A FMCW radar ranging method based on compressed sensing and spectrum refinement

Abstract

The present invention relates to an FMCW radar ranging method based on compressed sensing and spectrum refinement, comprising steps S1: obtaining a difference frequency signal; S2: performing an N-point fast Fourier transform on the difference frequency signal to obtain a frequency index of the maximum spectrum line; S3: determining a frequency shift frequency, performing frequency shift on the difference frequency signal to obtain a low-frequency signal; S4: obtaining a description signal according to the low-frequency signal, processing the description signal by compressed sensing to obtain an optimization model, solving the optimization model by a convex optimization method to obtain a sparse coefficient, and obtaining an estimated frequency of the low-frequency signal according to the sparse coefficient; S5: adding the frequency shift frequency and the estimated frequency of the low-frequency signal to obtain an estimated frequency of the difference frequency signal; S6: obtaining an estimated value of the distance according to the estimated frequency of the difference frequency signal. The FMCW radar ranging method of the present invention combines spectrum refinement with compressed sensing, which reduces the amount of calculation while ensuring accuracy.

Description

Technical Field

[0001] The present invention relates to the field of FMCW radar ranging, and more specifically to an FMCW radar ranging method based on compressed sensing and spectrum refinement. Background Art

[0002] FMCW radar is a technology that obtains distance information from radar signals by frequency modulating continuous signals. With the development of modern electronic circuits, the application scope of FMCW radar has become wider, not only limited to the military field, but also applied to the civilian field, involving the fields of precision guidance, security, unmanned driving, etc.

[0003] When FMCW radar is used to measure the distance of a target, the relevant distance information is obtained through the relationship between the transmitted wave and the reflected wave, and the estimated distance is obtained by estimating the frequency of the difference signal between the two. In order to improve the ranging accuracy of FMCW radar, many related algorithms have been proposed, including phase method, FFT and its improved algorithm, denoising algorithm and other directions. Hou Qingwen (Hou Qingwen, Chen Xianzhong, Wang Xiaopan, Yin Yixin, and Li Xiaoli, "Improved FMCW signal weighted compensation correction phase difference method," Journal of Scientific Instruments, no. 4, p. 6, 2010.) proposed an improved weighted compensation correction phase difference algorithm, and improved the window function for the frequency band where the correction accuracy is not ideal. Kim (S.Kim, Y.Ju, and J.Lee, "A Low-Complexity JointTOAs and AOAs Parameter Estimator Using Dimension Reduction for FMCW RadarSystems," ElektronikairElektrotechnika, vol.24, no.4, 2018.) designed a joint time delay and angle parameter estimator using dimensionality reduction, combined with DFT and MUSIC algorithms, for low-complexity FMCW radar systems, reducing complexity while ensuring the accuracy of the algorithm. Dao (X.Dao, M.Gao, C.Li, and Y.Wang, "Adaptiveleakage signal cancellation algorithm in heterodyne FMCW system," DigitalSignal Processing, vol.108, p.102882, 2021.) proposed an adaptive leakage signal cancellation algorithm. The basic principle of eliminating leakage signals is to generate a cancellation signal with the same amplitude and opposite phase as the leakage signal. The complex phase noise model is converted into the statistical characteristic calculation of the input signal using information geometry theory, and modified by the corresponding correction function.

[0004] These methods have improved the performance of FMCW radar systems to varying degrees, but their accuracy is still not high enough. In recent years, the theory of compressed sensing (Liu Shenggang, "Efficient Acquisition and Analysis of Information in the Big Data Era - A Review of "Introduction to Sparse Sensing", Physics, vol. 47, no. 2, p. 1, 2018.) has been widely studied. One of its characteristics is to use the sparsity of data. Therefore, the relevant principles of compressed sensing can also be applied to the frequency analysis of FMCW radar (Y. Zhang and G. Wang, "Application of Compressed Sensing in Vehicular LFMCW Millimeter Wave Radar Ranging," in International Conference on Microwave and Millimeter Wave Technology, 2018.). In the prior art, when compressed sensing is applied to FMCW radar, although the accuracy is high, the amount of calculation is also large. Summary of the invention

[0005] The object of the present invention is to provide a FMCW radar ranging method based on compressed sensing and spectrum refinement, which combines spectrum refinement and compressed sensing to reduce the amount of calculation while ensuring accuracy.

[0006] The present invention provides a FMCW radar ranging method based on compressed sensing and spectrum refinement, comprising the following steps:

[0007] S1: The difference frequency signal is obtained by mixing the transmission signal and the reception signal of the FMCW radar;

[0008] S2: Performing an N-point fast Fourier transform on the difference frequency signal to obtain a frequency index of the maximum spectral line;

[0009] S3: Determine the frequency shift frequency according to the frequency index of the maximum spectrum line and the N-point fast Fourier transform result, and shift the difference frequency signal to obtain a low-frequency signal;

[0010] S4: obtaining a description signal according to the low-frequency signal, processing the description signal by using compressed sensing to obtain an optimization model, solving the optimization model by a convex optimization method to obtain a sparse coefficient, and obtaining an estimated frequency of the low-frequency signal according to the sparse coefficient;

[0011] S5: adding the frequency shift frequency and the estimated frequency of the low-frequency signal to obtain the estimated frequency of the difference frequency signal;

[0012] S6: Obtain an estimated value of the distance according to the estimated frequency of the difference frequency signal.

[0013] Furthermore, the difference frequency signal satisfies the following relationship:

[0014]

[0015] Among them, x(n) is the difference frequency signal, a0=a r a t , a t is the transmission gain, a r is the receiving gain, f s is the sampling frequency, f0 is the initial frequency of the linear frequency modulation wave, τ is the time delay caused by the distance, f c is the frequency of the difference frequency signal, and v(n) is the noise signal.

[0016] Furthermore, the frequency shift satisfies the following relationship:

[0017]

[0018] Among them, k p is the frequency index of the maximum spectral line of the fast Fourier transform, f s is the sampling frequency, and X(k) is the corresponding spectrum obtained after the difference frequency signal is transformed by fast Fourier transform.

[0019] Furthermore, the description signal satisfies the following relationship:

[0020] h=[h(1),h(2),…,h(N)] T

[0021] Among them, h is the description signal and h(n) is the low-frequency signal.

[0022] Furthermore, the optimization model is:

[0023] min s ||s||1

[0024] st||y-Θs||2=ε

[0025] Among them, y is a P×1-dimensional observation signal, Θ=ΦΨ, Φ is a P×N-dimensional observation matrix, Ψ is a 1×M-dimensional sparse matrix, s is a sparse coefficient, and ε is the constraint range.

[0026] Furthermore, the sparse matrix satisfies the following relationship:

[0027]

[0028] Where M represents the refinement multiple, and N is the number of fast Fourier transform points;

[0029] The measurement matrix is ​​a random matrix and satisfies the following relationship:

[0030] Φ H Φ=I

[0031] The constraint range satisfies the following relationship:

[0032]

[0033] Where δ is the square root of the noise power of the noise signal.

[0034] Furthermore, the description signal satisfies the following relationship:

[0035]

[0036] Among them, H is the description signal, h(n) is the low-frequency signal, And N=N1+N2-1, N1>N2.

[0037] Furthermore, the optimization model is:

[0038] min s ||s||1

[0039] st(y'-Θsα)=W

[0040] ||W||2≤ε'

[0041] Among them, y' is a P×N2-dimensional observation signal, Θ=ΦΨ, Φ is a P×N-dimensional observation matrix, Ψ is an N1×M-dimensional sparse matrix, s is a sparse coefficient, and ε' is a constraint range.

[0042] Furthermore, the sparse matrix satisfies the following relationship:

[0043]

[0044] Among them, M represents the refinement multiple;

[0045] The measurement matrix is ​​a random matrix and satisfies the following relationship:

[0046] Φ H Φ=I

[0047] The constraint range satisfies the following relationship:

[0048]

[0049] Where δ is the square root of the noise power of the noise signal.

[0050] Furthermore, the estimated frequency of the low-frequency signal satisfies the following relationship:

[0051]

[0052] Among them, f h is the estimated frequency, k s is the maximum index of the sparse coefficient, f s is the sampling frequency;

[0053] The estimated value of the distance satisfies the following relationship:

[0054]

[0055] Among them, f n is the shift frequency, c is the speed of the electromagnetic wave in the air, and J is the slope of the linear frequency modulation wave.

[0056] The FMCW radar ranging method based on compressed sensing and spectrum refinement of the present invention combines the refined spectrum with the compressed sensing theory. By setting the sparse matrix to an N×M dimensional matrix and the corresponding sparse coefficient to an M×1 dimensional vector, if M<N, the dimensions of the sparse matrix and the sparse coefficient can be reduced, and the computational complexity (i.e., the amount of computation) can be reduced; the observation matrix is ​​set to be random and orthogonal, thereby ensuring the accuracy of the estimation result; and the description signal is converted from a column vector to a matrix, thereby effectively reducing the size of the observation matrix and the sparse matrix used in the operation process, thereby reducing the storage requirement. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 4 is a flow chart of an FMCW radar ranging method based on compressed sensing and spectrum refinement according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0058] The preferred embodiments of the present invention are given below in conjunction with the accompanying drawings and described in detail.

[0059] like Figure 1 As shown, the first embodiment of the present invention provides a FMCW radar ranging method based on compressed sensing and spectrum refinement, comprising the following steps:

[0060] S1: The difference frequency signal is obtained by mixing the transmission signal and the reception signal of the FMCW radar;

[0061] The transmission signal of FMCW radar is expressed as:

[0062]

[0063] When the transmitted signal touches the target object, it is reflected. The reflected signal (i.e., the received signal) received by the FMCW radar is:

[0064]

[0065] Where f0 is the initial frequency of the linear frequency modulation wave, is the slope of the linear FM wave, B is the frequency modulation bandwidth of the linear FM wave, T is the period of the linear FM wave, τ is the time delay caused by the distance r, c is the speed of electromagnetic waves in air, is the initial phase, a t is the transmission gain, a r is the receiving gain, a0=a r a t In this embodiment, the path loss and the loss caused by object reflection are ignored.

[0066] After mixing T(t) and R(t), the high-frequency components are filtered out to obtain the difference frequency signal:

[0067] x(t)=a0 exp{j2π(f0τ+Kτt)}+v(t) (3)

[0068] Where v(t) is the noise signal, with sampling frequency f s Sampling the time domain signal x(t) yields the discrete frequency domain signal of the difference frequency signal:

[0069]

[0070] Where v(n) represents the noise signal.

[0071] The frequency f of the difference frequency signal x(n) c =Kτ, we can get the distance r:

[0072]

[0073] Therefore, in order to accurately estimate the distance, it is only necessary to accurately estimate the frequency f c That's it.

[0074] S2: Perform N-point fast Fourier transform on the difference frequency signal to obtain the frequency index of the maximum spectrum line;

[0075] Perform N-point fast Fourier transform on the difference frequency signal x(n), and we get:

[0076]

[0077] Where k = 0, ..., N-1, the frequency resolution of the N-point fast Fourier transform (FFT) is

[0078] Find the frequency index k of the maximum spectral line of the fast Fourier transform p , thus obtaining the frequency estimate

[0079]

[0080] S3: Determine the frequency shift frequency according to the frequency index of the maximum spectrum line and the N-point fast Fourier transform result, and shift the difference frequency signal to obtain a low-frequency signal;

[0081] Shift frequency f n Determined by the frequency index of the maximum spectral line and the FFT result, it satisfies the following relationship:

[0082]

[0083] After the difference frequency signal x(n) is frequency shifted, the low frequency signal h(n) is obtained:

[0084]

[0085] S4: obtaining a description signal according to the low-frequency signal, processing the description signal by using compressed sensing to obtain an optimization model, solving the optimization model by using a convex optimization method to obtain a sparse coefficient, and obtaining an estimated frequency of the low-frequency signal according to the sparse coefficient;

[0086] When compressed sensing is used for signal analysis, the signal can be described and processed by its sparsity (JM Duarte-Carvajalino and G. Sapiro, "Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization," IEEE Transactions on Image Processing, vol. 18, no. 7, pp. 1395-1408, 2009.). In this embodiment, the description signal is a column vector h = [h (1), h (2), ..., h (N)] obtained from the low-frequency signal h (n) (n = 1, ..., N). T , since it is R N A vector in space, then h can be expressed as a set of standard orthogonal bases Ψ i ∈R N Linear combinations,

[0087]

[0088] where Ψ=[Ψ1,Ψ2,…,Ψ M ] is composed of the standard orthogonal basis Ψ i The matrix formed is s=[s(1),s(2),…,s(M)] T, represents the projection coefficient of h in the space formed by this set of orthogonal bases Ψ. If there are at most K non-zero elements in s, and K is much smaller than M, then the signal h is said to be sparse in the Ψ domain, or s is a sparse representation of h. Among them, Ψ is called a sparse matrix, and s is called a sparse coefficient. The number of non-zero elements K is also called sparsity, which can be expressed by the L0 norm:

[0089] K=||s||0 (10)

[0090] The purpose of sparse transform is to find a basis and obtain a sparse representation of the signal. After obtaining the sparse representation, the signal can be sparsely sampled. For the sampling mathematical model that does not satisfy the Nyquist theorem:

[0091] y=Φh (11)

[0092] If a sparse representation of h is found, the sampling model can be converted to sparse sampling:

[0093] y=ΦΨs=Θs (12)

[0094] Among them, Φ is the P×N dimensional observation matrix, y is the P×1 dimensional observation signal, and Θ is the P×M dimensional perception matrix. Then y can be regarded as the linear projection of s under the perception matrix Θ. When using the compressed sensing principle to analyze the low-frequency signal h(n), it is necessary to meet the relevant conditions of the compressed sensing principle (EJCandes and T.Tao, "Decoding by linear programming," IEEE Transactions on Information Theory, vol.51, no.12, pp.4203-4215, 2005.). Only when the perception matrix Θ satisfies the restricted isometry property (RIP), the compressed sensing theory can accurately recover the signal h from the received y. Experimental simulation shows that when the sparse matrix Ψ is a DFT transformation matrix (S.Hanumanthu and PRKumar, "Deterministic Compressed Sensing LFM Radar for Range-Doppler Estimation of Multiple Moving Targets," 2021.), the analysis of the signal frequency by the sparse coefficient s is consistent with the conclusion of direct FFT analysis of the signal, which illustrates the effectiveness of compressed sensing for analyzing sparse signals.

[0095] The core problem of compressed sensing is L0 norm minimization, as shown below:

[0096] mins ||s||0

[0097] sty=Θs (13)

[0098] Since the observed signal is usually contaminated by noise, the equality constraint in the above optimization problem is relaxed to an L0 norm minimization problem with an inequality constraint that allows a certain error perturbation ε ≥ 0:

[0099] min s ||s||0

[0100] st||y-Θs||2≤ε (14)

[0101] To directly solve the optimization problem (14), all possible non-zero elements in the sparse coefficient s must be screened out. This method is untraceable and is an NP-hard problem because its corresponding search space is too large. Since the L1 norm is the convex objective function closest to the L0 norm, from the optimization point of view, the L1 norm is called the convex relaxation of the L0 norm. Therefore, the minimization problem of the L0 norm is transformed into the convex relaxation of the L1 norm minimization problem. As shown below:

[0102] min s ||s||1

[0103] st||y-Θs||2≤ε (15)

[0104] Among them, ε is the constraint range and needs to be set according to actual conditions.

[0105] In order to solve the above optimization problem, in this embodiment, a sparse matrix Ψ is first constructed as shown below:

[0106]

[0107] Where M represents the refinement multiple, and N is the number of FFT transformation points. Since the sparse matrix Ψ constructed at this time does not meet the requirements of the orthogonal basis, the selection of the observation matrix Φ must be orthogonal in addition to being random, and it must satisfy the following relationship:

[0108] Φ H Φ=I (17)

[0109] And when h∈R N When Φ∈R P×N

[0110] When designing the convex optimization condition constraint range ε ​​in the basic algorithm of compressed sensing combined with refined spectrum, for the noise power δ 2 , additive noise v(n) (n=1,…,N) with a mean of 0, when the description signal h can be accurately estimated, the constraint range satisfies the following relationship:

[0111]

[0112] in(·) H represents the conjugate transpose, since Φ H Φ=I, then:

[0113]

[0114] Therefore, in this embodiment, the constraint range is set

[0115] Substituting the sparse matrix Ψ and the observation matrix Φ that meet the requirements into formula (15), the sparse coefficient s can be obtained. The calculation method thereof is well known in the art and will not be described in detail here.

[0116] Since the signal h should meet the sparse requirement, when there is only one FMCW detection target, the sparsity of the signal h is K = 1. At this time, the maximum value index of the sparse coefficient s is taken as k s , the low-frequency signal h(n) corresponds to the estimated frequency f h for:

[0117]

[0118] S5: adding the frequency shift frequency of the difference frequency signal and the estimated frequency of the low frequency signal to obtain the estimated frequency of the difference frequency signal;

[0119] Combining equation (8) and equation (20), we can get the estimated frequency f of the difference frequency signal x(n): c :

[0120] f c =f n +f h (twenty one)

[0121] S6: Obtain an estimated value of the distance according to the estimated frequency of the difference frequency signal.

[0122] The estimated frequency f of the difference frequency signal x(n) c Substituting into equation (5) we can get the estimated value of the distance.

[0123] The FMCW radar ranging method based on compressed sensing and spectrum refinement provided in the first embodiment of the present invention combines the refined spectrum with the compressed sensing theory. By setting the sparse matrix to an N×M dimensional matrix, the corresponding sparse coefficient is an M×1 dimensional vector. If MδN, the dimensions of the sparse matrix and the sparse coefficient can be reduced, thereby reducing the computational complexity. The observation matrix is ​​set to be random and orthogonal, thereby ensuring the accuracy of the estimation result.

[0124] In order to further reduce the size of the observation matrix Φ and the sparse matrix Ψ used in the operation process, thereby reducing the storage requirements, the second embodiment of the present invention replaces the vector h with the matrix H to describe the signal, that is, to describe the low-frequency signal by a matrix, where And N=N1+N2-1, N1>N2, the expression of matrix H is as follows:

[0125]

[0126] For the measurement matrix Φ, in addition to being random, it must also meet the orthogonal requirements. Therefore, the measurement matrix Φ satisfies equation (17), then the observation signal It satisfies:

[0127] y'=ΦH (23)

[0128] For the sparse coefficient svR M×1 , a sparse matrix The expression is:

[0129]

[0130] Introduction Then we have:

[0131] H=Ψsα (25)

[0132] If a sparse representation of H is found, the sampling model can be converted to sparse sampling:

[0133] y'=ΦΨsα=Θsα (26)

[0134] At this time, the observed signal Observation Matrix Sparse Matrix Perception matrix Θ∈R P×M , similar to the first embodiment, formula (15) becomes:

[0135] min s ||s||1

[0136] st(y'-Θsα)=W

[0137] ||W||2≤ε' (27)

[0138] For a noise power of δ 2 , additive noise v(n) (n=1,…,N) with a mean of 0, when the signal H can be accurately estimated, the constraint range ε ‘ The following relations are satisfied:

[0139]

[0140] in(·)H represents the conjugate transpose, since Φ H Φ=I, then:

[0141]

[0142] Therefore, in this embodiment, the constraint range

[0143] Substituting the sparse matrix Ψ and observation matrix Φ that meet the requirements into formula (27), the sparse coefficient s can be obtained, and then the estimated frequency of the low-frequency signal is obtained from the sparse coefficient, and finally the estimated value of the distance is obtained. The method is the same as that in the first embodiment and will not be repeated here.

[0144] In the second embodiment, by converting the description signal from a column vector into a matrix, the size of the observation matrix and the sparse matrix used in the operation process can be effectively reduced, thereby reducing the storage requirement.

[0145] Different matrix settings represent different degrees of relaxation of the constraint conditions. The size comparison of the correlation matrix and the vector involved in the first embodiment and the second embodiment of the present invention is shown in Table 1:

[0146] Table 1: Correlation matrix and vector size

[0147]

[0148] The performance indicators of the method of the present invention will be introduced below:

[0149] When the method of the present invention is used to measure the distance, the mean and variance of the estimated value of the distance are the main performance indicators. Since noise is involved in the process of setting parameters, and the noise is random, assuming that NUM Monte Carlo experiments are performed under different noise conditions, the mean of the estimated value of the distance is for:

[0150]

[0151] The variance is:

[0152]

[0153] According to equations (15) and (27), when estimating distance through compressed sensing combined with refined spectrum, the solution is obtained through convex optimization. Since the design of the convex optimization parameters will have a certain impact on the estimation result, the distance information cannot be estimated from the signal every time. Therefore, the detection rate and calculation time are also the main performance indicators. For NUM Monte Carlo experiments, NUM s Estimated distance Its detection rate η is:

[0154]

[0155] The average time required to complete NUM Monte Carlo experiments is taken as the calculation time T.

[0156] In order to analyze the performance of the method of the present invention, simulation experiments are performed using the methods of the first embodiment and the second embodiment of the present invention, the existing FFT method, and the existing compressed sensing method, and their respective performance indicators are calculated for comparison:

[0157] In the simulation experiment, the sampling rate f s =92.7835e3Hz, number of sampling points N = 256, initial frequency of linear FM wave f0 = 100KHz, frequency modulation bandwidth of linear FM wave B = 999.47055MHZ, period of linear FM wave Slope of the linear FM wave Initial Phase Send gaina t =1; the distance between the measured stationary object and the FMCW system is r = 3.25m, the speed of electromagnetic waves in the air is c = 299709Km / s, then the time delay caused by the distance r Receive gain a r =1, experiments were conducted in the range of SNR [-10dB, 30dB]. Under different SNRs, the methods of the first embodiment and the second embodiment, the existing FFT method, and the existing compressed sensing method were used to independently conduct NUM=500 Monte Carlo experiments. Then, their performance indicators were calculated respectively. The results are shown in Tables 2-5.

[0158] Table 2: Mean estimated distances obtained by simulation under different signal-to-noise ratios (m)

[0159]

[0160]

[0161] Table 3: Standard deviation of estimated distances obtained by simulation under different signal-to-noise ratios (m)

[0162]

[0163] In the simulation, the observation matrix parameter P=128. It can be seen from Tables 2 and 3 that the performance of directly using FFT is consistent with that of the existing compressed sensing method under high signal-to-noise ratio; under high signal-to-noise ratio conditions, the performance of the first embodiment of the present invention can be improved with the increase of M. The larger the M, the larger the sparse matrix, the higher the resolution, and the closer the obtained distance mean is to the true value; when the signal-to-noise ratio increases, the standard deviation of the first embodiment of the present invention shows a trend of gradual decrease; under the same M, when N2 is larger, the smaller the observation matrix and the sparse matrix, the corresponding storage consumption during the calculation process will become smaller; with the increase of the signal-to-noise ratio, the distance estimation value of the second embodiment of the present invention will tend to a stable value, and when N2 is smaller, it is easier to reach a stable value. According to the simulation results, the estimation result of N2=5 when the signal-to-noise ratio is 15dB reaches a stable value, and the estimation result of N2=10 when the signal-to-noise ratio is 20dB reaches a stable value. At a high signal-to-noise ratio, when the value of M is the same, the performance of the second embodiment of the present invention is better than that of the first embodiment of the present invention. The difference between the mean distance estimated by the second embodiment of the present invention and the true distance is smaller, and the standard deviation is also smaller.

[0164] Table 4: Average single-shot time consumption under different signal-to-noise ratios (s)

[0165]

[0166]

[0167] Table 5: Detection rate at different signal-to-noise ratios

[0168]

[0169] It can be seen from Table 4 that the first embodiment of the present invention has a faster calculation speed than the existing compressed sensing method; for the algorithm of the first embodiment of the present invention, if M takes a larger value, under the premise of other conditions being the same, its sparse matrix will be larger, so the operation time will be longer; with the increase of N2, the observation matrix and sparse matrix involved in the second embodiment of the present invention will be correspondingly reduced, so the storage consumption will be reduced, but because the observation signal involved becomes larger, the operation time will increase, so the larger N2 will also lead to an increase in the operation time of the second embodiment of the present invention. It can be seen from Table 5 that when the detection amount is sufficient, the detection rate of the first embodiment of the present invention is basically maintained at around 62%. Although the detection time of the second embodiment of the present invention does not have superiority, the detection rate has been greatly improved, and the detection rate can reach 100% when the signal-to-noise ratio is relatively good.

[0170] It can be seen from Tables 2-5 that the FMCW radar ranging method of the present invention can improve the ranging performance, and different parameters can be designed to have different effects on the ranging performance. The design of M in the sparse coefficient can directly affect the accuracy of the method of the present invention. The design of N2 can control the size of the related observation matrix and the sparse matrix. When the observation matrix and the sparse matrix occupy storage resources, the design of N2 can achieve the purpose of reducing storage resources. At the same time, under a higher signal-to-noise ratio, it can effectively improve the detection rate; and when other conditions are the same, the design of N2 has a certain improvement in the anti-noise performance of the method; compared with the prior art, the estimated distance performance and estimated time consumption of the method of the present invention have obvious advantages, and the detection rate is improved. Therefore, the method of the present invention improves the accuracy and robustness of FMCW radar ranging.

[0171] The above is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. The above embodiment of the present invention can also be modified in various ways. That is, all simple, equivalent changes and modifications made according to the claims and the description of the present invention fall within the scope of protection of the claims of the present invention. The contents not described in detail in the present invention are all conventional technical contents.

Claims

1. A FMCW radar ranging method based on compressed sensing and spectrum refinement, characterized in that: The following steps are involved: S1: The difference frequency signal is obtained by mixing the transmission signal and the reception signal of the FMCW radar; S2: Performing an N-point fast Fourier transform on the difference frequency signal to obtain a frequency index of the maximum spectral line; S3: Determine the frequency shift frequency according to the frequency index of the maximum spectrum line and the N-point fast Fourier transform result, and shift the difference frequency signal to obtain a low-frequency signal; S4: obtaining a description signal according to the low-frequency signal, processing the description signal by using compressed sensing to obtain an optimization model, solving the optimization model by a convex optimization method to obtain a sparse coefficient, and obtaining an estimated frequency of the low-frequency signal according to the sparse coefficient; S5: adding the frequency shift frequency and the estimated frequency of the low-frequency signal to obtain the estimated frequency of the difference frequency signal; S6: Obtain an estimated value of the distance according to the estimated frequency of the difference frequency signal.

2. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 1, characterized in that: The difference frequency signal satisfies the following relationship: Among them, x(n) is the difference frequency signal, a0=a r a t , a t is the transmission gain, a r is the receiving gain, f s is the sampling frequency, f0 is the initial frequency of the linear frequency modulation wave, τ is the time delay caused by the distance, f c is the frequency of the difference frequency signal, and v(n) is the noise signal.

3. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 2 is characterized in that: The frequency shift frequency satisfies the following relationship: Among them, k p is the frequency index of the maximum spectral line of the fast Fourier transform, f s is the sampling frequency, X(k) is the corresponding spectrum obtained after the difference frequency signal is transformed by fast Fourier transform, and N is the number of fast Fourier transform points.

4. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 1, characterized in that: The description signal satisfies the following relationship: h=[h(1),h(2),…,h(N)] T Among them, h is the description signal and h(n) is the low-frequency signal.

5. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 4 is characterized in that: The optimization model is: st‖y-Θs‖2≤ε Among them, y is a P×1-dimensional observation signal, Θ=ΦΨ, Φ is a P×N-dimensional observation matrix, Ψ is a 1×M-dimensional sparse matrix, s is a sparse coefficient, and ε is the constraint range.

6. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 5, characterized in that: The sparse matrix satisfies the following relationship: Where M represents the refinement multiple, and N is the number of fast Fourier transform points; The measurement matrix is ​​a random matrix and satisfies the following relationship: F H Φ=I The constraint range satisfies the following relationship: Where δ is the square root of the noise power of the noise signal.

7. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 1, characterized in that: The description signal satisfies the following relationship: Among them, H is the description signal, h(n) is the low-frequency signal, And N=N1+N2-1, N1>N2.

8. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 7, characterized in that: The optimization model is: st(y'-Θsα)=W ‖W‖2≤ε' Among them, y' is a P×N2-dimensional observation signal, Θ=ΦΨ, Φ is a P×N-dimensional observation matrix, Ψ is an N1×M-dimensional sparse matrix, s is a sparse coefficient, and ε' is a constraint range.

9. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 8, characterized in that: The sparse matrix satisfies the following relationship: Among them, M represents the refinement multiple; The measurement matrix is ​​a random matrix and satisfies the following relationship: F H Φ=I The constraint range satisfies the following relationship: Where δ is the square root of the noise power of the noise signal.

10. The FMCW radar ranging method based on compressed sensing and spectrum refinement according to claim 6 or 9, characterized in that: The estimated frequency of the low-frequency signal satisfies the following relationship: Among them, f h is the estimated frequency, k s is the maximum index of the sparse coefficient, f s is the sampling frequency; The estimated value of the distance satisfies the following relationship: Among them, f n is the shift frequency, c is the speed of the electromagnetic wave in the air, and K is the slope of the linear frequency modulation wave.

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