阅读说明：本技术 基于张量高阶奇异值分解的雷达角度和距离估计方法 (Radar angle and distance estimation method based on tensor high-order singular value decomposition ) 是由 王咸鹏 徐腾贤 黄梦醒 苏婷 吴迪 迟阔 简琳露 于 2020-12-18 设计创作，主要内容包括：本发明提供一种基于张量高阶奇异值分解的雷达角度和距离估计方法,包括下列步骤：构建包含k个子阵的MIMO雷达接收阵列,通过所述MIMO雷达接收阵列获取目标回波的接收数据,并构造三阶张量信号模型；采用高阶奇异值分解三阶张量信号模型,获得基于张量的信号子空间；提取所述信号子空间的接收矩阵,实现MIMO雷达目标DOA参数估计；提取每个子阵对应的信号子空间和发射矩阵,并消除因目标DOD参数和距离耦合造成的相位模糊问题,同时实现目标DOD和距离与DOA参数自动配对,最终实现对MIMO雷达目标DOD参数和距离参数的估计。(The invention provides a method for estimating radar angle and distance based on tensor high-order singular value decomposition, which comprises the following steps: constructing an MIMO radar receiving array comprising k sub-arrays, acquiring received data of a target echo through the MIMO radar receiving array, and constructing a third-order tensor signal model; decomposing a third-order tensor signal model by adopting a high-order singular value to obtain a tensor-based signal subspace; extracting a receiving matrix of the signal subspace to realize the DOA parameter estimation of the MIMO radar target; and extracting a signal subspace and a transmitting matrix corresponding to each subarray, eliminating the phase ambiguity problem caused by coupling of target DOD parameters and distances, realizing automatic pairing of the target DOD and the distances and DOA parameters, and finally realizing the estimation of the target DOD parameters and the distance parameters of the MIMO radar.)

1. The method for estimating the radar angle and the distance based on tensor high-order singular value decomposition is characterized by comprising the following steps of:

constructing an MIMO radar receiving array comprising k sub-arrays, acquiring received data of a target echo through the MIMO radar receiving array, and constructing a third-order tensor signal model;

decomposing a third-order tensor signal model by adopting a high-order singular value to obtain a tensor-based signal subspace;

extracting a receiving matrix of the signal subspace to realize the DOA parameter estimation of the MIMO radar target;

and extracting a signal subspace and a transmitting matrix corresponding to each subarray, eliminating the phase ambiguity problem caused by coupling of target DOD parameters and distances, realizing automatic pairing of the target DOD and the distances and DOA parameters, and finally realizing the estimation of the target DOD parameters and the distance parameters of the MIMO radar.

2. The method for estimating radar angle and distance based on tensor high-order singular value decomposition according to claim 1, wherein the step of obtaining the received data of the target echo through the MIMO radar receiving array and constructing a third-order tensor signal model comprises the following steps:

after receiving the L number of snapshots, the received data of the target echo is represented as:

X＝AS^T+N＝[A_r⊙A_ts]S^T+N

wherein A is_rTo receive steering matrices, A_tsFor the transmit steering matrix, N is the noise matrix, S^TIs a space signal vector matrix;

stacking the received data along three-dimensional different directions to form a tensor signal modelThe dimensionality is MxNxL, N is the number of radar receiving array antennas, M is the number of the receiving array antennas, and the tensor is formedAnd performing modulo-3 expansion to obtain a third-order tensor signal model:

3. the tensor higher order singular value decomposition-based radar angle and distance estimation method according to claim 2, wherein the tensor-based signal subspace is obtained by using a higher order singular value decomposition third order tensor signal model, and the method comprises the following steps:

p incoherent far-field targets are preset, and tensors are set simultaneouslyIs P, byBy using truncated higher order singular value decomposition, a tensor signal subspace can be obtained, which can be expressed as

In the formulaRepresenting the core tensor, U_s1、U_s2Representing column vector components corresponding to singular values;

its truncated core tensor is expressed as:

substituting the core tensor into the expression of the high-order singular value decomposition can obtain:

the reduction results can be tensor-basedSignal subspace:

4. the tensor higher order singular value decomposition-based radar angle and distance estimation method according to claim 3, wherein extracting the receiving matrix of the signal subspace comprises:

constructing a first selection matrix:

obtaining a receiving matrix of the signal subspace by adopting a least square criterion:

in the formula, 0_(N-1)×1Representing a zero matrix of (N-1). times.1 dimensions, I_M、I_(N-1)Each represents an identity matrix.

5. The method for estimating radar angle and distance based on tensor high-order singular value decomposition as claimed in claim 4, wherein performing eigenvalue decomposition on the receiving matrix to achieve DOA parameter estimation of the MIMO radar target comprises:

and decomposing the eigenvalue of the receiving matrix to obtain:

in the formula, E_r、Matrix representing the composition of the eigenvectors, Λ_rIs represented by characteristic valuesA diagonal matrix is formed;

will E_rThe method is divided into four sub-matrixes, and specifically comprises the following steps:

obtaining a matrix containing DOA information of the target according to the four sub-matrices:

to psi_rAnd (3) carrying out characteristic value decomposition:

in the formula, T represents a matrix composed of feature vectors, T^-1The inverse matrix, phi, of T_rRepresenting a diagonal matrix composed of eigenvalues;

the MIMO radar target DOA parameter estimation is realized through the following formula:

whereinRepresents phi_rThe p-th element, angle (·) denotes phase, c denotes speed of light, d_rRepresenting the receiving antenna spacing, f₁Representing the frequency of the first antenna.

6. The tensor high-order singular value decomposition-based radar angle and distance estimation method according to claim 5, wherein extracting the signal subspace and the subarray transmission matrix corresponding to each subarray comprises:

constructing a second selection matrix:

based on the second selection matrix, extracting a signal subspace corresponding to each subarray as:

constructing a third selection matrix:

obtaining a transmitting matrix of a signal subspace corresponding to each subarray by adopting a least square criterion:

7. the tensor higher order singular value decomposition-based radar angle and range estimation method as claimed in claim 6, wherein eliminating phase ambiguity problems due to coupling of target DOD parameters and range while achieving automatic pairing of target DOD and range with DOA parameters comprises:

obtaining a matrix psi containing target DOD and distance information by using rotation non-deformation and least square criterion_t ^k；

Using matrix T to matrix Ψ_t ^kDiagonalization is carried out, so that automatic pairing of target DOD and distance and DOA parameters is realized: phi_t ^k＝T^-1Ψ_t ^kT。

8. The tensor high-order singular value decomposition-based radar angle and distance estimation method according to claim 7, wherein the estimating of DOD and distance parameters of the MIMO radar target is realized by:

determining the maximum target detection distance of the radar:

in the formula (I), the compound is shown in the specification,representing the transmission frequency offset of the kth sub-array;

extracting the phase of the emission matrix of each subarray to obtain DOD and distance information:

whereinContaining phase information of the p-th target in the k-th sub-array

The phase ambiguity parameter is derived as:

the distance of the target can thus be derived:

determining k by using a rounding-down method_i：

Determining DOD parameter estimation of the target:

Technical Field

The invention relates to the technical field of bistatic MIMO radar systems, in particular to a method for estimating radar angle and distance based on tensor high-order singular value decomposition.

Background

The frequency control array MIMO radar is a new system radar which is continuously developed in recent years, has better promotion on the premise of keeping the advantages of a phase control array, has high resolution and excellent parameter estimation performance, and is a research hotspot in the field of signal processing at present. The frequency control array MIMO radar can be divided into two types according to the relative position of a receiving array and a transmitting array, and is respectively a single-machine ground frequency control array MIMO radar and a bistatic frequency control array MIMO radar. In recent years, research on frequency control array MIMO radars is mostly focused on the single-base field, and some algorithms, such as an esprit (estimation of signal parameters, a radio interference technique) algorithm and a music (multiple signal classification) algorithm, have appeared, but because the single-base frequency control array MIMO radars have weak interference resistance and are difficult to cope with the challenge of radar target detection under increasingly complex electromagnetic environments, the research on the double-base frequency control array MIMO radars is very important in order to develop the frequency control array MIMO radars with stronger interference resistance.

The bistatic MIMO radar can realize the estimation of DOA, DOD and distance of the target, thereby improving the anti-interference capability and the resolution capability of the false target. In order to realize DOD and range decoupling of bistatic frequency-controlled array MIMO radar, a sub-array division mode (IAEAC, pp.818-824, March 2017) is proposed for designing a radar transmitting array, however, the accuracy of the algorithm is established on a large amount of computational complexity, and a high snapshot number is required to guarantee. Another algorithm (IEEE Access, vol.6, No. pp.15431-15445, 2018) provides a new idea of subarray division, a plurality of subarrays form a transmitting array, and joint estimation of target DOA, DOD and distance is realized through rotation invariance. However, the above mentioned methods are all based on subspace algorithm of matrix decomposition, which simply stores the received echo data as a matrix, but this way loses the inherent multidimensional structure of the received data. Secondly, such algorithms perform poorly in low snapshots and low signal-to-noise ratios. In addition, parameter matching errors are easy to occur under the condition of multiple targets, in practical application, the condition of multiple targets is more common, and in a severe electromagnetic environment, the application performance of the method can be seriously influenced.

Disclosure of Invention

The invention aims to provide a method for estimating radar angle and distance based on tensor high-order singular value decomposition, so as to solve the problems in the background technology.

The invention is realized by the following technical scheme: the radar angle and distance estimation method based on tensor high-order singular value decomposition comprises the following steps of:

constructing an MIMO radar receiving array comprising k sub-arrays, acquiring received data of a target echo through the MIMO radar receiving array, and constructing a third-order tensor signal model;

decomposing a third-order tensor signal model by adopting a high-order singular value to obtain a tensor-based signal subspace;

extracting a receiving matrix of the signal subspace to realize the DOA parameter estimation of the MIMO radar target;

and extracting a signal subspace and a transmitting matrix corresponding to each subarray, eliminating the phase ambiguity problem caused by coupling of target DOD parameters and distances, realizing automatic pairing of the target DOD and the distances and DOA parameters, and finally realizing the estimation of the target DOD parameters and the distance parameters of the MIMO radar.

Preferably, the acquiring the received data of the target echo by the MIMO radar receiving array and constructing a third order tensor signal model includes:

after receiving the L number of snapshots, the received data of the target echo is represented as:

X＝AS^T+N＝[A_r⊙A_ts]S^T+N

wherein A is_rTo receive steering matrices, A_tsFor the transmit steering matrix, N is the noise matrix, S^TIs a space signal vector matrix;

stacking the received data along three-dimensional different directions to form a tensor signal modelThe dimensionality is MxNxL, N is the number of radar receiving array antennas, M is the number of the receiving array antennas, and the tensor is formedAnd performing modulo-3 expansion to obtain a third-order tensor signal model:

preferably, decomposing a third-order tensor signal model by using a higher-order singular value to obtain a tensor-based signal subspace, includes:

p incoherent far-field targets are preset, and tensors are set simultaneouslyIs P, byBy using truncated higher order singular value decomposition, a tensor signal subspace can be obtained, which can be expressed as

In the formulaRepresenting the core tensor, U_s1、U_s2Representing column vector components corresponding to singular values;

its truncated core tensor is expressed as:

substituting the core tensor into the expression of the high-order singular value decomposition can obtain:

the reduction results may result in a tensor-based signal subspace:

preferably, the extracting the receiving matrix of the signal subspace includes:

constructing a first selection matrix:

obtaining a receiving matrix of the signal subspace by adopting a least square criterion:

in the formula, 0_(N-1)×1Representing a zero matrix of (N-1). times.1 dimensions, I_M、I_(N-1)Each represents an identity matrix.

Preferably, the eigenvalue decomposition is performed on the receiving matrix to realize MIMO radar target DOA parameter estimation, including:

and decomposing the eigenvalue of the receiving matrix to obtain:

in the formula, E_r、Matrix representing the composition of the eigenvectors, Λ_rRepresenting a diagonal matrix composed of eigenvalues;

will E_rThe method is divided into four sub-matrixes, and specifically comprises the following steps:

obtaining a matrix containing DOA information of the target according to the four sub-matrices:

to psi_rAnd (3) carrying out characteristic value decomposition:

in the formula, T represents a matrix composed of feature vectors, T^-1The inverse matrix, phi, of T_rRepresenting a diagonal matrix composed of eigenvalues;

the MIMO radar target DOA parameter estimation is realized through the following formula:

whereinRepresents phi_rThe p-th element, angle (·) denotes phase, c denotes speed of light, d_rRepresenting the receiving antenna spacing, f₁Representing the frequency of the first antenna.

Preferably, the extracting the signal subspace and the sub-array transmission matrix corresponding to each sub-array includes:

constructing a second selection matrix:

based on the second selection matrix, extracting a signal subspace corresponding to each subarray as:

constructing a third selection matrix:

obtaining a transmitting matrix of a signal subspace corresponding to each subarray by adopting a least square criterion:

preferably, the method for eliminating phase ambiguity caused by coupling of target DOD parameters and range, and simultaneously realizing automatic pairing of target DOD and range with DOA parameters comprises the following steps:

obtaining a matrix containing target DOD and distance information by using a rotation non-deformation and least square criterion

Using matrix T to matrixDiagonalization is carried out, so that automatic pairing of target DOD and distance and DOA parameters is realized:

preferably, the estimation of the target DOD and the range parameter of the MIMO radar is realized, including:

determining the maximum target detection distance of the radar:

in the formula (I), the compound is shown in the specification,representing the transmission frequency offset of the kth sub-array;

extracting the phase of the emission matrix of each subarray to obtain DOD and distance information:

whereinContaining phase information of the p-th target in the k-th sub-array

The phase ambiguity parameter is derived as:

the distance of the target can thus be derived:

determining k by using a rounding-down method_i：

Determining DOD parameter estimation of the target:

compared with the prior art, the invention has the following beneficial effects:

the invention provides a radar angle and distance estimation method based on tensor high-order singular value decomposition, which comprises the following steps of (1) constructing a signal model by utilizing a tensor, and re-stacking and storing received data of a target echo, so that inherent multidimensional structure information of the received data is stored, and the method has great superiority compared with a traditional subspace algorithm;

(2) by adopting a tensor high-order singular value decomposition method to process a tensor signal model, compared with the traditional SVD/EVD method, the method can more effectively inhibit noise interference and improve the target parameter estimation performance, and compared with the traditional ESPRIT algorithm based on matrix decomposition, the method has better angle estimation performance;

(3) independent extraction of each subarray signal subspace is achieved in a tensor domain, so that target DOD and distance coupling information are obtained, and the problem of phase ambiguity of the coupling information is solved by utilizing different frequency gains among the subarrays and limitation of a target range;

(4) by utilizing the inherent multi-dimensional structural information of the tensor signal model, the estimation accuracy of the signal subspace is improved, the included angle between the signal subspace and the real signal subspace is reduced, and the automatic matching of the target DOA and the DOD and the distance parameter is realized by utilizing the rotational invariance.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only preferred embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without inventive exercise.

FIG. 1 is a structural diagram of a method for estimating radar angle and distance based on tensor high-order singular value decomposition according to the present invention;

FIG. 2 is a schematic diagram of a bistatic frequency-controlled array MIMO radar system;

FIG. 3 is a schematic diagram of a division structure of a transmitting array in a subarray mode;

FIG. 4 is a three-dimensional point cloud plot of target DOA, DOD and range parameter estimates;

FIG. 5 is a graph of tensor signal subspace accuracy versus fast beat number;

FIG. 6 is a graph of tensor signal subspace accuracy versus fixed signal-to-noise ratio;

FIG. 7 is a graph comparing different algorithm pairs against target DOA, DOD and range parameter root mean square error as a function of signal to noise ratio;

FIG. 8 is another comparison graph of different algorithm pairs versus target DOA, DOD and range parameter root mean square error as a function of signal-to-noise ratio

FIG. 9 is a comparison of different algorithm pairs versus target DOA, DOD and distance parameter root mean square error as a function of snapshot count;

FIG. 10 is another comparison of different algorithm pairs with target DOA, DOD and distance parameters root mean square error as a function of snapshot count.

Detailed Description

In order to better understand the technical content of the invention, specific embodiments are provided below, and the invention is further described with reference to the accompanying drawings.

Referring to fig. 1, the method for estimating radar angle and distance based on tensor high-order singular value decomposition comprises the following steps:

step 101: constructing an MIMO radar receiving array comprising k sub-arrays, acquiring received data of a target echo through the MIMO radar receiving array, and constructing a third-order tensor signal model;

referring to fig. 2 to 3, N bistatic frequency controlled array MIMO radar receiving array antennas are preset, M bistatic frequency controlled array MIMO radar receiving array antennas are preset, the receiving array antennas are divided into K sub-arrays, transmission waveforms between the transmitting antennas are orthogonal to each other, and a transmission frequency of an mth antenna of the kth sub-array in a sub-array mode can be expressed as

The receive steering vector may be expressed as:

the transmit steering vector for the kth sub-array may be expressed asThe method comprises the following specific steps:

in this embodiment, a non-overlapping sub-array is designed, and the number of antennas in each sub-array should be the same, so that

In addition, it is also necessary to ensure that the last antenna carrier frequency of a sub-array is equal to the first antenna carrier frequency of the next sub-array, i.e. the carrier frequency of the last antenna of the sub-array is equal to the carrier frequency of the first antenna of the next sub-arrayAndand Δ f₁<Δf₂…<Δf_K。

In the subarray mode, the signal model array prevalence matrix of the bistatic frequency control array MIMO radar can be expressed as:

after receiving L snapshot counts, arranging the received data as X ═ X (1), X (2), …, X (L), X can be expressed as:

X＝AS^T+N＝[A_r⊙A_ts]S^T+N

wherein the receiving matrix isa_r(θ_P) Representing the receive steering vector, the transmit matrix in subarray mode beingRepresents a transmit steering vector, and has N is a uniform white Gaussian noise matrix, andS^Tis a space signal vector matrix.

Stacking the received data X along three-dimensional different directions to form a tensor signal modelIts dimension is MxNxL, the tensor isAnd performing modulo-3 expansion to obtain a third-order tensor signal model:

step 102: decomposing a third-order tensor signal model by adopting a high-order singular value to obtain a tensor-based signal subspace;

in this embodiment, the tensor is processed using a higher order singular value decompositionCan be expressed as

WhereinThe tensor of the core is represented, andrespectively express by tensorThe left singular vector component of modulo n decomposition, i.e.

P incoherent far-field targets are preset, and tensors are set simultaneouslyIs P, byBy using truncated higher order singular value decomposition, a tensor signal subspace can be obtained, which can be expressed as

Wherein U is_sn(n-1, 2,3) is represented by U_nThe column vectors corresponding to the first P maximum singular values of (A), anda core tensor representing a truncated form;

substituting the core tensor into the expression of the high-order singular value decomposition can obtain:

will tensorPerforming a modulo-3 expansion, one can obtain a tensor-based signal subspace of

Wherein

Will be provided withIs decomposed into singular valuesSubstituting the signal into a tensor-based signal subspace, and simplifying to obtain the following results:

to this end, a tensor-based signal subspace U is obtained_s。

Step 103: extracting a receiving matrix of the signal subspace to realize the DOA parameter estimation of the MIMO radar target;

in this embodiment, to extract the reception matrix, the first selection matrix is defined as follows:

in the formula, 0_(N-1)×1Representing a zero matrix of (N-1). times.1 dimensions, I_M、I_(N-1) each represent an identity matrix.

According to the rotation invariance and the least square criterion, U is divided into_sThe decomposition into two parts is taken as a receiving matrix of the signal subspace, and the specific expression is as follows:

optionally, the method for implementing MIMO radar target DOA parameter estimation through the receiving matrix of the signal subspace includes:

performing eigenvalue decomposition on the receiving matrix to obtain:

in the formula, E_r、Matrix representing the composition of the eigenvectors, Λ_rRepresenting a diagonal matrix composed of eigenvalues;

will be provided withDivided into four sub-matrices, in particular

Wherein E_r11、E_r12、E_r21And E_r22All the dimensions of (c) are K, so that a matrix Ψ containing DOA information of the target is obtained_r；

To psi_rPerforming eigenvalue decomposition

T denotes a matrix of eigenvectors, T^-1The inverse matrix, phi, of T_rRepresenting a diagonal matrix composed of eigenvalues;

wherein phi_rThe method comprises the following specific steps:

obtaining the target DOA parameter by the following formula

WhereinRepresents phi_rThe p-th element, angle (·) denotes phase, c denotes speed of light, d_rRepresenting the receiving antenna spacing, f₁Representing the frequency of the first antenna. .

Step 104: and extracting a signal subspace and a transmitting matrix corresponding to each subarray, eliminating the phase ambiguity problem caused by coupling of target DOD parameters and distances, realizing automatic pairing of the target DOD and the distances and DOA parameters, and finally realizing the estimation of the target DOD parameters and the distance parameters of the MIMO radar.

In the subarray FDA-MIMO radar mode, each transmit subarray and receive array may be considered as a whole, containing a corresponding signal subspace. Therefore, a second selection matrix is constructed to select the signal subspace of each sub-matrix, and the constructed second selection matrix is specifically as follows:

whereinA selection matrix representing the kth sub-array,are all zero matrices, I_MtsAs a unitary matrix, then the signal subspace of each sub-arrayCan be expressed as:

by constructing a third selection matrix for obtaining the DOD and distance information of the target from each sub-matrix signal subspace, the third selection matrix is specifically constructed as follows:

obtaining a matrix containing target DOD and distance information by using the rotation non-deformation and least square criterion

Psi due to the presence of rotational invariance_rAndby stretching into the same subspace, this property can be exploited, using the matrix T pairsDiagonalized by a matrix T comprising the DOA information of the object Ψ_rThe method comprises the following steps of (1) forming a feature vector, thereby realizing automatic pairing of target DOD and distance with DOA parameters, specifically as follows:

matrix arrayThe specific form of (A) is as follows:

optionally, the method for estimating the target DOD and the range parameter of the MIMO radar includes:

determining the maximum target detection distance of the radar:

representing the transmission frequency offset of the kth sub-array;

extracting the phase of the emission matrix of each subarray to obtain DOD and distance information:

whereinContains phase information of the p-th target in the k-th sub-array, and

subtracting the previous equation from each equation in the above to obtain a new equation set as:

the phase ambiguity parameter is derived as:

phase blur parameter (k)_i+1-k_i) Substituting into the new equation set, and adopting least square criterion to obtain the distance of the targetComprises the following steps:

whereinRepresenting the estimated distance of the p-th target;

in the design of the array, the distance between the transmitting array antennas ensures 2d_tf₁C is less than or equal to 1, k can be obtained through derivation_i(i ═ 1,2, …, K) as follows:

whereinRepresents rounding down

According to k_iAnd distance parameterAnd obtaining the DOD of the p-th target by a least square method as follows:

so far, the DOA, the DOD and the distance parameters of the target are successfully estimated through the method and the device, and automatic pairing of the target parameters is realized.

The invention is further illustrated below with reference to the results of the MALTAB simulation experiment:

setting the transmitting frequency of the first transmitting antenna as f in the simulation experiment₁At 10GHz with antenna spacing ofWherein f is_maxIs the maximum transmit frequency. Presetting the number of transmitting antennas and receiving antennas as M-N-18, and dividing the transmitting array into K-3 sub-arrays, each sub-array having M_ts6 transmitting antennas. The increment of the transmitting frequency of each subarray is delta f₁＝5000Hz、Δf₂10000Hz and Δ f₃15000Hz, SNR 20dB, snapshot number 300, etc. The DOD, DOA and distance to three incoherent objects are preset to (-15 °, -50 °,30km), (20 °,35 °,9km) and (40 °,10 °,58km), respectively.

The specific results of the simulation results obtained after T-500 monte carlo experiments were performed for each simulation are shown in fig. 4-6.

Fig. 4 illustrates the position of the estimated target in the case where SNR is 20dB and L is 300, and X, Y and Z axes represent DOA, DOD and distance, respectively, and it can be seen from fig. 4 that the estimated target landing points are highly concentrated and identical to the position of the actual target. This can prove that the stability and accuracy of the present invention are excellent.

Fig. 5-6 show the accuracy of the signal subspace as a function of the signal-to-noise ratio and the number of snapshots. Fig. 5 shows a fixed fast beat number L of 300, and fig. 6 shows a fixed SNR of 20 dB. The radar structure and target parameters are consistent with the previous simulation, and the number of antennas is set to be M-N-9, 12,15 and 18.

It can be seen from the figure that the performance of the present invention gradually improves as the signal-to-noise ratio and the number of snapshots increase. Under the same conditions, the performance of the present invention is superior to the ESPRIT method. Meanwhile, as the number of antennas increases, the performance of the antenna is improved continuously, but the performance of the antenna is improved slightly by the ESPRIT method. This is because the present invention uses a tensor signal model to preserve the structural characteristics of the radar array antenna, and thus the tensor-based method performs better than the matrix decomposition-based method as the number of antennas increases.

Fig. 7-8 show the angle and distance RMSE of the estimation method as a function of the signal-to-noise ratio for the case of a fast beat number L-50.

It can be seen that the performance of the present invention is superior to the ESPRIT method. Meanwhile, the tensor is adopted to construct the signal model, inherent multidimensional structural information of the received data can be well utilized, and therefore the method has higher performance under the same signal-to-noise ratio and snapshot number and has more excellent performance under the condition of lower signal-to-noise ratio and snapshot number.

Fig. 9-10 show the angle and distance RMSE of the estimation method as a function of fast beat number for a signal-to-noise ratio of SNR of 5 dB.

It can be seen that the RMSE of the present invention decreases with increasing number of fast beats, indicating that the performance of the present invention is increasing and approaching CRB. In addition, when the number of snapshots is large, the curve of the present invention tends to be close to the trend of CRB, which indicates that the performance of the present invention tends to be gradually stable.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.