Method for measuring distance by appropriate fourier transform and radar system for implementing the method

Abstract

A radar system configured to determine radar-ground distance measurements. The radar system includes transmission and reception means configured to transmit two radiofrequency signals towards the ground and to receive the signals obtained by the reflection of the two transmitted signals by the ground and computation means configured to determine the frequential representations of the transmitted signals and of the received signals and determine a frequential quantity as a function of the frequential representations. The radar system is wherein the computation means are configured to sample the frequential quantity over a determined number of samples, which provides a sampled signal; determine a number of frequency measurements as a function of a constant distance measurement accuracy value; determine frequency measurements by applying to the sampled signal a spectral decomposition by fast Fourier transform using a decimation of the sampled signal in a ratio dependent on the distance measurement accuracy value, and determine a distance measurement corresponding to each frequency measurement.

Claims

1. A radar system configured to determine radar-ground distance measurements, the radar system comprising: transmission and reception means configured to transmit two radiofrequency signals towards the ground and to receive the signals obtained by the reflection of the two transmitted signals by the ground; computation means configured to: determine the frequential representations of the transmitted signals and of the received signals; determine a frequential quantity as a function of said frequential representations; the radar system being wherein the computation means are configured to: sample said frequential quantity over a determined number of samples, which provides a sampled signal; determine a number of frequency measurements as a function of a constant distance measurement accuracy value; determine frequency measurements by applying to the sampled signal a spectral decomposition by fast Fourier transform over said number of measurements, the Fourier transform using a decimation of the sampled signal in a ratio dependent on said distance measurement accuracy value, and determine a distance measurement corresponding to each frequency measurement.

2. The radar system according to claim 1, wherein the transmitted signals are composed of a first transmitted radiofrequency signal and of a second transmitted radiofrequency signal, the received signals being composed of a first received signal and of a second received signal, the first received signal corresponding to the signal obtained by the reflection of said first transmitted signal by the ground, the second received signal corresponding to the signal obtained by the reflection of said second transmitted signal by the ground, the computation means being configured to determine said frequential quantity by calculating the difference between a first frequential signal and a second frequential signal, said first frequential signal corresponding to the difference between the frequential representation of the first received signal and the frequential representation of the first transmitted signal, the second frequential signal corresponding to the difference between the frequential representation of the second received signal and the frequential representation of the second transmitted signal.

3. The radar system according to claim 1, wherein the computation means are configured to sample said frequential quantity according to a sampling period, the computation means being configured to determine a minimum sampling period as a function of a maximum frequency value and to determine a number of samples of the sampled signal as a function of a minimum frequency value and of said minimum sampling period.

4. The radar system according to claim 1, wherein the computation means are configured to determine an intermediate parameter as a function of said distance measurement accuracy value, said intermediate parameter being calculated by dividing a first value by a second value, said first value being calculated by adding said measurement accuracy value to the value two, said second value being calculated by subtracting said distance measurement accuracy value from the value two, the computation means being configured to determine said number of frequency measurements as a function of a minimum frequency value, of a maximum frequency value and of said intermediate parameter.

5. The radar system according to claim 4, wherein the computation means are configured to determine the number of frequency measurements by the division of a first logarithmic function by a second logarithmic function, the first logarithmic function corresponding to the Napierian logarithm of the ratio between the maximum frequency value and the minimum frequency value, the second logarithmic function corresponding to the Napierian logarithm of said intermediate parameter.

6. A method for determining radar-ground distance measurements comprising: the transmission of two radiofrequency signals towards the ground and the reception of the signals obtained by the reflection of the two transmitted signals by the ground; the determination of frequential representations of the transmitted signals and of the received signals; the determination of a frequential quantity as a function of said frequential representations; the method being wherein it comprises the steps comprising: the sampling of said frequential quantity over a determined number of samples, which provides a sampled signal; the determination of a number of frequency measurements as a function of a constant distance measurement accuracy value; the determination of frequency measurements by applying to the sampled signal a spectral decomposition by fast Fourier transform over said number of measurements, the Fourier transform using a decimation of the sampled signal in a ratio dependent on said distance measurement accuracy value, and the determination of a distance measurement corresponding to each frequency measurement.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The attached drawings illustrate the invention:

(2) FIG. 1 represents diagrams in a time-frequency reference frame of the transmitted signals and of the received signals according to the mode of operation of the radar system according to the invention.

(3) FIG. 2 represents the spectrum of the frequential signal derived from the frequential representations of the transmitted signals and of the received signals and the sampling of this signal according to the prior art.

(4) FIG. 3 represents a schematic view of a radar system, according to some embodiments of the invention.

(5) FIG. 4 represents a flow diagram illustrating a method for determining radar-ground distance measurements, according to some embodiments of the invention.

(6) FIG. 5 represents a flow diagram illustrating a method for determining frequency measurements by appropriate FFT, according to some embodiments of the invention.

DETAILED DESCRIPTION

(7) The embodiments of the invention provide a radar system and a method for determining radar-ground distance measurements according to a mode of operation which implements the spectral analysis of the frequential representations of the radiofrequency signals transmitted towards the ground and of the signals received following the reflection of the transmitted signals by the ground.

(8) The radar system and the method according to the invention may be used for example in airborne systems, helicopters or aircraft with or without pilot for example.

(9) Referring to FIG. 3, a radar system 300 configured to determine measurements of distance separating the radar from the ground is illustrated, according to some embodiments of the invention. The radar system 300 is configured to determine the distance measurements by using the mode of operation based on the transmission of radiofrequency signals towards the ground, the reception of these signals after reflection by the ground, and the spectral analysis of the transmitted and received signals. To this end, the radar system 300 can comprise transmission and reception means 301 configured to transmit two radiofrequency signals e.sub.0(t) and e.sub.1(t) towards the ground during a time interval T.sub.E and to receive the signals obtained by the reflection of the two transmitted signals by the ground, denoted r.sub.0(t) and r.sub.1(t). The frequency of the first signal e.sub.0(t) exhibits a positive linear variation during the first half of the time interval [0,T.sub.E/2] and the frequency of the second signal e.sub.1(t) exhibits a negative linear variation during the second half of the transmission time interval [T.sub.E/2,T.sub.E]. The frequencies of the transmitted signals vary in a frequency band B. The radiofrequency signals e.sub.0(t) and e.sub.1(t) are radiated by the transmission means 301, are linearly modulated in frequency as a function of time and are expressed by the expressions given in the equation (Math. 1).

(10) The transmitted signals e.sub.0(t) and e.sub.1(t) are reflected by the ground. The reflected signals are also signals that are linearly modulated in frequency, their frequencies vary over the band B and represent, relative to the transmitted signals, a temporal shift τ and a frequency shift denoted f.sub.D due to the Doppler effect generated by the movement of the carrier. The signals received by the reception means 301 comprise a first received signal r.sub.0(t) corresponding to the signal received following the reflection of the first transmitted signal e.sub.0(t) by the ground and a second received signal r.sub.1(t) corresponding to the signal received following the reflection of the second transmitted signal e.sub.1(t) by the ground. The received signals are expressed by the expressions given in the equations (Math. 2) and (Math. 3).

(11) The radar system 300 can comprise a mixer 303 configured to demodulate (or transpose) the received signals with the replica of the transmitted signals using an analogue-digital converter (CAN) 305 configured to convert the transposed signals into digital signals.

(12) The radar system 300 can also comprise computation means 307 configured to perform a spectral analysis of the converted demodulated signals in order to determine measurements of distance separating the radar from the ground from frequency measurements.

(13) Firstly, the computation means 307 may be configured to determine the frequential representations of the transmitted signals and of the received signals. For the instants t lying between 0 and T.sub.E/2, the frequential representations E.sub.0(t) and R.sub.0(t) of the first transmitted signal e.sub.0(t) and of the first received signal r.sub.0(t) are given respectively by the equations (Math. 4) and (Math. 6). For the instants t lying between T.sub.E/2 and T.sub.E, the frequential representations E.sub.1(t) and R.sub.1(t) of the second transmitted signal e.sub.1(t) and of the second received signal r.sub.1(t) are given respectively by the equations (Math. 5) and (Math. 7).

(14) According to one embodiment, the computation means 307 may be configured to determine a frequential quantity D as a function of the frequential representations of the transmitted signals and of the received signals. More specifically, the computation means 307 may be configured to determine the frequential quantity D by calculating the difference between a first frequential signal ΔF.sub.0 and a second frequential signal ΔF.sub.1, the first frequential signal ΔF.sub.0 corresponding to the difference between the frequential representation of the first received signal R.sub.0(t) and the frequential representation of the first transmitted signal E.sub.0(t) as expressed in the equation (Math. 8), the second frequential signal ΔF.sub.1 corresponding to the difference between the frequential representation of the second received signal R.sub.1(t) and the frequential representation of the second transmitted signal E.sub.1(t), as expressed in the equation (Math. 9).

(15) According to one embodiment of the invention, the computation means 307 may be configured to determine the temporal shift τ and consequently the measurements of radar-ground distance from the frequential quantity D according to the relationship given by the equation (Math. 10). More specifically, the computation means 307 may be configured to determine radar-ground distance measurements by performing a spectral analysis of the frequential quantity D. The spectral analysis comprises a step of sampling of the signal D by a clock signal with a sampling frequency F.sub.éch corresponding to a sampling period T.sub.éch>=1/F.sub.éch and a step of spectral decomposition by a fast Fourier transform.

(16) To perform the sampling of the frequential quantity D, the computation means 307 may be configured to determine a minimum sampling period T.sub.éch as a function of a maximum frequency value f.sub.N according to the relationship given by:
T.sub.éch=1/2f.sub.N  [Math. 13]

(17) The expression in the amplitude/time domain of the frequential quantity D may be given by the equation (Math. 11).

(18) The computation means 307 may be configured to determine a number Z of the samples x.sub.m to be acquired of the sampled signal as a function of a minimum frequency value f.sub.0 and of the sampling period according to the relationship given by:

(19) $\begin{array}{cc}Z=\frac{1}{f_0}/T_{é\mathrm{ch}}& \left[\mathrm{Math}.14\right]\end{array}$

(20) The computation means 307 may be configured to sample the frequential quantity represented by the signal x.sub.(t) over Z points (or samples).

(21) The determination of the distance measurements according to the invention is performed by the determination of a number N of frequency measurements by appropriate FFT applied to the sampled signal while retaining a constant distance measurement accuracy value P.

(22) The computation means 307 may be configured to determine a number N of frequency measurements as a function of a given distance measurement accuracy value P. More specifically, the computation means 307 may be configured to determine an intermediate parameter L as a function of a given distance measurement accuracy value P, the intermediate parameter being calculated by dividing a first value by a second value, the first value (2+P) being calculated by adding said measurement accuracy to the value two, the second value (2−P) being calculated by subtracting the distance measurement accuracy value P from the value two. The intermediate parameter is then expressed by:
L=(2+P)/(2−P)  [Math. 15]
In one embodiment of the invention, the computation means 307 may be configured to determine the number N of frequency measurements to be performed by the FFT, that is to say the number of spectral samples of the FFT, as a function of a minimum frequency value, of a maximum frequency value and of the intermediate parameter. More specifically, the computation means 307 may be configured to determine the number N of frequency measurements f.sub.j=X*.sub.j(F) to be calculated by the appropriate FFT by effecting the dividing of a first logarithmic function by a second logarithmic function, the first logarithmic function corresponding to the Napierian logarithm of the ratio between the maximum frequency value f.sub.N and the minimum frequency f.sub.0, the second logarithmic function corresponding to the Napierian logarithm of the intermediate parameter L. The number N of frequency measurements by FFT is thus expressed by:

(23) $\begin{array}{cc}N=\frac{\ln \left(f_N/f_0\right)}{\ln \left(L\right)}& \left[\mathrm{Math}.16\right]\end{array}$

(24) Once the number of frequency measurements to be performed is determined, the computation means 307 may be configured to determine the N frequency measurements f.sub.j=X*.sub.j(F) by applying to the sampled signal x.sub.(t) a spectral decomposition by fast Fourier transform over N points, the Fourier transform using a decimation of the sampled signal in a ratio dependent on the distance measurement accuracy value. More specifically, for each calculation of a frequency measurement f.sub.j=X*f.sub.j(F) of index j, the decimation of the sampled signal is performed in a ratio equal to 1/L.sup.(N-j) given by the inverse of the intermediate parameter to the power of the difference between the number of frequency measurements N and the index of the frequency measurement j.

(25) According to the embodiments of the invention, the frequency measurement by appropriate FFT are expressed by:

(26) $\begin{array}{cc}{f}_j=X_j^{*}\left(F\right)=\underset{m=0}{\overset{N-1}{.Math.}}{\chi }_m{e}^{-\frac{i2\pi }{N}{\mathrm{jmK}}^{\left(N-j\right)}}\mathrm{with}j=0,.Math.,N-1& \left[\mathrm{Math}.17\right]\end{array}$

(27) The determination of a frequency measurement f.sub.j allows the determination of a value of the delay τ according to the relationship of the equation (Math. 10) reformulated for the frequency measurements calculated by FFT by f.sub.j=2Kτ.The determination of the delay τ at the measured frequency allows the determination of a distance measurement d corresponding to this frequency measurement according to the relationship d=c. τ/2.

(28) In one embodiment of the invention, the distance measurement accuracy value may be given as a percentage.

(29) The appropriate FFT according to the invention makes it possible to adapt the frequential step of the frequency measurements by FFT, by decimation, to the distance measured, while keeping a constant distance measurement accuracy value as a function of the measured frequency. In effect, to maintain a constant distance measurement accuracy value, it is not necessary, according to the invention, to maintain a constant frequential resolution as a function of the increase in frequency.

(30) According to the embodiments of the invention, the frequential step of the FFT, denoted ΔF.sub.j, is widened gradually so as to maintain the constant distance measurement accuracy value P=ΔF.sub.j/f.sub.j. The values of f.sub.j are distributed in a non-constant manner and the values of x.sub.m are samples spaced apart differently in time as a function of the measured frequencies f.sub.j. The decimation of the sampled signal depends thus on the measured frequency as illustrated in the decimation ratio for the j.sup.th frequency measurement f.sub.j given by 1/(L(.sup.N-j)).

(31) The invention provides further a method for determining radar-ground distance measurements by spectral analysis of radiofrequency signals transmitted and received by a radar system while maintaining a constant distance measurement accuracy value as a function of the increase in measured frequencies.

(32) Referring to FIG. 4, the method can comprise steps for the transmission and the reception of two radiofrequency signals and steps for the processing of the received signals.

(33) In the step 400, two radiofrequency signals e.sub.0(t) and e.sub.1(t) may be transmitted towards the ground during a time interval T.sub.E such that the frequency of the first signal e.sub.0(t) exhibits a positive linear variation during the first half of the time interval [0,T.sub.E/2] and the frequency of the second signal e.sub.1(t) exhibits a negative linear variation during the second half of the transmission time interval [T.sub.E/2,T.sub.E]. The frequencies of the transmitted signals vary in a frequency band B. The radiofrequency signals e.sub.0(t) and e.sub.1(t) are linearly modulated in frequency as a function of time and are expressed by the expressions given in the equation (Math. 1).

(34) In the step 401, the signals obtained by the reflection of the transmitted signals by the ground may be received. The received signals comprise a first received signal r.sub.0(t) corresponding to the signal received following the reflection of the first transmitted signal e.sub.0(t) by the ground and a second received signal r.sub.1(t) corresponding to the signal received following the reflection of the second transmitted signal e.sub.1(t) by the ground. The received signals are expressed by the expressions given in the equations (Math. 2) and (Math. 3). The step 401 can comprise a substep for the demodulation of the received signals and the conversion of the demodulated signals into analogue signals.

(35) In the step 402, frequential representations of the transmitted signals and of the received signals may be determined. For the instants t lying between 0 and T.sub.E/2, the frequential representations E.sub.0(t) and R.sub.0(t) of the first transmitted signal e.sub.0(t) and of the first received signal r.sub.0(t) may be determined respectively by the equations (Math. 4) and (Math. 6). For the instants t lying between T.sub.E/2 and T.sub.E, the frequential representations E.sub.1(t) and R.sub.1(t) of the second transmitted signal e.sub.1(t) and of the second received signal r.sub.1(t) may be determined respectively by the equations (Math. 5) and (Math. 7).

(36) In the step 403, a frequential quantity D may be determined as a function of the frequential representations of the transmitted signals and of the received signals. More specifically, the frequential quantity D may be determined by calculating the difference between a first frequential signal ΔF.sub.0 and a second frequential signal ΔF.sub.1, the first frequential signal ΔF.sub.0 corresponding to the difference between the frequential representation of the first received signal R.sub.0(t) and the frequential representation of the first transmitted signal E.sub.0(t) as expressed in the equation (Math. 8), the second frequential signal ΔF.sub.1 corresponding to the difference between the frequential representation of the second received signal R.sub.1(t) and the frequential representation of the second transmitted signal E.sub.1(t) as expressed in the equation (Math. 9).

(37) In the step 404, N frequency measurements f.sub.j=X*.sub.j(F), j=1, . . . , N may be determined by performing a sampling of the frequential quantity D over a determined number of samples Z and by applying to the sampled signal a spectral decomposition by fast Fourier transform over the number N of frequency measurements, the Fourier transform using a decimation of the sampled signal in a ratio dependent on the distance measurement accuracy value.

(38) According to one embodiment, the number N of measurements may be determined in the step 404 as a function of a constant distance measurement accuracy value.

(39) In the step 405, radar-ground distance measurements may be determined from the frequency measurements determined in the step 404. This step can comprise a substep of determination of the temporal shift using the relationship f.sub.j=2Kτ between the temporal shift and each frequency measurement, and a substep of determination of a distance measurement d corresponding to the temporal shift measured for a given frequency measurement according to the relationship d=c. τ/2.

(40) FIG. 5 is a flow diagram illustrating the step 404 of determination of frequency measurements according to some embodiments of the invention.

(41) In the step 500, a minimum frequency value f.sub.0, a maximum frequency value f.sub.N, a constant measurement accuracy value P, and the frequency band B of the transmitted signals may be received.

(42) In the step 501, a minimum sampling period may be determined as a function of the maximum frequency value such that T.sub.éch<=1/2f.sub.N.

(43) In the step 502, a number of samples Z of the sampled signal to be acquired may be determined as a function of the sampling period and of the minimum frequency value as expressed in the equation (Math. 14).

(44) In the step 503, an intermediate parameter L may be determined as a function of the measurement accuracy value P as expressed in the equation (Math. 15).

(45) In the step 504, the number N of frequency measurements to be performed by the FFT, that is to say the number of spectral samples of the FFT, may be determined as a function of the minimum frequency value f.sub.0, of the maximum frequency value f.sub.N and of the intermediate parameter L as given in the equation (Math. 16).

(46) In the step 505, N frequency measurements f.sub.j=X*.sub.j(F) may be determined by applying to the sampled signal x.sub.(t) a spectral decomposition by fast Fourier transform over N points, the Fourier transform using a decimation of the sampled signal in a ratio dependent on the distance measurement accuracy value. More specifically, for each calculation of a frequency measurement f.sub.j=X*.sub.j(F) of index j, the decimation of the sampled signal is performed in a ratio equal to 1/L.sup.(N-j), given by the inverse of the intermediate parameter to the power of the difference between the number of frequency measurements N and the index of the frequency measurement j. The FFT frequency measurements are given by the equation (Math. 17).

(47) The invention also provides a computer program product comprising code instructions making it possible to perform the steps of the method when said program is run on a computer.

(48) Generally, the routines executed to implement the embodiments of the invention, whether they are implemented in the context of an operating system or of a specific application, of a component, of a program, of an object, of a module or of a sequence of instructions, or even of a subset thereof, can be designated herein as “computer program code” or simply “program code”. The program code typically comprises instructions that can be read by computer which reside at various moments in various memory and storage devices in a computer and which, when they are read and executed by one or more processors in a computer, cause the computer to perform the operations necessary to execute the operations and/or the elements specific to the various aspects of the embodiments of the invention. The instructions of a program, that can be read by computer, to perform the operations of the embodiments of the invention, may be, for example, the assembly language, or even a source code or an object code written in combination with one or more programming languages.