The invention relates to a method, a device and a computer program for estimating a travel speed of a vehicle with a wheel for rolling on the ground.
The field of application of the invention is in particular rolling land motor vehicles, aircrafts with a landing gear having wheels rolling on the ground on takeoff or landing.
The instantaneous speed of a vehicle is a very significant data in the field of inertial navigation. In the state of the art, the speed signal is generally measured by an additional speed sensor (odometer) placed on the wheel of the vehicle. The installation of such a sensor has a cost and cannot always be envisaged in some applications, particularly in aeronautics and in military land navigation.
The invention seeks to dispense with a direct speed sensor such as an odometer or a position sensor.
One goal of the invention is to develop a method, a device and a computer program for estimating a travel speed of a vehicle having a wheel for rolling on the ground, which are capable of estimating with accuracy the instantaneous speed of a wheeled vehicle from at least one inertial or vibratory sensor (which may for example be an accelerometer or gyroscope or microphone), by dispensing with a direct speed sensor such as an odometer or a position sensor.
In the state of the art, attempts have been made to overcome the problem of absence of a direct speed sensor by exploiting the information present in the inertial signals, as for example in the document “The Future of Automotive Localization Algorithms: Available, reliable, and scalable localization: Anywhere and anytime” by Rickard Karlsson and Fredrik Gustafsson, 2017. According to this document, the estimate of the instantaneous speed from an inertial signal is calculated by selecting at each instant the more energetic frequency of a spectrogram. This type of approach can be effectively applicable in some simple applications where the noise is low, but not in the application field mentioned above, where the noise-to-signal ratio is often very high. The method described by this document by Rickard Karlsson and Fredrik Gustafsson is not robust to environmental noise such as the combustion of an engine and requires a spectrum in which the peaks are easily identifiable, which is not possible in the presence of a combustion engine. In addition, the spectrum of the inertial or vibratory signal is rich in harmonics, and these undergo considerable energy leaks, which makes the identification of the peaks by Fourier transforms difficult. The great majority of the inertial navigation systems of the state of the art cannot be used in dominant environmental noise.
In some applications, in particular aeronautical applications and military land vehicles, where the number of sensors is very limited, the installation of a position sensor is very difficult, even impossible in aeronautics. The presence of an instantaneous speed signal is of great importance for a navigation system in order to estimate the position of a carrier in a very accurate manner. For this, there is a need to measure this instantaneous speed without the need to add hardware instrumentation on the wheels of the vehicle.
The invention aims to obtain a method, a device and a computer program for estimating a travel speed of a vehicle having a wheel rolling on the ground, which overcome the drawbacks mentioned above and achieves the goals mentioned above.
To this end, a first object of the invention is a method for estimating a travel speed of a vehicle having at least one wheel for rolling on the ground, characterized by:
The invention thus proposes a method for estimating the inertial or vibratory signal, which is robust to noise and which uses the frequency information present in the (inertial or vibratory) measured signal, and a methodology based on a specifically dedicated probabilistic approach. The invention, unlike the state of the art, makes it possible to overcome the environmental noise and to extract a speed signal of the vehicle without using an odometer and thus allows the exploitation of the data in real cases. It is expressed as a function of the amplitude at each point of the time-frequency plane and a transition law making it possible to promote the continuity, the direction and the smoothness of the trajectory while exploiting the kinematics of the system such as the harmonics. An inertial signal is always present in the event that a vehicle navigation system is present. In the case of the vibration sensor, the frequency of the vibrations emitted by the wheels of the vehicle is proportional to the speed of the vehicle (simply multiply by the perimeter of the wheel).
According to one embodiment of the invention, it is provided determining by the calculator a support of frequency values, estimating by the calculator the frequency trajectory as being for each instant in the support the frequency value that maximizes the a posteriori law of observation of the frequency trajectory until this instant.
According to one embodiment of the invention, it is provided determining by the calculator a support of frequency values, estimating by the calculator the frequency for each instant as being a barycenter of the a posteriori law of observation of the frequency, taken at the frequency values of the support and subjected to these frequency values.
According to one embodiment of the invention, it is provided determining by the calculator a support Ω of frequency values, estimating by the calculator the probability of observation knowing a trajectory as dependent on the calculated amplitude of the filtered and normalized spectrogram for each instant.
According to one embodiment of the invention, it is provided estimating by the calculator the probability pZ
p
Z
|ξ
=f
(zt)=|S(ft,t)·1[f
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[f
According to one embodiment of the invention, it is provided estimating by the calculator the probability pZ
where j is a positive integer or real number, satisfying
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).
According to one embodiment of the invention, a support of frequency values is determined by the calculator,
the probability pZ
for ξt=ft∈Ω
with pZ
p
Z
[f]|ξ
=f
(zt[f]=1)=0 for f≠ft
where Zt is a binary vector of observation having a size NS prescribed for the instant t∈{1, . . . , NS} such that Zt[f]=1 if
According to one embodiment of the invention,
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[f
According to one embodiment of the invention, it is provided determining by the calculator a support Ω of frequency values,
prescribing by the calculator the probability pξ(f1, . . . , fN
where NS is a prescribed integer, greater than or equal to two, of successive prescribed instants t,
where pξ
According to one embodiment of the invention, the probability pξ
According to one embodiment of the invention, 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.
According to one embodiment of the invention, it is provided estimating by the calculator the travel speed of the wheel of the vehicle by multiplying the frequency trajectory by 2πR, where R is the radius of the wheel and is predetermined or estimated.
According to one embodiment of the invention, the noise attenuation and/or deterministic feature extraction filter comprises a sliding median filter and/or a deterministic feature separation filter with respect to random features.
A second subject-matter of the invention is a device for estimating a travel speed of a vehicle having at least one wheel for rolling on the ground, characterized in that the device comprises:
an inertial or vibratory sensor of the vehicle for measuring an inertial or vibratory signal,
a calculator 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 filter for attenuating noise and/or extracting deterministic features in the spectrogram, to obtain at least one filtered spectrogram of the signal over the successive instants,
the calculator being configured to estimate a frequency trajectory, representative of the speed of the wheel of the vehicle in the filtered spectrogram over the successive instants, by:
estimation, by the calculator, of a probability of observation of the frequency trajectory from a calculated amplitude of the filtered spectrogram for each instant,
estimation, by the calculator, of an a posteriori law of observation of the frequency trajectory as being proportional to the product of a prescribed probability of transition of the frequency trajectory and of the probability of observation of the frequency trajectory,
estimation, by the calculator, of the frequency trajectory for the successive instants from the a posteriori law of observation of the frequency trajectory,
the calculator being configured to estimate the travel speed of the wheel of the vehicle for the successive instants from the frequency trajectory.
A third subject-matter of the invention is a computer program, comprising code instructions for the implementation of the method for estimating the travel speed of the vehicle as described above, when it is executed in a calculator.
The invention will be better understood upon reading the following description, given only by way of non-limiting example with reference to the figures below of the appended drawings.
Referring to
In the field of application of the invention, mentioned above, in the case where vibratory signals derived from complex mechanical systems such as land vehicles or aeronautical systems are used, these signals are strongly affected by noise (the ambient, combustion and aerodynamic noises, etc.), especially for interfering and asynchronous rotating sources. Thus, the identification of the correct trajectory representing the travel speed v of the vehicle VE 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 discriminated and false peaks due to noise can take their place locally. This first difficulty can be resolved by adding a step E4 of pre-processing the time-frequency representation by noise filtering to improve the emergence of the wheel signature with respect to the background noise. The proposed de-noising method E4 enables not only to attenuate the background noise but also to attenuate the quasi-stationary components in the time-frequency plane in the case where the component sought is strongly non-stationary (ascent regime, descent regime) and conversely attenuates the non-stationary components in the case where the component sought is quasi-stationary.
Then, the multi-component nature of the signal and the possibility of existence of asynchronous components in the engine as in an aircraft engine, means that in the same frequency band, several harmonics can coexist, cross, be very close or even confused. Thus, by simply following the maxima at each instant, one may deviate from the correct trajectory and therefore provide an erroneous estimate of the speed v. To overcome this problem, the invention provides in the estimation procedure, in addition to the amplitude of the spectrogram, additional constraints on the optimal trajectory resulting in the estimation of a probability of transition. Taking into account several harmonics and the direction of the trajectory of interest makes it possible, for example, to give more weight to trajectories closer to that of the instantaneous frequency sought, which is advantageous for the coupling moments between different components. The addition of these regularity constraints by the estimation of a probability of transition also makes it possible to avoid the jumps and discontinuities in the presence of isolated peaks related to the residual noise after the pre-processing step E4.
The objective is to search, among all the possible trajectories in the spectrograms over time, for an optimal frequency trajectory ξt or {circumflex over (ξ)}, which satisfies the considered constraints and which is representative of the speed v of the wheel RO of the vehicle VE. The optimality of one trajectory compared to another is measured by a cost function or in an equivalent way by a probability density. To do so, the information of the spectrogram and the constraints are expressed in the form of probabilities. More particularly, the frequency trajectory ξt or ξ1, . . . , ξN
In the figures, the method for estimating a travel speed v of a vehicle having one (or more) wheel(s) RO for rolling on the ground comprises a first step E1 of measuring a time signal X, which is inertial or vibratory from one (or more) inertial or vibratory sensor(s) CAP of the vehicle. This inertial or vibratory sensor CAP may be located outside the engine of the vehicle. The inertial or vibratory sensor CAP may be present on the wheel RO for rolling on the ground of the vehicle VE. Due to an extreme environment, a sensor is often subject to faults or measurement errors. The sensor(s) CAP can be or comprise one (or more) accelerometer(s) and/or one (or more) gyroscope(s) and/or one (or more) acoustic sensor(s) and/or one (or more) microphone(s). The invention can use inertial sensors that are not located in the engine. Moreover, in the case where the vehicle VE comprises an inertial unit composed of 6 inertial sensors (3 accelerometers and 3 gyroscopes), the invention can use the redundancy of sensors CAP formed by several or all of these 6 inertial sensors to improve the accuracy of the speed information v (the risk of simultaneous measurement error on 6 sensors being lower). An example of a raw signal X as a function of time on the abscissa is illustrated in
During a second step E2 subsequent to the first step E1, several spectra SPt of the time signal X are calculated by one (or more) calculator(s) CAL over respectively several successive (or sliding) time windows Wt, which are defined with respect to successive instants t, as represented for example in
The calculator(s) CAL can be or comprise one or more computer(s), one or more server(s), one or more machine(s), one or more processor(s), one or more microprocessor(s). The calculator CAL can comprise one or more physical data input interface(s) INT1, one or more physical data output interface(s) INT2. This or these physical data input interface(s) INT1 can be or comprise one or more computer keyboard(s), one or more physical data communication port(s), one or more touch screen(s), or the like. This or these physical data output interfaces INT2 can be or comprise one or more physical data communication port(s), one or more screen(s), or the like. The device 1 for estimating the travel speed v of the vehicle having one or more wheel(s) RO for rolling on the ground comprises in particular the sensor(s) CAP, the calculator(s) CAL and the filter(s) FIL, as illustrated by way of example in
The device 1 for estimating the travel speed v of the vehicle VE having a wheel RO can be embedded on the vehicle VE. The device 1 for estimating the travel speed v can be an inertial navigation aid tool and can be integrated into an inertial navigation device, which is comprised in an inertial unit present on the vehicle. The inertial unit can comprise 3 accelerometers in 3 non-parallel directions, 3 gyroscopes around 3 non-parallel directions, the inertial navigation device and navigation functions.
According to one embodiment of the invention, the calculator CAL calculates during the second step E2 for each partial time signal Y the spectrum SPt equal to a Fourier transform (which can be for example a fast Fourier transform FFT), limited to the respective time window Wt, of this partial time signal Y (short-time Fourier transform, also called STFT). The calculator CAL thus calculates the Fourier transform on the sliding windows Wt of the time signal X, and therefore the plurality of spectra SPt for respectively the plurality of successive instants t. Each spectrum SPt gives an amplitude of the spectrum as a function of the frequency f.
For each sensor CAP providing a measurement signal X, the series of spectra SPt thus obtained form, for the successive instants t, a spectrogram SP. The spectrogram SP is calculated by the calculator CAL. Each spectrum SPt forms a column of the spectrogram SP, as illustrated by way of example in
A representation in time-frequency plane, such as for example that of
In the vehicles VE having a wheel RO, the wheels RO can emit vibrations which are manifested in the time-frequency plane by a series of peaks (frequency trajectory ξt). The sources related to the wheels are manifested by continuous and smooth trajectories (frequency trajectory ξt) without sudden jumps in the speed v. The fundamental frequency (frequency trajectory ξt) and its harmonics (other frequency components COMPF) are the most energetic in the time-frequency plane. The frequency of the speed v of the wheel RO of the vehicle VE is manifested in the successive spectra by a smooth trajectory varying according to the state of the system (acceleration, deceleration, stop, etc.). Thus, a simple way of estimating the instantaneous frequency of the signal X then amounts to seeking the positions of the most energetic peaks in the frequency band of the component to be followed (frequency trajectory ξt). Taking into account the multiple harmonics of the fundamental of the wheels and the addition of continuity constraints and the information on the direction make it possible to attenuate the continuous trajectories related to interference components such as the combustion of the engine of the vehicle.
During a fourth step E4 subsequent to the second step E2, the spectra SP t are filtered by one (or more) noise attenuation and/or deterministic feature extraction filter(s) FIL, to obtain a filtered spectrogram S(ft, t) of the signal X over the successive instants t. In the spectrogram S(ft, t), the frequency for the instant t is denoted by ft. This pre-processing E4 makes it possible to provide a cleaner time-frequency representation. In this step E4, it is possible to differentiate the two cases where the target component (speed v) is quasi-stationary or highly non-stationary. In the case of a quasi-stationary target component (speed v), the filter FIL can comprise a separation filter (DRS: deterministic random separation) of deterministic (and therefore predictable) features with respect to random (and therefore not predictable) features, comprising background noise and non-stationary interfering components. In the case of a highly non-stationary target component (speed v), the filter FIL can be configured to reduce the background noise and the time-invariant frequencies (for example ventilation noise, electrical components) and can comprise for this purpose a sliding median filter. An example of a spectrogram S(ft, t) filtered from the signal of
During a fifth step E5 subsequent to the fourth step E4, a frequency trajectory ξt, representative of the instantaneous speed v of the wheel RO of the vehicle VE in the filtered spectrogram S(ft, t) over the successive instants t, is estimated by the calculator CAL. This step E5 comprises the sub-steps E51, E52, E53 which will be described below. In what follows, the frequency trajectory ξt is also denoted ξ.
Indeed, the travel speed v of the wheel RO of the vehicle VE results in a certain frequency component in the time-frequency plane of the spectrogram S(ft, t), this frequency component possibly having a certain frequency (equal in what follows to the frequency trajectory ξt) varying over time and a certain amplitude varying over time. This frequency ξt varying over time t in the spectrogram S(ft, t) therefore forms a frequency trajectory ξt of the speed v of the wheel RO of the vehicle VE as a function of time t in the spectrogram S(ft, t) (and therefore in the time-frequency plane of
Let NS the number (greater than or equal to 2) of time segments or successive instants t in the spectrogram S(ft, t) (abscissa axis in
According to one embodiment of the invention, a support Ω of frequency values {f1, . . . , fL
The frequency trajectory ξt to be estimated is also denoted
The chain of the successive frequencies ξ1, . . . , ξN
According to one embodiment, during the third step E3 subsequent to the second step E2 and prior to the fourth step E4, a probability of transition pξ of the frequency trajectory ξt is prescribed by the calculator CAL according to a Markov chain linking the probability of transition from the frequency ξt of this trajectory at the present instant t to the frequency ξt+1 of this trajectory at the following instant t+1, starting from the given initial probability pξ
According to one embodiment of the invention, the calculator CAL calculates during step E3 the probability pξ(f1, . . . , fN
pξ
We therefore have the joint law of the frequency trajectory ξ, which is given by:
∀(f1, . . . , fN
According to one embodiment of the invention, the calculator CAL calculates during step E3 the probability pξ
pξ
According to one embodiment of the invention, the calculator CAL calculates during step E3 the standard deviation σt of the conditional Gaussian law N as being σt=Δt·γt, where Δt is a calculated time resolution of the filtered spectrogram (S(ft, t), γt is a calculated average speed with which the frequency trajectory ξt evolves between instant t and the next instant t+1. Thus, by decreasing the variance σt2, the smoothing effect will be stronger. The calculation of the transition law pξ
At the first sub-step E51 of the fifth step E5, a probability pZ
According to one embodiment of the invention, the calculator CAL calculates during the sub-step E51 the probability pZ
According to one embodiment of the invention, the calculator CAL calculates during the sub-step E51 the probability pZ
The calculator CAL calculates during the sub-step E51 the binary vector Z or Zt of observation having a size NS prescribed for the instant t∈{1, . . . , NS} (and for each frequency ft∈Ω, that is to say each f1, . . . , fN
Z
t
[f]=1 if
otherwise Zt[f]=0 for f≠
In the foregoing, Z=(Z1, . . . , ZN
The probability of observation pZ
The main idea of the method used is to calculate a probability density from the spectrogram describing the distribution of the observations knowing the target frequency ξt at each instant t. Indeed, for a given ξt=ft∈Ω, the coefficient of Zt for the frequency ft has a high probability of being equal to 1 at the instant t, that is to say it is very probable that the true frequency
According to one embodiment of the invention, the calculator CAL calculates during the sub-step E51 the probability pZ
for ξt=ft∈Ω
with pZ
p
Z
[f]|ξ
=f
(zt[f]=1)=0 for f≠ft.
According to one embodiment of the invention, the calculator CAL calculates during the sub-step E51 the probability pZ
p
Z
|ξ
=f
(zt)=|S(ft, t)|·1[f
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[f
According to one embodiment of the invention, the calculator CAL calculates during the sub-step E51
where |S(ft, t)| is the calculated amplitude of the spectrogram S(ft, t) filtered for each instant t.
The calculator CAL calculates during the sub-step E51 the divisor coefficient c t as being the maximum of zt[f] for the frequency f located between the minimum frequency trajectory fmin(t) and the maximum frequency trajectory fmax(t), that is to say:
The calculator CAL measures or determines during the sub-step E51 the minimum frequency trajectory fmin(t). The calculator CAL measures or determines during the sub-step E51 the maximum frequency trajectory fmax(t). The frequency trajectory ξt of the travel speed v of the vehicle VE is comprised between the minimum frequency trajectory fmin(t) and the maximum frequency trajectory fmax(t). We therefore have fmin(t)≤ξt≤fmax(t).
The calculator CAL calculates during the sub-step E51 the function 1[f
The minimum frequency trajectory fmin(t) and the maximum frequency trajectory fmax(t) make it possible to take into account only the peaks of the components in the vicinity of the frequency trajectory ξt to be followed and define a frequency band in which the frequency trajectory ξt is located.
According to one embodiment of the invention, the minimum frequency trajectory fmin(t) is fixed over time t, that is to say fmin(t)=fmin.
According to one embodiment of the invention, the maximum frequency trajectory fmax(t) is fixed over time t, that is to say fmax(t)=fmax.
According to another embodiment of the invention, the minimum frequency trajectory fmin(t) is variable over time t.
According to another embodiment of the invention, the maximum frequency trajectory fmax(t) is variable over time t.
In the case where the target frequency trajectory ξt is spread over a wide frequency band (for example ramp) where other interference harmonics can coexist, it is preferable to choose a variable frequency band over time t. This amounts to defining two trajectories fmin(t) and fmax(t) surrounding the frequency trajectory ξt. For example, the chosen frequency band contains only one complete continuous trajectory ξt over the entire period of the considered time t. The continuity constraints which are introduced by the transition law pξ have the effect of giving more weight to the peaks linked to a smooth curve of the frequency trajectory ξt. According to one embodiment of the invention, the trajectories fmin(t) and fmax(t) can be calculated automatically by the calculator CAL. According to one embodiment of the invention, the trajectories fmin(t) and fmax(t) can be prescribed by a user to the calculator CAL by random selection of the points of the spectrogram S(ft, t) surrounding the sequence of the peaks to be followed (amplitude maxima) of the spectrogram S(ft, t), then by interpolation of these points. The definition of the frequency band is optional but makes it possible to considerably improve the performance of the method and to minimize the calculation cost, especially in the case where the observed signal contains a large number of harmonics. It is also possible to identify the stop intervals and include this information in the definition of fmin and fmax and also in the transition law thereafter. If this information is not available, a simple way to estimate the stop instants from the spectrogram S(ft, t) is to compare the sum of the amplitudes of the spectrogram S(ft, t) at each instant t0 on all the frequencies f to a given threshold (if ΣfA(f, t0)<ε, then stop at instant t0, where ε>0 is a threshold to be set (for example the median of all the values on the entire time axis)). The minimum frequency trajectory fmin(t) and/or the maximum frequency trajectory fmax(t) can be entered by the user on the physical data input interface INTI or have been pre-recorded in the calculator CAL. In the case where the device 1 is integrated into a navigation device of the vehicle VE, a priori possible data such as for example fmin=0 and fmax can be entered by the user on the physical data input interface INTI or have been pre-recorded in the calculator CAL, for real-time navigation.
The probability of the observation Zt at each instant t is calculated by the calculator CAL knowing the target frequency ξt=ft∈Ω.
According to one embodiment of the invention, in the case of a single-component signal with an IF, if the spectrogram S(ft, t) of the noise-free signal is available, then pZ
where j can be any positive integer or real number, satisfying
and where Fs is a threshold frequency, that has been predetermined as a function of the spectrogram S(ft, t).
In the second sub-step E52 of the fifth step E5, an a posteriori law pξ|Z of observation of the frequency trajectory ξt or of the frequency ξt is estimated by the calculator CAL. This a posteriori law pξ|Z of observation is proportional to the product of the probability of transition pξ of the frequency trajectory ξt and of the probability pZ
According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the calculator CAL calculates the a posteriori law pξ|Z of observation
p
ξ|Z(f1, . . . , fN
According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the calculator CAL calculates the a posteriori law pξ|Z of observation
According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the calculator CAL calculates the a posterior law pξ|Z of observation equal to the product of the probability of transition pξ of the frequency trajectory ξt, of the probability pZ
According to one embodiment of the invention, the multiplicative factor C can be taken equal to 1.
According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the calculator CAL calculates the multiplicative factor C equal to:
According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the calculator CAL calculates the a posteriori law pξ|Z of observation equal to:
p
ξ|Z(f1, . . . , fN
According to one embodiment of the invention, in the second sub-step E52 of the fifth step E5, the calculator CAL calculates the a posteriori law pξ|Z of observation
In the third sub-step E53 of the fifth step E5, the calculator CAL estimates 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 calculates as frequency trajectory ξt the optimal trajectory {circumflex over (ξ)}=({circumflex over (f)}1, {circumflex over (f)}2, . . . , ) among all the possible trajectories in the spectrogram(s) S(ft, t) from the a posteriori lawn pξ|Z of observation of the frequency trajectory ξt, knowing the observations Z given by the probability pZ
According to one embodiment of the invention, in the third sub-step E53 of the fifth step E5, the calculator CAL estimates for each instant t the frequency trajectory ξt as being the one of the frequency values f1, . . . , fL
According to one embodiment of the invention, in the third sub-step E53 of the fifth step E5, the calculator CAL calculates the a posteriori law pξ|Z of observation by (for example two-dimensional) convolution of the probability pZ
According to one embodiment of the invention, in the third sub-step E53 of the fifth step E5, the calculator CAL recursively calculates the a posteriori law pξ
p
ξ
|Z
, . . . Z
∝(pξ
Where * is the convolution operator and N is a Gaussian kernel representing the density pξ
It then estimates for each instant t the frequency trajectory ξt or the frequency ξt as being a barycenter of the a posteriori law pξ
The frequency trajectory ξt is thus a kind of an a posteriori mean, which generates smoother results.
During a sixth step E6 subsequent to the fifth step E5, the calculator CAL estimates the travel speed v of the wheel RO of the vehicle VE for the successive instants t from the frequency trajectory ξt. The travel speed v of the wheel RO of the vehicle VE can be provided by the calculator CAL on the physical data output interface INT2, for example by being displayed on a screen. In the case of a navigation device, the travel speed v of the wheel RO of the vehicle VE can be stored in the memory MEM or in another memory and be evaluated in real time in another filter for real-time navigation.
According to one embodiment of the invention, in the sixth step E6, the calculator CAL estimates the travel speed v of the wheel RO of the vehicle VE for the instant t by multiplying the frequency trajectory ξt of the travel speed v of the vehicle VE 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 the navigation by any method. The speed v is also denoted {circumflex over (v)} and is in this case a tangential speed. We therefore have {circumflex over (v)}=2πRξt or {circumflex over (v)}=2πR{circumflex over (f)}. The radius R and/or the diameter of the wheel RO and/or the perimeter 2πR of the wheel RO may have been entered by the user on the physical data input interface INTI or have been pre-recorded in the calculator CAL.
According to another embodiment of the invention, in the sixth step E6, the calculator CAL estimates the travel speed v of the wheel RO of the vehicle VE for the instant t as being the frequency of rotation of the wheel RO of the vehicle VE (number of revolutions per seconds), equal to the frequency trajectory ξt at the instant t.
The invention has in particular the following advantages:
Of course, the embodiments, characteristics, possibilities and examples described above can be combined with each other or selected independently of each other.
Number | Date | Country | Kind |
---|---|---|---|
FR2102407 | Mar 2021 | FR | national |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/FR2022/050421 | 3/9/2022 | WO |