FDA-MIMO radar multi-target distance angle joint super-resolution method and system

Abstract

The invention discloses a FDA-MIMO radar multi-target distance angle joint super-resolution method and system, and mainly solves the problem that the existing phased array only depends on the angle to identify multiple targets, resulting in low resolution ability, and the implementation scheme of the method comprises the steps of obtaining FDA-MIMO radar echo data, and performing separation aliasing on the FDA-MIMO radar echo data to obtain a data matrix; performing conversion stacking on the data matrix to obtain NM * L-dimensional data, and calculating a covariance matrix of the NM * L-dimensional data; performing reverse array decoherence processing on the covariance matrix to obtain a new source signal covariance matrix; constructing a two-dimensional spatial spectrum function of a target distance and a target angle for the new source signal covariance matrix through a MUSIC algorithm; and performing spectrum peak search on the two-dimensional spatial spectrum function, and detecting a local maximum value of the two-dimensional spatial spectrum function to obtain a distance and angle joint estimation value of a plurality of targets. The method can improve the angle resolution capability of the target when the target angle interval is lower than the traditional resolution, reduces the influence of the amplitude-phase error on the resolution capability when the target distance interval is large enough, and can be used for target recognition.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar signal processing, and particularly relates to a FDA-MIMO radar multi-target range-angle joint super-resolution method and system, which can be used for target identification under the condition that the multi-target angle interval is lower than the angle resolution of traditional beam forming. BACKGROUND

[0002] Multi-target super-resolution is one of the important tasks of radar system to accurately estimate target parameters. The super-resolution method aims to break through the Rayleigh limit of traditional beam forming method to achieve higher resolution and accuracy of target positioning. It mainly includes target range, angle and velocity parameter estimation. Frequency diversity technology FDA can obtain flexible range / time-angle transmitting beam pattern characteristics by increasing a frequency step in the transmitting array element dimension, which has been widely concerned by scholars and has played an important advantage in parameter estimation field. The combination of FDA technology and MIMO technology can obtain independent transmitting dimension range freedom and better play the advantage of FDA technology.

[0003] The transmitting pattern of FDA radar at a specific time node has the characteristics of mutual coupling of range and angle, and its transmitting steering vector mainly focuses on the range information of the target. In order to accurately analyze the range data of the target, MIMO technology is usually added to separate the transmitting waveform. Compared with traditional MIMO radar, FDA-MIMO radar has more advantages in freedom, especially in the performance of range dimension, which shows higher flexibility and accuracy.

[0004] The patent document with publication number CN 119716832 A discloses a target angle super-resolution estimation method based on array radar. It is first based on phased array radar, calculates the digital beam synthesis weight coefficient according to the subarray distribution, and performs digital beam synthesis on the subarray by row to obtain M elevation dimension beam synthesis data, then performs two-dimensional target information extraction on the M elevation dimension beam synthesis data respectively to obtain two-dimensional one-time snapshot data, and finally performs de-coherent source MUSIC direction finding on the obtained two-dimensional one-time snapshot data to obtain the target elevation incidence angle. The method can only improve the angle resolution because it is limited by the traditional phased array radar which has only one degree of freedom in angle dimension.

[0005] The patent document with the publication number CN 115616563 A discloses an "FDA-MIMO radar super-resolution target positioning based on multi-dimensional parameter spectrum reconstruction". The method first receives far-field target signals using a MIMO radar transceiver array; then processes the received signals to obtain signal and noise subspaces; then uses matrix subspace root technology to construct a root polynomial of the angle spectrum, and then performs root operation on the angle spectrum polynomial to obtain the angle estimation value of the target; finally, the angle estimation value is substituted into the reconstruction cost function, and the distance estimation value of the target signal is obtained according to the root super-resolution algorithm. The method only uses the super-resolution algorithm to estimate the distance and angle of a single target, and does not consider the resolution capability of the radar between multiple targets, so it can only improve the distance and angle resolution in a single target scene, and cannot effectively solve the coupling problem between multiple targets. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art and provide a FDA-MIMO radar multi-target range-angle joint super-resolution method and system to effectively identify multiple targets when the angle interval between multiple targets is lower than the angle resolution of traditional beamforming.

[0007] The technical idea of the present application is to use the coupling relationship between the target distance and angle in the FDA-MIMO radar transmit steering vector to enable effective identification of multiple targets through the MUSIC algorithm.

[0008] According to the above idea, the technical solution of the present application includes the following:

[0009] 1. A FDA-MIMO radar multi-target range-angle joint super-resolution method, characterized in that it comprises:

[0010] Obtain FDA-MIMO radar echo data and separate the aliasing to obtain a data matrix x k ;

[0011] Convert and stack the data matrix x k to obtain an NM×L-dimensional data X, and calculate its covariance matrix R x ;

[0012] Perform inverse array de-coherent processing on the covariance matrix R x to obtain a new source signal covariance matrix

[0013] Perform MUSIC algorithm on the new source signal covariance matrix Construct a two-dimensional spatial spectrum function f(R, θ) of the target distance R and the target angle θ;

[0014] The two-dimensional spatial spectrum function f(R, θ) is subjected to a spectrum peak search, and local maximum values are detected to obtain distance and angle joint estimation values of multiple targets.

[0015] Further, the new source signal covariance matrix A two-dimensional spatial spectrum function f(R, θ) of target distance R and target angle θ is constructed through a MUSIC algorithm, which includes:

[0016] The two-dimensional spatial spectrum function f(R, θ) is subjected to a spectrum peak search, and local maximum values are detected to obtain distance and angle joint estimation values of multiple targets. Eigenvalue decomposition is performed to obtain NM eigenvalues and eigenvectors;

[0017] The largest P eigenvalues are selected from the NM eigenvalues, and eigenvectors corresponding to the P eigenvalues are combined to form a signal subspace matrix U S , and the remaining NM-P eigenvectors are combined to form a noise subspace matrix U N .

[0018] The two-dimensional spatial spectrum function f(R, θ) of target distance R and target angle θ is obtained through a MUSIC algorithm by utilizing the orthogonality of the noise subspace and the signal subspace.

[0019] Further, the two-dimensional spatial spectrum function f(R, θ) is subjected to a spectrum peak search, and local maximum values are detected to obtain distance and angle joint estimation values of multiple targets, which includes:

[0020] A distance range and an angle range to be scanned are selected, and a two-dimensional search is performed on multiple target spatial spectrums that satisfy corresponding conditions between the distance and the angle of multiple targets, with the distance R and the angle θ as variables;

[0021] Multiple local maximum values formed by the two-dimensional spatial spectrum are searched through a grid search, and distance and angle values corresponding to multiple targets are obtained according to positions of the local maximum values.

[0022] 2. An FDA-MIMO radar multiple target distance and angle joint super-resolution system, characterized in that it comprises:

[0023] An echo separation aliasing module is configured to perform a two-dimensional search on a data matrix x k after the echo signal passes through a multi-channel matched filter.

[0024] A covariance matrix calculation module is configured to perform conversion and stacking on the data matrix x k , and calculate a covariance matrix R k of the data matrix x x .

[0025] A reverse array de-coherent module is configured to perform reverse array de-coherent processing on the covariance matrix R x , and obtain a new source signal covariance matrix

[0026] a two-dimensional spatial spectrum construction module for constructing a new source signal covariance matrix a two-dimensional spatial spectrum function f(R, θ) of target distance R and target angle θ is constructed by a MUSIC algorithm;

[0027] a multi-target distance-angle estimation module for performing a spectrum peak search on the two-dimensional spatial spectrum function f(R, θ), detecting local maximum values, and obtaining joint estimation values of distances and angles of multiple targets.

[0028] Compared with the prior art, the present application has the following advantages:

[0029] First, the present application fully excavates target distance information by utilizing the distance dimension freedom of the FDA-MIMO radar, and improves the angle dimension resolution capability by utilizing the distance difference of targets based on the target distance-angle coupling characteristics, thereby effectively improving the multi-target resolution performance, and significantly improving the target angle resolution capability compared with the traditional array super-resolution algorithm.

[0030] Second, the present application cooperates the reverse array de-coherent algorithm with the FDA-MIMO system to perform coherent processing on the received target echo of coherent signals, effectively alleviates the problem of low resolution of the traditional super-resolution method when facing coherent signals, and significantly improves the distance and angle resolution capability of targets compared with the traditional array super-resolution method. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a flow chart of the FDA-MIMO radar multi-target distance-angle joint super-resolution method of the present application;

[0032] Figure 2 is a block diagram of the FDA-MIMO radar multi-target distance-angle joint super-resolution system of the present application;

[0033] Figure 3 is a curve of the change of the target detection success rate with the signal-to-noise ratio simulated by the method of the present application under the condition of 2 times super-resolution, different amplitude errors, and target distance intervals less than one distance gate;

[0034] Figure 4 is a curve of the change of the root mean square error of the target distance with the signal-to-noise ratio simulated by the method of the present application under the condition of different resolutions and target distance intervals less than one distance gate;

[0035] Figure 5 is a curve of the change of the root mean square error of the target angle with the signal-to-noise ratio simulated by the method of the present application under the condition of different resolutions and target distance intervals less than one distance gate;

[0036] Figure 6 is the simulation curve of the detection success rate of the target with the change of the signal-to-noise ratio under the condition of different resolutions and target distance intervals less than one distance gate by using the method of the application;

[0037] Figure 7 is the simulation curve of the detection success rate of the target with the change of the signal-to-noise ratio under the condition of 10 times super resolution, different amplitude errors and target distance intervals greater than one distance gate by using the method of the application.

[0038] Figure 8 is the simulation curve of the root mean square error of the distance of the target with the change of the signal-to-noise ratio under the condition of different resolutions and target distance intervals greater than one distance gate by using the method of the application;

[0039] Figure 9 is the simulation curve of the root mean square error of the angle of the target with the change of the signal-to-noise ratio under the condition of different resolutions and target distance intervals greater than one distance gate by using the method of the application;

[0040] Figure 10 is the simulation curve of the detection success rate of the target with the change of the signal-to-noise ratio under the condition of different resolutions and target distance intervals greater than one distance gate by using the method of the application; DETAILED DESCRIPTION

[0041] In order to make the personnel in the technical field better understand the application scheme, the technical scheme in the embodiments of the application will be described clearly and completely in combination with the drawings in the embodiments of the application. Obviously, the described embodiments are only a part of the embodiments of the application but not all the embodiments of the application. Based on the embodiments in the application, other embodiments obtained by the person skilled in the art without creative labor should belong to the protection scope of the application.

[0042] Embodiment one, FDA-MIMO radar multi-target range-angle joint super resolution method

[0043] Reference Figure 1 The implementation steps of the present example include the following:

[0044] Step 1, obtain the FDA-MIMO radar echo data, and separate the aliasing to obtain the data matrix x k .

[0045] (1.1) According to the time delay between the FDA-MIMO radar transmitting signal and the receiving signal, the echo data at the receiving end is obtained;

[0046] Consider that the transmitting array and receiving array of the FDA-MIMO radar are both one-dimensional uniform linear array, assume that the number of transmitting array elements is M and the number of receiving array elements is N, and take the first transmitting array element as reference, then the transmitting signal s m (t) of the mth transmitting array element of the FDA-MIMO radar can be expressed as:

[0047]

[0048] Wherein, is the baseband linear frequency modulation pulse signal of the mth transmitting array element, t ∈ (0, T r ), T r is the pulse repetition period, T p is the pulse width, rect(t / T p ) is a rectangular window function, μ = B / T r is the frequency modulation of the linear frequency modulation signal, and B is the bandwidth of a single sub-band signal;

[0049] f m = f0 + (m-1)Δf represents the carrier frequency of the mth transmitting array element, m = 1, 2, …, M, M is the number of transmitting array elements, f0 is the reference carrier frequency, and Δf is the frequency step size;

[0050] Assume that there is a point target in the spatial far field, L pulses are transmitted during the coherent processing interval, the distance of the point target is R0, the angle is θ0, and the point target is approaching the radar at a constant speed v0, in the narrowband case, the two-way time delay τ m,n,k of the signal corresponding to the mth transmitting unit and the nth receiving unit for the kth pulse is:

[0051]

[0052] Wherein, c is the speed of light, d t and d r are the element spacings of the transmitting array and the receiving array respectively, d t = d r = λ0 / 2, and λ0 = c / f0 is the wavelength of the reference carrier frequency.

[0053] According to the transmitting signal s m (t) and the two-way time delay τ m,n,k , the echo signal s n,k (t) received by the nth receiving array element from the target reflection of the kth pulse is:

[0054]

[0055] Wherein, β represents the complex echo amplitude, which is jointly affected by various factors, including the size of the transmitting power, the reflectivity of the target object, and the channel propagation effect, etc.

[0056] (1.2) Matched filtering on the received signal s n,k (t) is the signal corresponding to the kth pulse, the mth transmitting element and the nth receiving element is:

[0057]

[0058] where h mLPF (t) is a low-pass filter with the starting frequency of 0 Hz and the passband of B in the mth channel, is the reflection coefficient containing exponential term, denotes the convolution operation;

[0059] (1.3) Matched filtering on the above signal to obtain the output Y(t, t k ) of the kth pulse:

[0060]

[0061] where, is the Doppler shift matrix of the FDA-MIMO radar, diag() is the diagonal matrix operation,

[0062] is the receiving steering vector,

[0063] is the transmitting steering vector,

[0064] Φ(t-τ(t k )) is a diagonal matrix, and the main diagonal is the ideal response of the corresponding matched filter in sequence, which can be considered as a sinc function in the ideal case,

[0065] β represents the complex echo amplitude, which is jointly affected by multiple factors including the size of the transmitting power, the reflectivity of the target object, and the channel propagation effect,

[0066] t k =(k-1)T r denotes the slow time, k = 1, 2, …, L represents the pulse number, v0 represents the target speed, T r represents the pulse repetition period, θ0 represents the target angle, R0 represents the target distance, (·) T denotes the matrix transpose operation;

[0067] According to the case that the envelope time delay effect caused by target motion can be ignored in the analysis scene of constant speed target, and assuming that the target is always located within the predetermined detection distance unit, the output Y(t, t k) is simplified as Y(t k ):

[0068]

[0069] When considering the thermal noise of FDA-MIMO radar, the output Y(t k ) of the kth pulse is rewritten as the data matrix x k :

[0070]

[0071] where f d is the Doppler frequency, and n k is the noise echo satisfying the zero-mean Gaussian distribution.

[0072] Step 2, convert and stack the data matrix x k to obtain an NM×L-dimensional data X and calculate its covariance matrix R s .

[0073] (2.1) Convert x k to an NM×1 matrix to obtain the converted matrix

[0074]

[0075] where denotes the Kronecker product, and n k is converted to an NM×1 matrix.

[0076] (2.2) Stack the converted matrix to obtain an NM×L-dimensional stacked matrix X:

[0077]

[0078] where denotes the signal matrix with the Doppler frequency,

[0079] and n x is the noise matrix.

[0080] (2.3) Solve the covariance matrix R s of the stacked matrix X:

[0081]

[0082] where R RT is the covariance matrix of the source signal, A 2 denotes the transmit-receive joint steering vector, and σ 2 is the noise power, INM is an identity matrix of size NM x NM, and H denotes the conjugate transpose operation on a matrix.

[0083] Step 3, inverse array decorrelation processing is performed on the covariance matrix R x to obtain a new source signal covariance matrix R

[0084] (3.1) Let J be an inverse diagonal matrix of size NM x NM, and solve the inverse covariance matrix R x of the covariance matrix R B :

[0085]

[0086] where Φ is a diagonal matrix, and the diagonal elements are e jmφ , m = 1, …, P, P is the number of targets, and * denotes the conjugate operation on a matrix.

[0087] (3.2) Using the covariance matrix R s and the inverse covariance matrix R B , a new source signal covariance matrix R

[0088]

[0089] Step 4, through the MUSIC algorithm, a two-dimensional spatial spectrum function f(R, θ) of target distance R and target angle θ is constructed based on the new source signal covariance matrix R .

[0090] The MUSIC algorithm is a current algorithm for estimating target distance and angle, which estimates the distance and angle of the target by constructing a spatial spectrum function and searching for local maximum values, and its implementation is as follows:

[0091] (4.1) Perform eigenvalue decomposition on the new source signal covariance matrix R to obtain NM eigenvalues and eigenvectors;

[0092] (4.2) Select the largest P eigenvalues from the MN eigenvalues, and combine the eigenvectors corresponding to the eigenvalues to form a signal subspace matrix U S , and combine the eigenvectors corresponding to the remaining NM-P eigenvalues to form a noise subspace matrix U N ;

[0093] (4.3) Based on the orthogonality of the noise subspace U S and the signal subspace U N , a two-dimensional spatial spectrum function f(R, θ) of target distance R and target angle θ is obtained:

[0094]

[0095] Step 5, performing a spectrum peak search on the two-dimensional spatial spectrum function f(R, θ) to detect local maximum values to obtain a plurality of target distance and angle joint estimation values.

[0096] (5.1) Selecting a distance range and an angle range to be scanned, taking distance R and angle θ as variables, and setting conditions to be met by the multi-target distance interval and the angle interval:

[0097] wherein R t = 2ΔfΔr / c is a transmitting spatial frequency distance increment, Δr = |R1-R2| is a multi-target distance interval, R1 is a distance of target 1, R2 is a distance of target 2, B Res is a 3dB bandwidth of a target in the spatial spectrum, θ t = d t Δθ / λ0 is a transmitting spatial frequency angle increment, θ r = d r Δθ / λ0 is a receiving spatial frequency angle increment, Δθ = sin(θ1)-sin(θ2) is a multi-target angle sine difference value, θ1 is an angle of target 1, and θ2 is an angle of target 2.

[0098] (5.2) Setting a frequency step size Δf equal to a transmitting signal bandwidth B according to R t = 2ΔfΔr / c, so that the multi-target distance and angle intervals meet the above conditions, and then performing a grid search on a plurality of local maximum values formed by the two-dimensional spatial spectrum to obtain distance and angle values corresponding to the multi-targets according to positions of the local maximum values, so as to realize effective identification of the multi-targets; otherwise, the targets will not be effectively identified due to insufficient resolution.

[0099] It should be noted that the flowchart representation or method representation of the above-mentioned embodiments can be understood as a module, a segment or a part of code including one or a group of executable instructions configured to realize a specific logic function or process. The present application is not limited to the disclosed preferred embodiments, and its implementation can not be performed in the order shown or discussed.

[0100] Embodiment two, FDA-MIMO radar multi-target distance and angle joint super-resolution system

[0101] Referring to Figure 2The present example comprises an echo separation and aliasing module 1, a covariance matrix calculation module 2, an inverse array decorrelation module 3, a two-dimensional spatial spectrum construction module 4 and a multi-target range and angle estimation module 5, wherein the echo separation and aliasing module 1 comprises an echo signal acquisition submodule 11, a multi-channel mixing submodule 12, a low-pass filter submodule 13 and a matched filter submodule 14; the two-dimensional spatial spectrum construction module 4 comprises an eigenvalue decomposition submodule 41, a subspace construction submodule 42 and a spatial spectrum construction submodule 43. The working principle of the whole system is as follows:

[0102] The echo separation and aliasing module 1 is used to filter the echo signal of the receiving end through a multi-channel matched filter to obtain a data matrix, wherein the echo signal acquisition submodule 11 is used to obtain the echo signal of the receiving end according to the time delay between the FDA-MIMO radar transmitting signal and the receiving signal; the multi-channel mixing submodule 12 is used to perform multi-channel mixing processing on the echo signal and convert it to a set frequency range; the low-pass filter submodule 13 is used to perform low-pass filtering on the multi-channel mixed signal after frequency conversion to separate it into multiple waveforms; the matched filter submodule 14 is used to perform matched filtering on the filtered signal, extract the target signal and reduce the background noise, obtain the data matrix of multiple pulses, and transmit the data matrix to the covariance matrix calculation module 2;

[0103] The covariance matrix calculation module 2 is used to convert and stack the data matrix, calculate the covariance matrix of the data matrix, and then transmit the covariance matrix to the inverse array decorrelation module 3;

[0104] The inverse array decorrelation module 3 is used to perform inverse array decorrelation processing on the covariance matrix to obtain a new source signal covariance matrix, and then transmit the new source signal covariance matrix to the two-dimensional spatial spectrum construction module 4;

[0105] The two-dimensional spatial spectrum construction module 4 is used to construct a two-dimensional spatial spectrum function of target range and target angle by using the MUSIC algorithm on the new source signal covariance matrix; wherein the eigenvalue decomposition submodule 41 is used to perform eigenvalue decomposition on the new source signal covariance matrix to obtain NM eigenvalues and eigenvectors; the subspace construction submodule 42 is used to decompose the noise subspace and the signal subspace in the signal space; and the spatial spectrum construction submodule 43 is used to construct a two-dimensional spatial spectrum function of target range and target angle, and then transmit it to the multi-target range and angle estimation module 5;

[0106] The multi-target range and angle estimation module 5 is used to perform spectral peak search on the two-dimensional spatial spectrum function, detect its local maximum value, and obtain the joint estimation value of the range and angle of multiple targets.

[0107] It should be noted that: the above-mentioned function modules can be realized by software, hardware, firmware or any combination thereof, in whole or in part. When implemented by software, it can be realized in whole or in part in the form of program instruction product. The program instruction product includes one or a group of program instructions. When the program instructions are loaded and executed on a computer, the flow or function is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. Program instructions can be stored in a computer readable and writable storage medium, or transferred from one computer readable and writable storage medium to another computer readable and writable storage medium.

[0108] The direct coupling or communication connection between the modules shown or discussed in the embodiments can be realized by indirect coupling or communication connection of some interfaces, devices or modules. The function modules and sub-modules in the embodiments can be dynamically in one processing component, or each module can be physically present alone, or two or more modules can be dynamically in one processing component. When the above dynamic components are realized in the form of software function modules and sold or used as independent products, they can also be stored in a computer readable and writable storage medium. The storage medium can be a memory, a magnetic disk or an optical disk, etc.

[0109] The effect of the present example is further illustrated below in combination with simulation experiments:

[0110] 1. Simulation experiment conditions:

[0111] The hardware platform is: the processor is Intel(R) Core(TM) i7-10700 CPU, the main frequency is 2.90GHz, and the memory is 16GB.

[0112] The operating system is: Windows 11

[0113] The software platform is: MATLAB R2022b.

[0114] The parameter settings of the simulation experiment are shown in Table 1:

[0115] Table 1 FDA-MIMO radar simulation parameters

[0116] Parameter name Value Parameter name Value Number of transmitting elements M 8 Pulse width T p ]] 1.5us Number of receiving elements N 8 Signal bandwidth B 10MHz Number of pulses K 600 Frequency step size Δf 1MHz ​ 5GHz Sampling frequency f s ]]> 30MHz Pulse repetition period T r ]]> 100us Coherent processing time CPI 60ms Target angle interval [0.7,1,1.4,2,3.5]° Distance interval 4m / 20m Angle super-resolution multiple [10, 7, 5, 3, 2] times Accumulation signal-to-noise ratio SNR [21, 91]dB Number of snaps L 600 Number of Monte Carlo experiments 500 Amplitude error 0.4dB Phase error 5°

[0117] 2. Simulation experiment content and results:

[0118] Simulation experiment 1: under the above conditions, set 2 times super resolution, different amplitude error and 4m target distance interval, estimate the range and angle values of multiple targets by the method of the present application, and count the detection success rate, the results are shown in Figure 3

[0119] From Figure 3 ​It can be seen that the detection success rate under 2 times super resolution gradually decreases with the increase of amplitude error, and 2 times super resolution can be achieved when the amplitude error is small, and the detection success rate is high.

[0120] In simulation experiment 2, under the above conditions, different resolutions and a target distance interval of 4m are set, the distance and angle values of multiple targets are estimated by the method of the application, and the root mean square error of the target distance is counted, and the results are shown in Figure 4 .

[0121] From Figure 4 It can be seen that the root mean square error of the target distance gradually decreases with the increase of SNR, which shows that the estimation accuracy of the target distance is higher with the increase of SNR.

[0122] In simulation experiment 3, under the above conditions, different resolutions and a target distance interval of 4m are set, the distance and angle values of multiple targets are estimated by the method of the application, and the root mean square error of the target angle is counted, and the results are shown in Figure 5 .

[0123] From Figure 5 It can be seen that the root mean square error of the target angle gradually decreases with the increase of SNR, which shows that the estimation accuracy of the target angle is higher with the increase of SNR.

[0124] In simulation experiment 4, under the above conditions, different resolutions and a target distance interval of 4m are set, the distance and angle values of multiple targets are estimated by the method of the application, and the detection success rate of the target is counted, and the results are shown in Figure 6 .

[0125] From Figure 6 It can be seen that the detection success rate of the target gradually increases with the increase of SNR, which shows that 2 times and 3 times super resolution can be achieved, and the problem of low angle resolution caused by the traditional beam forming algorithm is solved.

[0126] In simulation experiment 5, under the above conditions, 10 times super resolution, different amplitude errors and a target distance interval of 20m are set, the distance and angle values of multiple targets are estimated by the method of the application, and the detection success rate of the target is counted, and the results are shown in Figure 7 .

[0127] From Figure 7 It can be seen that the detection success rate under 10 times super resolution remains basically unchanged with the increase of amplitude error, because the FDA-MIMO radar transmitting steering vector has the freedom of distance dimension, and the target can be distinguished according to the distance interval, so that the influence of the target on the amplitude error is reduced.

[0128] Simulation Experiment 6: Under the above conditions, different resolutions and target distance intervals of 20m were set. The distance and angle values ​​of multiple targets were estimated using the method of this invention, and the root mean square error of the target distance was statistically analyzed. The results are as follows: Figure 8 As shown.

[0129] from Figure 8 As can be seen, the root mean square error of target distance gradually decreases as the SNR increases. Therefore, when the target distance interval is sufficient, multiple targets can be effectively identified based solely on the distance dimension.

[0130] Simulation Experiment 7: Under the above conditions, different resolutions and target distance intervals of 20m were set. The method of this invention was used to estimate the distance and angle values ​​of multiple targets, and the root mean square error of the target angles was statistically analyzed. The results are as follows: Figure 9 As shown.

[0131] from Figure 9 As can be seen, the root mean square error of the target angle gradually decreases as the SNR increases. Therefore, when the target distance interval is sufficient, multiple targets can be effectively identified based solely on the distance dimension.

[0132] Simulation Experiment 8: Under the above conditions, different resolutions and target distance intervals of 20m were set. The method of this invention was used to estimate the distance and angle values ​​of multiple targets, and the target detection success rate was statistically analyzed. The results are as follows: Figure 10 As shown.

[0133] from Figure 10 As can be seen, the success rate of target detection gradually increases with the increase of SNR. Therefore, when the target distance interval is sufficient, multiple targets can be effectively identified based solely on the distance dimension.

[0134] The simulation results demonstrate that, addressing the issue of low target resolution in traditional beamforming algorithms, the method of this invention, by combining the range and angular degrees of freedom provided by the FDA-MIMO radar, achieves effective target identification in multi-target scenarios. When the target angular interval is too low, the resolution can be significantly improved by utilizing the range dimension, solving the problem of low angular resolution caused by traditional beamforming algorithms. Furthermore, when the target range interval is greater than a range threshold, the target can be distinguished solely by the target range interval, overcoming the performance limitations of traditional beamforming algorithms due to amplitude and phase errors. This also proves the advantages of FDA-MIMO radar in multi-target super-resolution. The simulation results also verify the correctness, effectiveness, and reliability of this invention.

Claims

1. A method for joint range-angle super-resolution of multiple targets in FDA-MIMO radar, characterized in that, Comprise: Obtain FDA-MIMO radar echo data, and separate the aliasing to obtain data matrix x k ; Transform the data matrix x k Stack the transformed data to get the NM x L dimensional data X and compute its covariance matrix R x ; The new source signal covariance matrix R is obtained by performing reverse array de-coherent processing on the covariance matrix R x The new source signal covariance matrix R is obtained by performing reverse array de-coherent processing on the covariance matrix R for a new source signal covariance matrix By the MUSIC algorithm, a two-dimensional spatial spectrum function f(R, θ) of the target distance R and the target angle θ is constructed. Performing spectral peak search on the two-dimensional spatial spectrum function f(R, θ) to detect local maximum values to obtain distance and angle joint estimation values of multiple targets.

2. The method of claim 1, wherein, The FDA-MIMO radar echo data is acquired, and is separated to obtain a data matrix x k It comprises: (2a) According to the time delay between the FDA-MIMO radar transmitting signal and the receiving signal, the echo data at the receiving end is obtained; (2b) The echo signal is processed by multi-channel mixing to convert it to a set frequency range using multiple local carrier signals; (2c) The multi-channel mixed signal after frequency conversion is filtered by a low-pass filter with a passband B to separate it into multiple waveforms; (2d) Based on the characteristics of the transmitting waveform, an accurate matched filter is constructed for each receiving channel to perform matched filtering on the filtered signal, extract the target signal and reduce the background noise, and obtain the output of the kth pulse: where β represents a complex echo amplitude, which includes the size of the transmit power, the reflectivity of the target object, and the channel propagation effect, θ0represents a target angle, R0represents a target distance, v0represents a target speed, T r represents a pulse repetition period, t k = (k-1)T r represents a slow time, k = 1, 2, …, L represents a pulse number, L represents a total number of received pulses, a T (R0, θ0) represents a transmit steering matrix, a R (θ0) represents a receive steering vector, Ω(t k , v0) represents a matrix of transmit carrier frequency and target speed coupling; (2e) The output of the kth pulse is rewritten as x k : where n k denotes the noise echo, which is assumed to satisfy a zero-mean Gaussian distribution.

3. The method of claim 1, wherein, The pair data matrix x k The conversion stack is performed to obtain the NM x L dimensional data X and its covariance matrix R x , comprising: (3a) the data transformed to obtain NMx1 dimensional data where β represents a complex echo amplitude, which includes the magnitude of the transmitted power, the reflectivity of the target object, and channel propagation effects, denotes the Kronecker product, denotes the noise n k is converted into an NMx1 dimensional matrix. f d denotes the Doppler frequency, θ0denotes the target angle, R0denotes the target distance, T r denotes the pulse repetition period, t k = (k - 1)T r denotes the slow time, k = 1, 2,..., L denotes the pulse number, L denotes the total number of pulses received, a T (R0, θ0) denotes the transmit dimension steering matrix, a R (θ0) denotes the receive dimension steering vector; (3b) The data after accumulating L pulses is stacked to obtain an NMxL matrix X: wherein, denotes the k-th pulse train vector of X, k = 1, 2,..., L (3c) Compute the covariance matrix R of the NM x L dimensional data X x : wherein (·) H denotes a conjugate transpose operation on a matrix.

4. The method of claim 1, wherein, The covariance matrix R x The reverse array de-coherent processing is performed, and its formula is as follows: where J is an anti-diagonal matrix of size NMxNM, R s is the covariance matrix of the source signals, and Φ is a diagonal matrix with the e jmφ ,m = 1, …, P, P is the target number, and (·) * denotes the conjugate operation on a matrix.

5. The method of claim 1, wherein, The pair of new source signal covariance matrices By the MUSIC algorithm, a two-dimensional spatial spectrum function f(R, θ) of the target distance R and the target angle θ is constructed, which includes: (5a) performing eigenvalue decomposition on the matrix to obtain NM eigenvalues and eigenvectors; and performing eigenvalue decomposition to obtain NM eigenvalues and eigenvectors; and (5b) selecting the largest P eigenvalues from the NM eigenvalues, and taking their respective corresponding eigenvectors to combine into a signal subspace matrix U S , and the remaining NM-P eigenvalues corresponding to the eigenvectors to combine into a noise subspace matrix U N ; (5c) The orthogonality of the noise subspace and the signal subspace is used to obtain the two-dimensional spatial spectrum function f(R, θ) of the target distance R and the target angle θ by the MUSIC algorithm: where a T (R, θ) denotes the transmit dimension steering matrix, a R (θ) denotes the receive dimension steering vector.

6. The method of claim 1, wherein, The two-dimensional spatial spectrum function f(R, θ) is searched for spectral peaks, and local maximum values are detected to obtain distance and angle joint estimation values of multiple targets, which comprises: (6a) Select the distance range and angle range to be scanned, and take the distance R and the angle θ as variables to perform two-dimensional search on the multiple target spatial spectrum whose distance and angle interval meets the corresponding condition; (6b) A plurality of local maximum values formed by the two-dimensional spatial spectrum are searched by grid search, and the distance and angle values corresponding to the multiple targets are obtained according to the positions of the local maximum values.

7. The method of claim 6, wherein, The multiple target distance and angle interval meets the corresponding condition, which is expressed as: where R t = 2ΔfΔr / c is the transmit spatial frequency range increment, Δr is the multi-target range separation, θ t = d t Δθ / λ0is the transmit spatial frequency angle increment, θ r = d r Δθ / λ0is the receive spatial frequency angle increment, Δθ = sin(θ1) - sin(θ0) is the multi-target angle sine difference, B Res is the 3dB bandwidth of the target in two-dimensional spatial spectrum.

8. An FDA-MIMO radar multi-target range-angle joint super-resolution system, characterized in that, Comprise: echo separation aliasing module for the data matrix x after the echo signal has passed through the multichannel matched filter k ; covariance matrix computation module for data matrix x k perform transform stacking and compute covariance matrix R k of data matrix x s ; a reverse array de-coherence module configured to perform reverse array de-coherence processing on the covariance matrix R s to obtain a new source signal covariance matrix a two-dimensional spatial spectrum construction module for constructing a new source signal covariance matrix a two-dimensional spatial spectrum function f(R, θ) of the target distance R and the target angle θ is constructed by the MUSIC algorithm. The multi-target distance and angle estimation module is used for performing spectral peak search on the two-dimensional spatial spectrum function f(R, θ) to detect local maximum values to obtain distance and angle joint estimation values of multiple targets.

9. The system of claim 8, wherein, The echo separation and aliasing module comprises: The echo signal acquisition submodule is used for obtaining the echo signal at the receiving end according to the time delay between the FDA-MIMO radar transmitting signal and the receiving signal; The multi-channel mixing submodule is used for processing the echo signal by multi-channel mixing to convert it to a set frequency range; The low-pass filter submodule is used for low-pass filtering the multi-channel mixed signal after frequency conversion to separate it into multiple waveforms; The matched filter submodule is used for performing matched filtering on the filtered signal to extract the target signal and reduce the background noise, and obtaining the data matrix accumulated by multiple pulses.

10. The system of claim 8, wherein, The two-dimensional spatial spectrum construction module comprises: The eigenvalue decomposition submodule is configured to perform eigenvalue decomposition on the matrix to obtain NM eigenvalues and eigenvectors. perform eigenvalue decomposition to obtain NM eigenvalues and eigenvectors; The subspace construction submodule is used for decomposing the noise subspace and the signal subspace in the signal space; The spatial spectrum construction submodule is used for obtaining the two-dimensional spatial spectrum function f(R, θ) of the target distance R and the target angle θ by the MUSIC algorithm.

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