A multi-antenna based fmcw radar ranging method and system

Abstract

The application discloses a kind of FMCW radar ranging method and system based on multi-antenna, belong to radar signal processing technical field, comprising: S1, the beat signal of each antenna of FMCW radar is sampled respectively, and the discrete beat signal of each antenna is obtained;S2, based on the discrete beat signal of each antenna, the joint probability density function of FMCW radar is obtained;S3, select any antenna Ant, respectively the time delay of remaining antenna is expressed with the time delay of antenna Ant, and is substituted into joint probability density function;By maximizing joint probability density function, the time delay estimation value of antenna Ant is obtained, based on the relationship between target distance and antenna time delay, the distance between FMCW radar and target is obtained;Wherein, the time delay of antenna is the time difference between radar echo received by antenna and transmission signal.The beat signal of all antennas is combined to carry out ranging in the application, greatly reduce the influence of noise interference, and the ranging precision is higher.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar signal processing, and more particularly relates to a FMCW radar ranging method and system based on multiple antennas. BACKGROUND

[0002] Frequency Modulation Continuous Wave (FMCW) radar was mainly used in military fields such as radar altimeter in the early years. In recent years, with the relaxation of national radar frequency control policy and the continuous development of radar technology, FMCW radar has been widely used in automobile collision avoidance, vital sign detection, and industrial vibration measurement, etc. These application scenarios have high requirements for measurement accuracy, therefore, it is of great significance to study a high-precision FMCW radar ranging method.

[0003] Most of the existing FMCW radar ranging methods are based on the beat signal after mixing the radar echo received by a single antenna with the transmitted signal, which is greatly affected by noise interference and has low ranging accuracy. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a FMCW radar ranging method and system based on multiple antennas to solve the technical problem of low ranging accuracy in the prior art.

[0005] In order to achieve the above purpose, in a first aspect, the present application provides a FMCW radar ranging method based on multiple antennas, comprising the following steps:

[0006] S1, sampling the beat signals of each antenna of the FMCW radar respectively to obtain the discrete beat signals of each antenna;

[0007] S2, obtaining the joint probability density function of the FMCW radar based on the discrete beat signals of each antenna;

[0008] S3, selecting any antenna Ant, representing the time delay of the remaining antennas with the time delay of the antenna Ant, and substituting into the joint probability density function; after obtaining the time delay estimation value of the antenna Ant by maximizing the joint probability density function, obtaining the distance between the FMCW radar and the target based on the relationship between the target distance and the antenna time delay;

[0009] Wherein, the time delay of the antenna is the time difference between the radar echo received by the antenna and the transmitted signal.

[0010] Further preferably, the joint probability density function is:

[0011]

[0012]

[0013]

[0014] wherein k = 0, 1, …, K-1 represents the antenna number; K is the total number of antennas; Z k (n) is the beat signal of the antenna numbered k; is the time delay of the antenna numbered k; σ is the noise variance of the radar system; N is the number of sampling points of the beat signal; is the real part of the beat signal of the antenna numbered k at the n-th sampling point; is the imaginary part of the beat signal of the antenna numbered k at the n-th sampling point; A k is the amplitude of the beat signal of the antenna numbered k; B is the bandwidth of the radar transmitting signal; f0is the center frequency of the radar transmitting signal.

[0015] Further preferably, the time delay of the antenna numbered k is:

[0016]

[0017] wherein t d is the time delay of the antenna Ant; p k is the distance of the antenna numbered k relative to the antenna Ant; λ is the wavelength corresponding to the starting frequency of the transmitting signal; τ is the wave path time delay difference when the antenna spacing is half the wavelength of the transmitting signal.

[0018] Further preferably, the above step S3 comprises:

[0019] S31, frequency estimation is performed on the discrete beat signal of each antenna using a spectrum estimation method to obtain a frequency estimation result and a corresponding spectrum peak value, and the distance between the antenna and the target is calculated based on the frequency estimation result;

[0020] S32, the distance between the FMCW radar and the target is weighted least squares estimated based on the distance between each antenna and the target and the spacing between each antenna and the antenna Ant, to obtain a distance estimation value between the FMCW radar and the target; wherein the weighting coefficient is the normalized result of the spectrum peak value of the beat signal corresponding to the antenna.

[0021] Further preferably, the distance estimation value between the FMCW radar and the target is:

[0022]

[0023]

[0024] wherein K is the total number of antennas; is the weighting coefficient corresponding to the antenna numbered k; A k is the spectral peak value of the beat signal corresponding to the antenna numbered k; R k is the distance between the antenna numbered k and the target; p k is the distance between the antenna numbered k and the antenna Ant.

[0025] Further preferably, the distance between the antenna numbered k and the target is:

[0026]

[0027] wherein c is the speed of light; T is the sweep frequency repetition period of the transmitted signal; is the frequency estimation result of the antenna numbered k; B is the modulation bandwidth of the transmitted signal.

[0028] Further preferably, the method for frequency estimation of the discrete beat signal of the antenna by using the spectrum estimation method comprises:

[0029] performing Fourier transform on the discrete beat signal of the antenna, and taking the frequency at the peak of the obtained Fourier transform spectrum as the coarsely estimated frequency; within a distance resolution unit on both sides of the coarsely estimated frequency, performing CZT refinement on the Fourier transform spectrum, multiplying the CZT refined spectrum with the phase expression represented by frequency, taking the real part of the multiplied result to obtain the coherent CZT spectrum, and taking the frequency at the peak of the coherent CZT spectrum as the frequency estimation result of the antenna.

[0030] Correspondingly, the above weighting coefficient is the normalized result of the peak of the coherent CZT spectrum of the antenna.

[0031] Further preferably, the above phase expression represented by frequency is:

[0032]

[0033] wherein f0is the starting frequency of the transmitted signal; B is the modulation bandwidth of the transmitted signal; f s is the sampling rate for sampling the beat signal of the antenna, and N is the corresponding sampling point number; f1' is the starting refinement frequency for CZT refinement of the Fourier transform spectrum; m = 0, 1, …, M; M is the refinement point number for CZT refinement of the Fourier transform spectrum.

[0034] In a second aspect, the present application provides a multi-antenna based FMCW radar ranging system, comprising a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the FMCW radar ranging method provided in the first aspect of the present application.

[0035] In a third aspect, the present application further provides a computer readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls a device where the storage medium is located to perform the FMCW radar ranging method provided in the first aspect of the present application.

[0036] Overall, the above technical solutions conceived by the present application can achieve the following beneficial effects:

[0037] 1. The present application provides a multi-antenna based FMCW radar ranging method, which establishes a joint probability density function of FMCW radar beat signals by integrating the beat signals of all antennas, and maximizes the joint probability density function by using the time delay of a single antenna to represent the time delays of all antennas in the joint probability density function based on the relationship between the time delays of all antennas, so as to solve the distance between the FMCW radar and the target. The present application integrates the beat signals of all antennas for ranging, greatly reducing the influence of noise interference and improving the ranging accuracy.

[0038] 2. The present application proposes a more practical multi-antenna based FMCW radar ranging method according to the relationship between the maximum likelihood estimation expression and the beat signal spectrum. The method uses the normalized result of the spectrum peak of the beat signal corresponding to the antenna as the weighting coefficient, and performs weighted least squares estimation on the distance between each antenna and the target and the distance between each antenna and the antenna Ant, to obtain the final multi-antenna joint distance estimation result, eliminating the heteroscedasticity of the distance measurement results of different antennas, making the final joint estimation result more accurate, and providing specific implementation steps for maximizing the joint probability density function, which has certain practical value.

[0039] 3. The multi-antenna based FMCW radar ranging method provided by the present application utilizes the characteristics that the phase and frequency of the FMCW radar beat signal do not change independently, obtains a spectrum containing phase information, i.e. a coherent CZT spectrum, and uses the spectrum for frequency estimation to obtain higher ranging accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 Flowchart of the multi-antenna based FMCW radar ranging method provided for Embodiment 1 of the present application;

[0041] Figure 2The CRB of single-antenna distance estimation and the CRB of single-antenna distance estimation provided by the embodiment 1 of the present application when the antenna is a uniform linear array and the amplitudes of the antenna beat signals are the same;

[0042] Figure 3 The CRB of single-antenna distance estimation and the CRB of single-antenna distance estimation provided by the embodiment 1 of the present application when the antenna is a non-uniform linear array and the amplitudes of the antenna beat signals are the same;

[0043] Figure 4 The CRB of single-antenna distance estimation and the CRB of single-antenna distance estimation provided by the embodiment 1 of the present application when the antenna is a uniform linear array and the amplitudes of the antenna beat signals are different;

[0044] Figure 5 The CRB of single-antenna distance estimation and the CRB of single-antenna distance estimation provided by the embodiment 1 of the present application when the antenna is a non-uniform linear array and the amplitudes of the antenna beat signals are different. DETAILED DESCRIPTION

[0045] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0046] Embodiment 1,

[0047] The embodiment provides a multi-antenna-based FMCW radar ranging method for measuring the distance between the FMCW radar and the target. The FMCW radar ranging method provided by the embodiment is suitable for the field of high-precision ranging of linear frequency modulation continuous wave radar, and the ranging precision is improved compared with the single-antenna ranging precision.

[0048] In the embodiment, the noise variances of the antennas are the same, and the noise variance σ 2 Experiments are performed in the range of 0.0025-0.0158. Because the amplitudes of the beat signals on the antennas are not necessarily the same, the signal-to-noise ratios of the antennas are different, so the equivalent signal-to-noise ratio is proposed as an independent variable for the experiment, and the expression is as follows:

[0049]

[0050] The FMCW radar parameters are set as follows:

[0051] Table 1

[0052]

[0053]

[0054] Specifically, as shown in Figure 1 the above FMCW radar ranging method comprises the following steps:

[0055] S1, respectively, the beat signal of each antenna of the FMCW radar is sampled to obtain the discrete beat signal of each antenna;

[0056] The basic model of the multi-antenna FMCW radar beat signal is as follows:

[0057]

[0058] Wherein, k = 0, 1, L, K-1 represents the antenna number, Z k (n) is the beat signal of the antenna numbered k, A k is the amplitude of the beat signal of the antenna numbered k, B is the bandwidth of the radar transmitting signal, f0 is the center frequency of the radar transmitting signal, N is the number of beat signal sampling points, W k (n) represents the complex Gaussian white noise on the kth antenna, is the time delay of the antenna numbered k; wherein, the time delay of the antenna is the time difference between the radar echo received by the antenna and the transmitting signal.

[0059] S2, based on the discrete beat signal of each antenna, the joint probability density function of the FMCW radar is obtained;

[0060] Specifically, the above beat signal is decomposed into real and imaginary parts, wherein the real and imaginary parts of the beat signal of the antenna numbered k at the nth sampling point are respectively:

[0061]

[0062]

[0063] Wherein,

[0064]

[0065]

[0066] When taking as an unknown parameter, the joint probability density function of Z k (n) is:

[0067]

[0068] ​wherein, sigma is noise variance of the radar system.

[0069] S3, selecting any antenna Ant, respectively, time delay of the remaining antennas is represented by time delay of the antenna Ant, and is substituted into the joint probability density function; by maximizing the joint probability density function, the time delay estimation value of the antenna Ant is obtained, and based on the relationship between the target distance and the antenna time delay, the distance between the FMCW radar and the target is obtained.

[0070] Specifically, the time delay of the antenna numbered k is:

[0071]

[0072] wherein, t d is the time delay of the antenna Ant; p k is the distance of the antenna numbered k relative to the antenna Ant; lambda is the wavelength corresponding to the starting frequency of the transmitted signal; tau is the wave path time delay difference corresponding to the half wavelength of the transmitted signal when the antenna spacing is the half wavelength of the transmitted signal, specifically,

[0073]

[0074] wherein, theta is the included angle between the target incident direction and the antenna.

[0075] Selecting any antenna Ant, respectively, time delay of the remaining antennas is represented by time delay of the antenna Ant, and is substituted into the joint probability density function; the joint probability density function obtained by substituting into the joint probability density function is f(Z; t d ,tau), and the present application proposes a maximum likelihood (ML) estimation method for the multi-antenna model to obtain the distance estimation result.

[0076] The ML estimation value of t d refers to the value of t d that maximizes the joint probability density function f(Z; t d ,tau) of the beat signal when the FMCW radar beat signal Z is the observation sample vector, that is, The value of logf(Z; t d ,tau) is maximum, that is, the following formula is maximum;

[0077]

[0078] After simplification, to make L0 maximum is equivalent to making the following formula maximum;

[0079]

[0080] Substituting the expression of t into the above formula obtains:

[0081]

[0082] The parameter value to be estimated can be obtained by two-dimensional search

[0083]

[0084] The ML estimation value of t d After that, the estimation value of the distance between the radar and the target can be obtained:

[0085]

[0086] In order to improve the calculation efficiency, the present application obtains a suboptimal algorithm according to the derivation process of the ML estimation; specifically, because the complexity of the two-dimensional search according to the expression of L is high, there is the following suboptimal algorithm, that is:

[0087]

[0088] Wherein, L k represents the ML function expression of the kth antenna. The optimal solution of the time delay parameter of each antenna can be obtained by maximizing L k , that is:

[0089]

[0090] In an ideal case According to the least square principle, the estimation value of t d can be obtained, but in practice, it will be disturbed by noise, at this time The estimation value of t

[0091]

[0092] The estimation variance of t k is the variance of the noise n

[0093]

[0094] When the noise disturbance of each antenna is the same, the standard least square method can be used for calculation, when the noise disturbance of each antenna is different, that is, n k is different, The estimation variance of t

[0095] According to , it can be known that:

[0096] ​

[0097] where CRB(R k ) denotes the CRB of each single antenna, whose expression is:

[0098]

[0099] According to the expression of CRB(R k ), it can be known that when the antenna noise is constant, the variance of the single antenna distance estimation is inversely proportional to the square of the signal amplitude, so the amplitude A k of the antenna beat signal is different, which shows that the heteroscedasticity of the distance parameters measured by each antenna is caused by the different amplitudes of the antenna beat signals.

[0100] Because CRB(R k ) is inversely proportional to the square of the amplitude of the antenna beat signal, the weight w k should be proportional to the amplitude, and for the convenience of calculation, the weight is normalized as follows:

[0101]

[0102] At this time

[0103] According to the principle of weighted least squares, we can get:

[0104]

[0105]

[0106] Substituting p k = λd k 2 into the above formula, we can get:

[0107]

[0108]

[0109] where R k denotes the distance measured by the kth antenna.

[0110] Observing the expression of L k , it can be found that it represents the calculation expression of the coherent CZT spectrum of each antenna, so it can be known that the multi-antenna maximum likelihood algorithm has a certain relationship with the coherent CZT spectrum, and the ML estimation result of each antenna is equal to the time delay corresponding to the maximum value of the coherent spectrum of each antenna, so we can get a practical multi-antenna-based FMCW radar high-precision ranging algorithm, and the specific steps are as follows:

[0111] ​​S31, frequency estimation is performed on the discrete beat signal of each antenna by using a spectrum estimation method to obtain a frequency estimation result and a corresponding spectrum peak value, and a distance between the antenna and the target is calculated based on the frequency estimation result;

[0112] It should be noted that there are various spectrum estimation methods, such as an FFT zero padding method and an amplitude ratio method. In the FFT zero padding method, a certain number of zeros are padded at the end of the beat signal, so that the number of points of the beat signal is N1, and then N1-point FFT is performed on the beat signal after zero padding to obtain an FFT spectrum, and the frequency corresponding to the FFT spectrum peak value is the frequency estimation result. Correspondingly, in this method, the subsequent weighting coefficient is the result of normalization of the FFT spectrum peak value of the antenna. In the amplitude ratio method, Fourier transform is first performed on the beat signal to obtain a Fourier spectrum, and an equation of the frequency difference is established by using the spectrum peak value and the information of its adjacent spectrum to estimate the frequency. Correspondingly, in this method, the subsequent weighting coefficient is the result of normalization of the spectrum peak value corresponding to the estimated frequency of the antenna.

[0113] Preferably, in the embodiment, the method for performing frequency estimation on the discrete beat signal of the antenna by using the spectrum estimation method comprises:

[0114] Fourier transform is performed on the discrete beat signal of the antenna, and the frequency at the Fourier transform spectrum peak value is taken as a coarse estimation frequency. Within a distance resolution unit on both sides of the coarse estimation frequency, the Fourier transform spectrum is refined by CZT, multiplied by a phase expression represented by a frequency, the real part of the multiplied result is taken to obtain a coherent CZT spectrum, and the frequency at the coherent CZT spectrum peak value is taken as the frequency estimation result of the antenna. Correspondingly, the above-mentioned weighting coefficient is the result of normalization of the coherent CZT spectrum peak value of the antenna.

[0115] The phase expression represented by the frequency is:

[0116]

[0117] wherein f0 is a starting frequency of the transmitted signal; B is a modulation bandwidth of the transmitted signal; f s is a sampling rate for sampling the beat signal of the antenna, and N is a corresponding sampling point number; f1' is a starting refinement frequency for refining the Fourier transform spectrum by CZT; m = 0, 1, …, M; M is a refinement point number for refining the Fourier transform spectrum by CZT.

[0118] Further, the distance between the antenna numbered k and the target is:

[0119]

[0120] Wherein, c is the speed of light; T is the sweep repetition period of the transmitted signal; is the frequency estimation result of the antenna numbered k; B is the modulation bandwidth of the transmitted signal.

[0121] S32, based on the distance between each antenna and the target and the distance between each antenna and the antenna Ant, the distance between the FMCW radar and the target is weighted least square estimated to obtain the distance estimation value between the FMCW radar and the target; wherein the weighting coefficient is the normalized result of the frequency spectrum peak value of the beat signal corresponding to the antenna.

[0122] Specifically, the distance estimation value between the FMCW radar and the target is:

[0123]

[0124]

[0125] Wherein, K is the total number of antennas; is the weighting coefficient corresponding to the antenna numbered k; A k is the frequency spectrum peak value of the beat signal corresponding to the antenna numbered k; R k is the distance between the antenna numbered k and the target; p k is the distance between the antenna numbered k and the antenna Ant.

[0126] In order to further illustrate the FMCW radar ranging method based on multiple antennas provided by the present application, the following will be described in detail with an optional embodiment as an example:

[0127] In this optional embodiment, the total number of antennas K is 4, and the antenna numbered 0 is selected as the antenna Ant; the distance p between each antenna and the antenna Ant is k Set as follows:

[0128]

[0129] Wherein q is an arbitrary constant, when the antenna is a uniform linear array, q=k.

[0130] The FMCW radar ranging method provided by the present embodiment is used for signal processing by Matlab, and the specific process is as follows:

[0131] C1, generate the discrete beat signals of the four antennas sampled by N points by Matlab,

[0132]

[0133] Wherein, A k is the amplitude of the four antenna beat signals, are the time delays corresponding to the four antennas respectively; W k (n) is noise.

[0134] C2, Fourier transform the discrete beat signals of the four antennas respectively to obtain Fourier transform spectrum of the discrete beat signals; take the frequency at the peak of the Fourier transform spectrum as the coarse frequency estimate

[0135] C3, at the coarse frequency estimate two distance resolution units, i.e. f s N, multiply the Fourier spectrum after M-point CZT refinement with the phase expression represented by frequency, take the real part of the result after multiplication to obtain the coherent CZT spectrum; take the frequency at the peak of the coherent CZT spectrum of each antenna as the fine frequency estimate At the same time, record the peak value of the coherent CZT spectrum as

[0136] Specifically, perform M-point CZT refinement on the Fourier transform spectrum within the range of ±f s / 2N on both sides of the peak to obtain its spectrum as S k (z m ) and multiply it with the phase expression represented by frequency.

[0137] Specifically, the phase expression represented by frequency is:

[0138]

[0139] wherein, m = 0, 1, …, M; indicates the CZT refinement starting frequency corresponding to the kth antenna.

[0140] The expression after multiplying the phase expression represented by frequency is:

[0141]

[0142] Take the real part to obtain the coherent CZT spectrum as:

[0143]

[0144] Find the peak position of the coherent CZT spectrum The final frequency estimate is obtained as:

[0145]

[0146]

[0147] C4, based on the fine frequency estimate of each antenna​ The distance between each antenna of the FMCW radar and the target is calculated.

[0148] Specifically, the distance between each antenna of the FMCW radar and the target is:

[0149]

[0150] C5, the peak value of the coherent CZT spectrum of each antenna is approximately equal to the amplitude of the antenna beat signal, which is used as a weighting coefficient; specifically, the peak value of the coherent CZT spectrum is denoted as The weighting coefficient w is obtained k , w k After normalization, we get

[0151]

[0152] C6, the weighted result and the calculated distance R between each antenna and the target are brought into the following formula to obtain the distance estimation result of the multi-antenna: k

[0153]

[0154]

[0155] In order to more clearly illustrate that the FMCW radar distance estimation algorithm based on multi-antenna proposed by the present application has higher precision, the joint measurement result based on four antennas is compared with the four measurement results based on a single antenna. According to the antenna distribution and the difference in antenna received signal amplitude, the following four cases are used for experiments.

[0156] (1) The antennas are uniform linear arrays, and the antenna beat signal amplitudes are the same. At this time

[0157]

[0158] A k = 1, k = 0, 1, 2, 3

[0159] The experimental simulation results are shown in Figure 2 , wherein the CRB of each antenna is the same.

[0160] (2) The antennas are non-uniform linear arrays, and the antenna beat signal amplitudes are the same. At this time

[0161]

[0162] A k = 1, k = 0, 1, 2, 3

[0163] The experimental simulation results are shown in Figure 3 , wherein the CRB of each antenna is the same.​

[0164] (3) Antennas are uniform linear arrays, and the beat signal amplitudes of the antennas are different.

[0165]

[0166] A k ={1, 1, 0.5, 0.5}, k = 0, 1, 2, 3

[0167] The experimental simulation results are shown in Figure 4 , wherein the beat signal amplitudes of the antenna 1 and the antenna 2 are the same, and the beat signal amplitudes of the antenna 3 and the antenna 4 are the same.

[0168] (4) Antennas are non-uniform linear arrays, and the beat signal amplitudes of the antennas are different.

[0169]

[0170] A k ={1, 1, 0.5, 0.5}, k = 0, 1, 2, 3

[0171] The experimental simulation results are shown in Figure 5 , wherein the beat signal amplitudes of the antenna 1 and the antenna 2 are the same, and the beat signal amplitudes of the antenna 3 and the antenna 4 are the same.

[0172] It can be seen from Figures 2-5 that the CRB of the joint distance estimation of the four antennas is smaller than the CRB of the single-antenna distance estimation in any case, and the root mean square error of the distance estimation of the FMCW radar beat signal by using the method provided in the application approximates to the CRB of the multi-antenna distance estimation, while the root mean square error of the distance estimation based on the single antenna can only approximate to the CRB of the single antenna, thereby proving that the multi-antenna based FMCW radar high-precision ranging method provided in the application has higher precision and better ranging performance than the existing single-antenna ranging algorithm. Figures 2-3 Comparing Figures 4-5 , it can also be seen that the influence of the signal amplitude on the distance estimation result is greater than the influence of the antenna spacing on the distance estimation result.

[0173] In order to further illustrate the accuracy of the multi-antenna based FMCW radar ranging method provided in the application, the following is derived theoretically:

[0174] The unbiased Cramer-Rao bound is the inverse diagonal element of the Fisher information matrix J, and the elements of J are:

[0175] J ij =E{H i H j}=-E{H ij}

[0176] where i,j = 1,2, E denotes expectation, H i , H j is a function of Z, specifically:

[0177]

[0178]

[0179] Thus the Cramer-Rao bound of the unknown parameter t d and τ is:

[0180]

[0181]

[0182] is the first diagonal element of J -1 is the second diagonal element of J -1

[0183] According to the expression of

[0184]

[0185]

[0186]

[0187]

[0188] Accordingly, the elements of matrix J can be calculated as:

[0189]

[0190]

[0191]

[0192] Thus the matrix J is:

[0193]

[0194] The inverse matrix of J is:

[0195]

[0196] Thus the Cramer-Rao bound of the unknown parameter t d is:

[0197] ​​​

[0198] FMCW radar beat signal time delay t d The relationship with the target distance R is as follows:

[0199] R = t d c / 2

[0200] Therefore, the Cramer-Rao bound of the target distance estimation can be obtained as:

[0201]

[0202] In particular, there are three special cases as follows:

[0203] (1) Considering that the amplitudes of the antennas are different, the antennas are uniform linear arrays, and at this time,

[0204]

[0205] where Δr is the spacing between adjacent antennas. Therefore, the CRB of the target distance estimation in this case is:

[0206]

[0207] (2) Considering that the amplitudes of the antennas are the same, the antennas are non-uniform linear arrays, and at this time,

[0208] A k = A

[0209] Therefore, the CRB of the target distance estimation in this case is:

[0210]

[0211] (3) Considering that the amplitudes of the antennas are the same, the antennas are uniform linear arrays, and at this time,

[0212] A k = A

[0213]

[0214] Therefore, the CRB of the target distance estimation in this case is:

[0215]

[0216] When K = 1, it represents the Cramer-Rao bound of single-antenna distance estimation, at this time, the parameter d does not exist, and the matrix J = J 11 Therefore,

[0217]

[0218] where A represents the amplitude of the single-antenna beat signal, and SNR = A 2 2σ 2, which represents the signal-to-noise ratio of the single-antenna radar beat signal.

[0219] Therefore, the ratio of the Cramer-Rao bound of the single-antenna distance estimation to the Cramer-Rao bound of the multi-antenna estimation is:

[0220]

[0221] When K>1, CRB(R1)CRB(R)>1, so the Cramer-Rao bound of the multi-antenna distance estimation is less than the Cramer-Rao bound of the single-antenna, so theoretically, the ranging accuracy of the multi-antenna is higher than that of the single-antenna.

[0222] The present application improves the FMCW radar ranging accuracy from the perspective of multi-antenna, and theoretically derives the CRB expression of the multi-antenna distance estimation, and theoretically demonstrates that the radar ranging based on multi-antenna has improved ranging accuracy compared with single-antenna.

[0223] Embodiment 2,

[0224] A multi-antenna-based FMCW radar ranging system, comprising a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the FMCW radar ranging method provided in Embodiment 1 of the present application.

[0225] The related technical solutions are the same as those in Embodiment 1, which will not be repeated here.

[0226] Embodiment 3,

[0227] A computer-readable storage medium, the computer-readable storage medium includes a stored computer program, wherein when the computer program is run by a processor, the storage medium controls the device where the storage medium is located to execute the FMCW radar ranging method provided in Embodiment 1 of the present application.

[0228] The related technical solutions are the same as those in Embodiment 1, which will not be repeated here.

[0229] Those skilled in the art will readily understand that the above description is only a preferred embodiment of the present application, and is not intended to limit the present application, and any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A multi-antenna based FMCW radar ranging method, characterized by, The method comprises the following steps: S1, sampling the beat signals of each antenna of the FMCW radar to obtain discrete beat signals of each antenna; S2, obtaining a joint probability density function of the FMCW radar based on the discrete beat signals of each antenna; S3, selecting any antenna Ant, representing the time delay of the remaining antennas with the time delay of the antenna Ant, and substituting into the joint probability density function; after obtaining the time delay estimation value of the antenna Ant by maximizing the joint probability density function, obtaining the distance between the FMCW radar and the target based on the relationship between the target distance and the antenna time delay; Wherein, the time delay of the antenna is the time difference between the radar echo received by the antenna and the transmitted signal; The joint probability density function is: wherein, denotes the antenna number; K is the total number of antennas; is the beat signal of the antenna numbered k ; is the time delay of the antenna numbered k ; is the noise variance of the radar system; N is the number of points of the beat signal sampling; is the real part of the beat signal of the antenna numbered k at the n-th sampling point; is the imaginary part of the beat signal of the antenna numbered k at the n-th sampling point; is the amplitude of the beat signal of the antenna numbered k ; B is the bandwidth of the radar transmitted signal; is the center frequency of the radar transmitted signal.

2. The FMCW radar ranging method of claim 1, wherein, The time delay of the antenna numbered k is : wherein, is the time delay of the antenna Ant; , is the distance of the antenna numbered k to the antenna Ant; is the wavelength corresponding to the start frequency of the transmitted signal; is the wave path time delay difference when the antenna spacing is half the wavelength of the transmitted signal.

3. The FMCW radar ranging method according to any one of claims 1-2, characterized in that, The step S3 comprises: S31, performing frequency estimation on the discrete beat signals of each antenna using a spectrum estimation method to obtain frequency estimation results and corresponding spectrum peak values, and calculating the distance between the target and the antenna based on the frequency estimation results; S32, performing weighted least squares estimation on the distance between the FMCW radar and the target based on the distances between the antennas and the target and the distances between the antennas and the antenna Ant to obtain the distance estimation value between the FMCW radar and the target; wherein, the weighting coefficient is the normalized result of the spectrum peak value of the beat signal corresponding to the antenna.

4. The FMCW radar ranging method of claim 3, wherein, The distance estimate between the FMCW radar and the target Is: Wherein, K is the total number of antennas; is the weight coefficient corresponding to the antenna numbered k ; is the spectral peak value of the beat signal corresponding to the antenna numbered k ; is the distance between the antenna numbered k and the target; is the distance between the antenna numbered k and the antenna Ant.

5. The FMCW radar ranging method of claim 3, wherein, The distance between the antenna and the target is: k ​ wherein, is the speed of light; is the sweep repetition period of the transmitted signal; is the frequency estimate for the antenna numbered k is the modulation bandwidth of the transmitted signal.​ 6. The FMCW radar ranging method of claim 3, wherein, The method for performing frequency estimation on the discrete beat signals of the antenna using the spectrum estimation method comprises: Performing Fourier transform on the discrete beat signals of the antenna, and taking the frequency at the peak value of the obtained Fourier transform spectrum as a coarse estimation frequency; within a distance resolution unit on both sides of the coarse estimation frequency, after refining the Fourier transform spectrum by CZT, multiplying the refined result by a phase expression represented by frequency, taking the real part of the multiplied result to obtain a coherent CZT spectrum, and taking the frequency at the peak value of the coherent CZT spectrum as the frequency estimation result of the antenna; Correspondingly, the weighting coefficient is the normalized result of the coherent CZT spectrum peak value of the antenna.

7. The FMCW radar ranging method of claim 6, wherein, The phase expression represented by frequency is: wherein is a start frequency of the transmitted signal; is a modulation bandwidth of the transmitted signal; is a sampling rate at which the beat signal is sampled from the antenna, is a corresponding number of samples; ; is a start refinement frequency of the CZT refinement of the Fourier transformed spectrum; ; M is a number of refinement points of the CZT refinement of the Fourier transformed spectrum.

8. A multi-antenna based FMCW radar ranging system, characterized by, Comprise: A memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the FMCW radar ranging method of any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium comprises a stored computer program, wherein the computer program controls the device where the storage medium is located to execute the FMCW radar ranging method of any one of claims 1-7 when the computer program is run by the processor.

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