each instant t, the trajectory çt of frequency or the frequency ξ t as being a barycenter of the law a posteriori p ξt | Z 1,... Z t , which is taken in respectively the values f 1< , ... , f Ls< frequency of the support Ω and which is respectively affected by these values f 1< , ... , f Ls< of frequency. The frequency çt, thus obtained, is in this case a linear combination of the values f 1< , ... , f Ls< frequency of the support Ω, whose weights are formed by the a posteriori law p ξ | Z , taken respectively the values f 1< , ... , f Ls< of frequency of the support Ω. Therefore, in this case, we have the trajectory ξ t of speed frequency v of vehicle movement VE, which is equal to f ^ t = ∑ f ∈ Ω f . p ξ = f Z 1 , … , Z t

[0086] The trajectory ξ t frequency is thus a kind of a posteriori average, which generates smoother results.

[0087] During a sixth step E6 following the fifth step E5, the computer CAL estimates the speed v of the wheel RO of the vehicle VE for successive times t from the trajectory ξ t of frequency. The wheel speed v of the vehicle's RO (reverse wheel speed) can be provided by the CAL (electronic control unit) on the INT2 physical data output interface, for example, by being displayed on a screen. In the case of a navigation device, the wheel speed v of the vehicle's RO can be stored in MEM (memory memory) or another memory location and evaluated in real time by a separate filter for real-time navigation.

[0088] According to one embodiment of the invention, in the sixth step E6, the computer CAL estimates the speed v of the wheel RO of the vehicle VE for time t by multiplying the trajectory ξ t The speed frequency v of vehicle movement VE is defined by the perimeter 2πR of the wheel RO, where R is the radius of the wheel RO and is predetermined or estimated, for example during navigation by some method. The speed v is also denoted v̂ and in this case is a tangential velocity. Therefore, we have v̂ = 2 πRξ t Or v̂ = 2 πRf̂. The radius R and / or the diameter of the wheel RO and / or the perimeter 2nR of the wheel RO may have been entered by the user on the physical data input interface INT1 or may have been pre-recorded in the computer CAL.

[0089] According to another embodiment of the invention, in the sixth step E6, the computer CAL estimates the speed v of the wheel RO of the vehicle VE at time t as being the rotational frequency of the wheel RO of the vehicle VE (number of revolutions per second), equal to the trajectory ξ t frequency at time t.

[0090] The invention offers the following advantages in particular: Removing a sensor eliminates the need for an odometer. This is very interesting, especially in aeronautics where sensors are very expensive not only because of their resistance to extreme environments (high pressure and temperature) but also for logistical reasons, as even the smallest sensor changes the modal properties of the structure. A precise estimation of the instantaneous velocity v is achieved using information present in a multitude of linearly related harmonics, allowing for the estimation of fine variations in this velocity instead of a coarse estimate. The problem of frequency or speed interception (commonly encountered in aircraft engines) is also considered, as well as the continuity of this variation. The method offers the possibility of progressively improving the accuracy of the estimation by allowing the user to provide prior assumptions about the velocity (for example, whether the engine is accelerating or in a quasi-steady state, depending on the figure 4 Although this information is not mandatory, it can significantly improve the quality of the signal obtained.

[0091] Of course, the embodiments, characteristics, possibilities and examples described above can be combined with each other or selected independently of each other.

Claims

1. A method for estimating a travel speed (v) of a vehicle (VE) having at least one wheel (RO) for rolling on the ground, characterized by: - measuring (E1) an inertial or vibratory signal by at least one inertial or vibratory sensor (CAP) of the vehicle, - calculating (E2) by at least one calculator (CAL) a plurality of spectra (SPt) of the signal over a plurality of successive time windows (Wt) defined with respect to successive instants (t), the plurality of spectra (SPt) forming at least one spectrogram (SP) as a function of the successive instants (t), - filtering (E4) the spectrogram (SP) by at least one noise attenuation and / or deterministic feature extraction filter (FIL), to obtain at least one filtered spectrogram (S(ft, t)) of the signal on the successive instants (t), - estimating (E5) by the calculator (CAL) a frequency trajectory (ξt) representative of the speed (v) of the wheel (RO) of the vehicle (VE) in the filtered spectrogram (S(ft, t)) on the successive instants (t), by: estimating (E51) by the calculator (CAL) a probability (pzt|ξt) of observation of the frequency trajectory (ξt) from a calculated amplitude of the filtered spectrogram (S(ft,t)) for each instant (t), estimating (E52) by the calculator (CAL) an a posteriori law (pξ|Z) of observation of the frequency trajectory (ξt) as being proportional to the product of a prescribed probability (pξ) of transition of the frequency trajectory (ξt) and of the probability (pZt|ξt) of observation of the frequency trajectory (ξt), estimating (E53) by the calculator (CAL) the frequency trajectory (ξt) for the successive instants (t) from the a posteriori law (pξ|Z) of observation of the frequency trajectory (ξt), estimating (E6) by the calculator (CAL) the travel speed (v) of the wheel of the vehicle for the successive instants (t) from the frequency trajectory (ξt), that has been estimated.

2. The method according to claim 1, characterized by determining (E2) by the calculator (CAL) a support (Ω) of frequency values ({f1, ... , fLs}), estimating (E53) by the calculator (CAL) the frequency trajectory (ξt) as being for each instant (t) in the support (Ω) the frequency value (f1, ... , fLs) that maximizes the a posteriori law (pξ|Z) of observation of the frequency trajectory (ξt) until this instant (t).

3. The method according to claim 1, characterized by determining (E2) by the calculator (CAL) a support (Ω) of frequency values ({f1, ... , fLs}), estimating (E53) by the calculator (CAL) the frequency (ξt) for each instant (t) as being a barycenter of the a posteriori law (pξt|Z) of observation of the frequency ((t), taken at the frequency values (f1, ... , fLs) of the support (Ω) and subjected to these frequency values (f1, ... , fLs).

4. The method according to any one of the preceding claims, characterized by determining (E2) by the calculator (CAL) a support Ω of frequency values ({f1, ... , fLs}), estimating (E51) by the calculator (CAL) the probability (pZt|ξt) of observation knowing a trajectory as dependent on the calculated amplitude of the filtered and normalized spectrogram (S(ft, t)) for each instant (t).

5. The method according to claim 4, characterized by estimating (E51) by the calculator (CAL) the probability pZt|ξt of observation is according to the following equation: p Z t ξ t = f t z t = S f t t .1 f min t , f max t f t where |S(ft, t)| is the calculated amplitude of the spectrogram S(ft, t) filtered for each instant t, fmin(t) is a minimum frequency trajectory that has been measured, fmax(t) is a maximum frequency trajectory that has been measured, fmin(t) and fmax(t) are such that fmin(t) ≤ ξt ≤ fmax(t), 1[fmin(t),fmax(t)](ft) is a function taking the value 1 for ft between fmin(t) and fmax(t) and taking the value 0 for ft below fmin(t) or above fmax(t).

6. The method according to claim 4, characterized by estimating (E51) by the calculator (CAL) the probability pZt|ξt of observation according to the following equation: p Z t ξ t = f t z t = ∏ j j . f t < F s 2 1 c t S j . f t , t 1 f min t , f max t f t where j is a positive integer or real number, satisfying j . f t < F s 2 where ft denotes the frequencies of each filtered spectrogram S(ft, t) at the instant t, and where Fs is a threshold frequency that has been predetermined as a function of the filtered spectrogram S(ft, t).

7. The method according to any one of the preceding claims, characterized by determining (E2) by the calculator (CAL) a support Ω of frequency values ({f1, ... , fLs}), prescribing (E3) by the calculator (CAL) the probability pξ(f1, ... , fNs) of transition of the frequency trajectory ξt for the instant Ns starting from a given initial probability pξ1 of the instant 1, for t ∈ {1, ... , Ns} and for each frequency ft ∈ Ω according to the following equation: p ξ f 1 , … , f N s = p ξ 1 f 1 ∏ t = 1 N s − 1 p ξ t + 1 ξ t = f t f t + 1 where Ns is a prescribed integer, greater than or equal to two, of successive prescribed instants t, where pft+1|ξt=ft(ft+1) is the probability of transition from the frequency ξt of the trajectory of the present instant t to the frequency ξt+1 of the frequency trajectory of the next instant t+1.

8. The method according to claim 7, characterized in that the probability pξt+1|ξt=ft(ft+1) of transition from the frequency ξt of the frequency trajectory of the present instant t to the frequency ξt+1 of the frequency trajectory of the next instant t+1 follows a conditional Gaussian law centered on the frequency ft of the filtered spectrogram (S(ft, t)) at the instant t.

9. The method according to claim 8, characterized in that the conditional Gaussian law centered on the frequency ft has a standard deviation σt = Δt.γt where Δt is a calculated time resolution of the spectrogram of the instant t, γt is a calculated average speed with which the frequency trajectory ξt evolves between the instant t and the next instant t+1.

10. The method according to any one of the preceding claims, characterized by estimating (E6) by the calculator (CAL) the travel speed (v) of the wheel of the vehicle by multiplying the frequency trajectory (ξt) by 2πR, where R is the radius of the wheel (RO) and is predetermined or estimated.

11. The method according to any one of claims 8 to 10, characterized in that the noise attenuation and / or deterministic feature extraction filter (FIL) comprises a sliding median filter and / or a deterministic feature separation filter with respect to random features.

12. A device (1) for estimating a travel speed (v) of a vehicle (VE) having at least one wheel (RO) for rolling on the ground, characterized in that the device comprises: an inertial or vibratory sensor (CAP) of the vehicle for measuring (E1) an inertial or vibratory signal, a calculator (CAL) configured to calculate (E2) a plurality of spectra (SPt) of the signal over a plurality of successive time windows (Wt) defined with respect to successive instants (t), the plurality of spectra (SPt) forming at least one spectrogram (SP) as a function of the successive instants (t), a filter (FIL) for attenuating noise and / or extracting deterministic features in the spectrogram (SP), to obtain (E4) at least one filtered spectrogram (S(ft, t)) of the signal over the successive instants (t), the calculator (CAL) being configured to estimate (E5) a frequency trajectory (ξt), representative of the speed (v) of the wheel (RO) of the vehicle (VE) in the filtered spectrogram (S(ft, t)) over the successive instants (t), by: estimation (E51), by the calculator (CAL), of a probability (pZt|ξt) of observation of the frequency trajectory (ξt) from a calculated amplitude of the filtered spectrogram (S(ft,t)) for each instant (t), estimation (E52), by the calculator (CAL), of an a posteriori law (pξ|Z) of observation of the frequency trajectory (ξt) as being proportional to the product of a prescribed probability of transition (pξ) of the frequency trajectory (ξt) and of the probability (pZt|ξt) of observation of the frequency trajectory (ξt), estimation (E53), by the calculator (CAL), of the frequency trajectory (ξt) for the successive instants (t) from the a posteriori law (pξ|Z) of observation of the frequency trajectory (ξt), the calculator (CAL) being configured to estimate (E6) the travel speed (v) of the wheel of the vehicle for the successive instants (t) from the frequency trajectory (ξt).

13. A computer program, comprising code instructions for the implementation of the method for estimating the travel speed (v) of the vehicle according to any one of claims 1 to 11, when it is executed in a calculator (CAL).