CN110196417A

CN110196417A - The bistatic MIMO radar angle estimating method concentrated based on emitted energy

Info

Publication number: CN110196417A
Application number: CN201910544141.2A
Authority: CN
Inventors: 赵永波; 黄�隆; 徐保庆
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2019-06-21
Filing date: 2019-06-21
Publication date: 2019-09-03
Anticipated expiration: 2039-06-21
Also published as: CN110196417B

Abstract

The invention discloses the bistatic MIMO radar angle estimating methods concentrated based on emitted energy, realize are as follows: in the case where known target is relative to emission array angular regions, by solving convex optimization problem design launching beam domain matrix and scaling to it；The transmitted waveform based on launching beam domain matrix is defined, to obtain receiving echo model；Matched filtering is carried out to wave pattern is received back, and filtered data are converted into column vector and construct new echo model；Its autocorrelation matrix is solved to the echo model of neotectonics, and Eigenvalues Decomposition is carried out to autocorrelation matrix and obtains the signal subspace comprising wave digression and direction of arrival information；The estimated value of target wave digression and direction of arrival is obtained according to signal subspace；Mapping relations are established to compensate wave digression difference error during solving convex optimization problem, obtain the optimal estimation value of target wave digression.The present invention solves prior art emitted energy and the problems in does not collect, and improves angle measurement accuracy, can be used for target acquisition.

Description

Bistatic MIMO radar angle estimation method based on emission energy concentration

Technical Field

The invention belongs to the technical field of radars, and further relates to a bistatic MIMO radar angle estimation method which can be used for solving the problem of energy loss caused by relatively uniform emission gain of each direction in the angle measurement process of the traditional bistatic MIMO radar.

Background

Compared with the traditional phased array radar, the MIMO radar has attracted wide attention in recent years, the MIMO radar requires a transmitting antenna to transmit incompletely correlated waveforms on the basis of the conventional phased array radar, the coverage range of signals in an airspace can be wider when orthogonal waveforms are transmitted, and multiple beams can be formed to cover the airspace range simultaneously when the signals are processed.

In the bistatic MIMO radar, the DOD refers to the included angle between the direction of a radar transmitted signal and the normal of a transmitting antenna, and the DOA refers to the included angle between the direction of a target echo and the normal of a receiving antenna. Angular measurement of the departure angle and arrival angle is an important research area of bistatic MIMO radars. The bistatic MIMO radar wave departure angle and wave arrival angle measuring method is mainly based on subspace algorithm at the present stage, and ESPRIT algorithm and MUSIC algorithm are commonly used in the subspace algorithm. Compared with the MUSIC algorithm, the ESPRIT algorithm avoids the spectrum peak search of the MUSIC algorithm by two sub-arrays with completely same characteristics and utilizing a rotation invariant technology, and has better robustness.

An Angle estimation method of a bistatic MIMO radar based on an ESPRIT algorithm is proposed in a document 'Angle estimation using ESPRIT in MIMO radar', wherein the ESPRIT algorithm in the document adopts a waveform diversity technology, namely the transmitting waveforms are completely orthogonal, and a signal subspace containing information of a target ionization Angle and a target arrival Angle is obtained by solving an autocorrelation matrix for target echo data and decomposing characteristic values; however, since the use of completely orthogonal transmit waveforms results in a relatively uniform transmit gain in all directions, given the angular area of the target relative to the transmit array, the coherent gain of the transmit is actually reduced and the angle measurement performance is reduced, which is a significant disadvantage of conventional bistatic MIMO radar angle measurement.

Disclosure of Invention

The invention aims to provide a bistatic MIMO radar angle estimation method based on emission energy concentration to improve the angle measurement accuracy of a target departure angle and an angle of arrival.

The technical scheme of the invention is that under the condition that the angular area of the target relative to the transmitting array is known, designing a transmitting beam domain matrix by solving a convex optimization problem and scaling the transmitting beam domain matrix, defining a transmitting waveform based on the transmitting beam domain matrix, obtaining a receiving echo model by utilizing the transmitting waveform, matched filtering is carried out on the echo model by docking, the filtered data is converted into a column vector to construct a new echo model, solving the autocorrelation matrix of the newly constructed echo model, and carrying out eigenvalue decomposition on the autocorrelation matrix to obtain a signal subspace containing the information of the departure angle and the arrival angle, and finally, establishing a mapping relation to carry out error compensation on the difference error of the wave departure angles caused in the process of solving the convex optimization problem, thereby obtaining the optimal estimation value of the target wave departure angle. The method comprises the following implementation steps:

(1) setting the number of transmitting array elements of the bistatic MIMO radar as M, the number of receiving array elements as N, the total transmitting energy of the bistatic MIMO radar as E, the spatial dimension of a transmitting beam domain as L, the total echo pulse number in one coherent processing interval CPI of the radar as Q, and G targets in a target space domain;

(2) designing a transmitting wave beam domain matrix W by using a convex optimization method according to the angle region of a target relative to a transmitting array, and scaling W to meet tr (W)^*W^T) L, a scaled transmit beam domain matrix W' is obtained, where [ ·]^*Conjugate of representation matrix [ ·]^TRepresents the transpose of the matrix, tr (-) represents the trace of the matrix;

(3) according to transmit waveforms based on transmit beam domainCalculating to obtain an echo signal matrix X of the q-th received pulse_qThen to X_qTaking Q values from 1 to Q in sequence to obtain an echo signal matrix X ═ X₁,X₂,…,X_q,...,X_Q],

wherein ,[·]^*The conjugate of the matrix is represented as,represents L mutually orthogonal waveforms transmitted by a bistatic MIMO radar transmission array, and SS^H＝I_L，I_LAn identity matrix denoted L × L, T1, 2.. T, T denotes the number of samples per pulse period,the waveform transmitted by the mth array element in the transmitted waveform S is shown, Q is 1, …, and Q represents a pulse number;

(4) echo signal X for the q-th received pulse_qPerforming matched filtering, and performing matched filtering on the data matrix Y_qConversion to column vector y_qFurther constructing a new echo signal matrix Y;

(5) calculating the autocorrelation matrix R of the newly constructed echo signal matrix Y, and performing eigenvalue decomposition on the autocorrelation matrix R to determine a signal subspace E_s；

(6) According to the signal subspace E_sAnd calculating to obtain the estimated value of the target wave departure angleSum angle of arrival estimateWherein k is 1.. G, which represents a target number;

(7) establishing a noise-free echo signal matrix model:

where A is the transmit steering matrix, B is the receive steering matrix, and C is the reflection coefficient matrix [. C]^HRepresents the conjugate transpose of the matrix, ⊙ represents the Khatri-Rao product;

(8) according to the noise-free echo matrix model in (7), when the array structure of the transmitting antenna and the receiving antenna is a half-wavelength equal-interval uniform linear array ULA, the following mapping relationship can be obtained:

wherein J_t,1＝[I_L-1,0],J_t,2＝[0,I_L-1]，I_L-1Is a unit matrix of L-1 order, theta_iAn angle value, a (theta), representing the ith sample point within the angular region of the target relative to the transmit array_i) Is the transmitted steering vector of the target airspace,a mapped angle value representing the ith sample point within the angular region of the target relative to the transmit array,and theta_iThe method comprises the following steps of one-to-one correspondence, wherein I is 1, I is the number of sampling points in an angle area of a target relative to an emission array;

(9) according to the mapping relation obtained in the step (8), calculating the corresponding wave separation angle of the signal model in the step (7)

(10) The departure angle corresponding to the model of the noise-free signalTo find an estimate of the departure angle from each targetClosest departure angleThen finding out the corresponding theta through the mapping relation in the step (8)_iAnd the optimal estimated value of the corresponding target departure angle is taken as the optimal estimated value.

Compared with the prior art, the invention has the following advantages:

first, the invention designs the transmit beam domain matrix of the MIMO radar by using a convex optimization method, so that the transmit energy of the MIMO radar is concentrated on the spatial sector where the target is located, and the loss of the transmit energy is reduced.

Secondly, compared with the traditional ESPRIT angle measurement method of the MIMO radar, the method has the advantages that the signal-to-noise ratio of the target echo signal is enhanced and the angle measurement precision of the departure angle and the arrival angle is improved because the transmitting energy of the transmitting array in the angle area of the space sector where the target is located is high.

Thirdly, the method carries out error compensation on the estimated value of the target wave divergence angle by establishing a mapping relation, thereby reducing the wave divergence angle error caused when a convex optimization method is used for solving the matrix of the transmitting wave beam domain.

Drawings

FIG. 1 is a flow chart of an implementation of the present invention;

FIG. 2 is a graph comparing the emission energy distribution of the bistatic MIMO radar based on the emission energy concentration in the present invention with that of the conventional bistatic MIMO radar;

FIG. 3 is a graph comparing the root mean square error of the present invention and a conventional angle measurement method for two uncorrelated target angle measurements with the change of signal-to-noise ratio;

FIG. 4 is a graph comparing the root mean square error of the present invention and a conventional method of angle measurement for two unrelated targets as a function of pulse number.

Detailed Description

The embodiments and effects of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is to be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1, the implementation steps of this embodiment are as follows:

step 1, setting bistatic MIMO radar parameters

Setting the number of transmitting array elements of the bistatic MIMO radar as M, wherein M is more than 0, the number of receiving array elements is N, N is more than 0, the total transmitting energy of the bistatic MIMO radar is E more than 0, the space dimension of a transmitting beam field is L, L is less than M, the number of total echo pulses in a radar one-coherent processing interval CPI is Q, Q is 1,2, once.Q, Q is the total echo pulse number in the radar one-coherent processing interval CPI, the target number in a target airspace is G, and G is more than 0;

and 2, designing a transmitting beam domain matrix W by using a convex optimization method according to the position of the target relative to the angle region of the transmitting array.

The convex optimization method is a method for solving the optimization problem that an objective function is a convex function and a set to which a variable belongs is a convex set.

In this example, a transmit beam domain matrix W is designed according to an angle region of a target relative to a transmit array by using a convex optimization method, which is implemented as follows:

(2.1) determining an angle region theta of the target relative to the transmitting array and a complementary set angle region theta of the target relative to the transmitting array

Setting the angular region theta of the target relative to the transmitting array to [ delta ]_min,δ_max]，δ_minRepresenting the minimum expected angle of occurrence of the target, delta_maxRepresents the maximum expected angle of occurrence of the target;

complementary angular region of the target with respect to the angular region Θ of the transmit arrayIs [ -90 °, δ_min-1°]And [ delta ]_max+1°,90°]；

(2.2) setting a virtual transmission guide vector of Lx 1 pointing to the angular region theta according to the parameters in (2.1)When the array structure of the transmitting antenna and the receiving antenna is a half-wavelength equal-interval uniform linear array ULA:

wherein ,[·]^TRepresenting the transpose of the vector, theta_iE, theta, I is 1,2, I represents the total number of sampling points of theta;

(2.3) according to the parameters in (2.1), when the array structure of the transmitting antenna and the receiving antenna is a half-wavelength uniform linear array ULA with equal intervals, the transmitting guide vector a (theta) pointing to the angle area theta is guided to_i) And pointing angle regionIs transmitted to the vector a (theta)_β) Respectively expressed as:

wherein ,[·]^TRepresenting the transpose of the vector, theta_iE Θ, I ═ 1,2, I denotes the total number of sample points Θ,β is 1,2, J, J stands forThe total number of sampling points;

(2.4) designing the transmit beam domain matrix W by solving the following convex optimization problem according to the parameters of (2.1), (2.2) and (2.3):

wherein ,[·]^HRepresenting the conjugate transpose of the matrix, representing the 2-norm of the matrix, α representing the maximum acceptable W in Θ^Ha(θ_i) and the error between the two is required to be as small as possible on the premise of ensuring the solution of the optimization problem, and the empirical value is generally 0 < α < 1.

Step 3, scaling the transmitting beam domain matrix W to meet tr (W)^*W^T) A scaled transmit beam domain matrix W' is obtained.

And 4, obtaining an echo signal matrix X according to the zoomed transmitting beam domain matrix W'.

(4.1) obtaining a transmitting waveform based on the transmitting beam domain according to the scaled transmitting beam domain matrix:

wherein ,[·]^*The conjugate of the matrix is represented as,represents L mutually orthogonal waveforms, and SS^H＝I_L，I_LAn identity matrix denoted L × L, T1, 2.. T, T denotes the number of samples per pulse period,represents the mth orthogonal waveform in the transmit waveform S;

(4.2) determining a transmitting steering matrix A and a receiving steering matrix B:

when the transmitting and receiving array is a half-wavelength uniform linear array ULA with equal interval, the departure angle and arrival angle of the kth target are respectively theta_kAndindicating that k is 1,2, …, G, the transmit steering matrix a and the receive steering matrix B can be represented as:

A＝[a(θ₁),a(θ₂),...a(θ_k),...,a(θ_G)]

wherein ,a transmit steering vector representing the kth target,

a receive steering vector representing a kth target;

(4.3) the reflection coefficient diagonal matrix Lambda of the q-th echo pulse for G targets_qExpressed as:

Λ_q＝diag(c_q)，

wherein diag (. circle.) represents the diagonalization operation, c_q＝[α_1,q,α_2,q,…α_k,q,…,α_G,q]^TVector of reflection coefficients representing the q-th echo pulse of G targets, α_k,qRepresenting the reflection coefficient of the kth target in the qth echo pulse;

(4.4) transmitting the waveform sum according to (4.1) (4.2)Reflection coefficient diagonal matrix Λ in medium transmission steering matrix a, reception steering matrix B, and (4.3)_qCalculating the echo signal matrix X of the q-th received pulse_q：

wherein ,[·]^TRepresenting a matrix transposition [ ·]^*Representing a matrix conjugate; n is a radical of_qA noise matrix representing the q-th echo pulse, the mean of which is zero and obeys Gaussian white noise distribution;

(4.5) for X_qTaking Q values from 1 to Q in sequence to obtain an echo signal matrix X ═ X₁,X₂,...,X_q,...,X_Q]。

Step 5, using the echo signal X of the q-th received pulse obtained in step 4_qAnd constructing a new echo signal matrix Y.

(5.1) Signal matrix X for the q-th echo pulse_qRight riding S^HPerforming matched filtering to obtain a signal matrix Y of the q pulse after matched filtering_q：

wherein ,[·]^TRepresenting a matrix transposition [ ·]^HRepresenting a matrix conjugate transpose; s is L mutually orthogonal waveforms transmitted by a bistatic MIMO radar transmitting array;representing a noise matrix matching the filtered q-th pulse,Λ_qreflection coefficient of q-th echo pulse representing G targetsA diagonal matrix; a is a transmitting guide matrix; b is a receiving steering matrix;representing a scaled transmit beam domain matrix;

(5.2) according to the formula in (5.1), mixing Y_qObtaining a signal column vector y of the q pulse after matched filtering according to column arrangement_q：

wherein ,representing a column vector formed by the matched filtered noise, vec (-) representing vectorizing the matrix; c. C_q⊙ represents the Khatri-Rao product;

(5.3) taking Q values from 1 to Q, according to the formula in (5.2), obtaining the following matrixes respectively:

signal column vector y of the matched filtered 1 st pulse₁Signal column vector y to the Q-th pulse after matched filtering_QNote as new echo signal matrix: y ═ Y₁,y₂,...,y_q,...,y_Q]；

Vector c of reflection coefficient of 1 st pulse of G targets₁Vector c of reflection coefficients of the Q-th pulse of the G targets_QAnd is recorded as a reflection coefficient matrix: c ═ C₁,c₂,...,c_q,...,c_Q]；

Noise matrix of matched filtered 1 st pulseNoise matrix to the Q-th pulse after matched filteringAnd (3) recording as a noise matrix after matched filtering:

(5.4) substituting the formula in (5.2) into Y ═ Y₁,y₂,...,y_q,...,y_Q]According to the reflection coefficient matrix C in (5.3) and the noise matrix after matched filteringObtaining a new echo signal matrix Y:

step 6, determining a signal subspace E according to the new echo signal matrix Y obtained in the step 5_s。

(6.1) calculating an autocorrelation matrix R of the new echo signal matrix Y:

wherein ,[·]^HRepresenting the conjugate transpose of the matrix, y_qTo match the signal column vector of the q pulse after filtering.

(6.2) carrying out eigenvalue decomposition on the autocorrelation matrix R to obtain:

wherein ,u_kK-th feature representing autocorrelation matrix RValue v_kK-th eigenvalue u representing the autocorrelation matrix R_kCorresponding feature vector, σ²Representing the noise power, I_LNRepresenting an LN order unit matrix;

(6.3) determining the Signal subspace

The 1 st eigenvalue u of the autocorrelation matrix R in (6.2)₁Corresponding feature vector v₁To the G-th eigenvalue u of the autocorrelation matrix R_GCorresponding feature vector v_GForming an MN G dimensional matrix by columns, and recording the matrix as a signal subspace E_s。

Step 7, according to the signal subspace E_sAnd calculating to obtain the estimated value of the target wave departure angleSum angle of arrival estimate

(7.1) defining the transmit angle matrix Ψ_tAnd the reception angle matrix Ψ_r

When the transmitting and receiving array is a half-wavelength uniform linear array ULA with equal interval, the departure angle and arrival angle of the kth target are respectively theta_kAnddenotes that k 1, 2.., G, defines the transmit angle matrix Ψ_tAnd the reception angle matrix Ψ_rHas the following structure:

Ψ_t＝T^-1Φ_tT

Ψ_r＝T^-1Φ_rT

wherein ,Φ_tIs Ψ_tThe matrix of eigenvalues of (a),

Φ_ris Ψ_rThe matrix of eigenvalues of (a),

t is a specific non-singular matrix of GXG;

(7.2) according to the properties of the signal subspace and the radar array structure, obtaining the following two equations:

wherein, the symbolRepresents the Kronecker product, E_sRepresenting a signal subspace, J_t,1＝[I_L-1,0],J_t,2＝[0,I_L-1],J_r,1＝[I_N-1,0]，J_r,2＝[0,I_N-1]Represents a selection matrix, I_L-1An identity matrix representing (L-1) × (L-1), I_N-1An identity matrix representing (N-1) × (N-1), I_NRepresenting an NxN identity matrix, I_LAn identity matrix representing L;

(7.3) substituting (7.1) into the equation in (7.2), solving the transmit angle matrix Ψ_tAnd the reception angle matrix Ψ_r：

wherein ,representing a pseudo-inverse of the matrix;

(7.4) the determined transmission angle matrix Ψ_tAnd the reception angle matrix Ψ_rPerforming characteristic decomposition:

wherein ,γ_kRepresenting the transmit angle matrix Ψ_tOf the kth characteristic value, q_kRepresenting the transmit angle matrix Ψ_tK characteristic value gamma of_kCorresponding feature vector, mu_kRepresenting the reception angle matrix Ψ_rThe k-th characteristic value of (f)_kRepresenting the reception angle matrix Ψ_rIs the k characteristic value mu_kA corresponding feature vector;

(7.5) the γ according to (7.4)_k and μ_kIn this example, γ is considered_k and μ_kThe specific angle matching method does not belong to the innovation content of the invention, and the following formula is used for obtaining the wave departure angle estimated value of the kth targetAnd angle of arrival estimate for kth target

Wherein, angle () represents the phase taking operation;

step 8, establishing a noise-free echo signal matrix model:

where A is the transmit steering matrix, B is the receive steering matrix, and C is the reflection coefficient matrix [. C]^HRepresenting the conjugate transpose of the matrix and ⊙ representing the Khatri-Rao product.

Step 9, establishing a mapping relation according to the noiseless echo signal matrix model in the step 8, and calculating a departure angle corresponding to the signal model

(9.1) according to the noiseless echo matrix model in the step 8, when the array structure of the transmitting antenna and the receiving antenna is a half-wavelength equal-interval uniform linear array ULA, obtaining the following mapping relation:

wherein ,J_t,1＝[I_L-1,0],J_t,2＝[0,I_L-1]，I_L-1Is a unit matrix of L-1 order, theta_iE Θ, I ═ 1,2, I denotes the sampling of ΘTotal number of dots, a (θ)_i) Is the transmitted steering vector of the target airspace,denotes theta_iThe value of the mapping angle of (a),and theta_iOne-to-one correspondence is realized;

(9.2) calculating I wave separation angles corresponding to the signal model in the step 8 according to the mapping relation obtained in the step (9.1)

And step 10, obtaining the optimal estimation value of each target wave departure angle through searching.

(10.1) the departure angle calculated in (9.2)I1.. I, finding the estimated value of the departure angle of each target in step 7Closest departure angle

(10.2) finding out the departure angle found in (10.1) according to the mapping relation in (9.1)Corresponding sampling angle theta_iAnd sampling the angle theta_iAs the optimal estimation value of the corresponding target departure angle.

The effects of the present invention will be further described by the following simulation experiments.

1. Simulation experiment conditions are as follows:

the number M of transmitting antennas of the bistatic MIMO radar is 8, the number N of receiving antennas is 4, the transmitting array and the receiving array are both half-wavelength uniformly-spaced linear arrays, the total transmitting energy E is 8, and an angle region theta of a target relative to the transmitting array is [ -15 degrees and 15 degrees °]Assume that there are two incoherent objects in Θ, which are located separatelyAndthe number of monte carlo experiments is P ═ 500.

2. Emulated content

Simulation 1, under the above conditions, assuming that the transmit beam field dimension L in the present invention is 6, the maximum acceptable W in Θ^Ha(θ_i) and the error α between the two signals is 0.04, and the energy distribution of the bistatic MIMO radar based on the transmitted energy concentration and the energy distribution of the conventional bistatic MIMO radar in the present invention are simulated respectively, and the result is shown in fig. 2.

As can be seen from fig. 2, the transmission energy of the conventional bistatic MIMO radar is uniform, whereas the transmission energy of the bistatic MIMO radar of the present invention is concentrated in the angular region of the target relative to the transmission array, the loss of the transmission energy is less, and the signal-to-noise ratio of the target echo signal is higher.

Simulation 2, under the above simulation conditions, the total number Q of echo pulses in a coherent processing interval CPI of the radar is set to 50, and in the present invention, the transmit beam domain dimension L is set to 6, which is set to the maximum acceptable W in Θ^Ha(θ_i) and the error between α and 0.04, respectively simulating the present invention and three traditional angle measuring methods, namely, traditional ESPRIT method and traditional P methodThe root mean square error RMSE of the M method and the conventional U-ESPRIT method varies with the signal-to-noise ratio, and the results are shown in fig. 3.

As can be seen from fig. 3, the root mean square error RMSE of the bistatic MIMO radar angle measurement of the present invention is smaller than that of other angle measurement methods, and the angle measurement accuracy is higher.

Simulation 3, under the above simulation conditions, the SNR of the radar is 0db, and in the present invention, the dimension L of the transmitting beam field is 6, and the maximum acceptable W in Θ is^Ha(θ_i) and the error between α and 0.04, the root mean square error RMSE of the simulation of the present invention and three traditional angle measurement methods, the traditional ESPRIT method, the traditional PM method and the traditional U-ESPRIT method, respectively, varies with the total number of echo pulses, and the result is shown in fig. 4.

As can be seen from fig. 4, the root mean square error RMSE of the bistatic MIMO radar angle measurement of the present invention is smaller than that of other angle measurement methods, and the angle measurement accuracy is higher.

The root mean square error is defined as:

wherein ,andrepresents the optimal estimated values of the departure and arrival angles, θ, for the kth target, the p-th Monte Carlo test_kAndshowing the departure angle and arrival of the kth targetThe true value of the angle.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and the present invention shall be covered thereby. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims

1. A bistatic MIMO radar angle estimation method based on emission energy concentration (bistatic MIMO radar angle measurement optimization method based on emission energy concentration) is characterized by comprising the following steps:

(2) according to the purpose of the eyeDesigning a transmitting beam domain matrix W by utilizing a convex optimization method in an angle region of the target relative to the transmitting array, and scaling W to meet tr (W)^*W^T) L, a scaled transmit beam domain matrix W' is obtained, where [ ·]^*Conjugate of representation matrix [ ·]^TRepresents the transpose of the matrix, tr (-) represents the trace of the matrix;

(3) according to transmit waveforms based on transmit beam domainCalculating to obtain an echo signal matrix X of the q-th received pulse_qThen to X_qTaking Q values from 1 to Q in sequence to obtain an echo signal matrix X ═ X₁,X₂,...,X_q,...,X_Q],

wherein ,[·]^*The conjugate of the matrix is represented as,represents L mutually orthogonal waveforms transmitted by a bistatic MIMO radar transmission array, and SS^H＝I_L，I_LAn identity matrix denoted L × L, T1, 2.. T, T denotes the number of samples per pulse period,the waveform of the m-th array element in the transmission waveform S is shown, and Q is 1.

(7) establishing a noise-free echo signal matrix model:

wherein J_t,1＝[I_L-1,0],J_t,2＝[0,I_L-1]，I_L-1Is a unit matrix of L-1 order, theta_iAn angle value, a (theta), representing the ith sample point within the angular region of the target relative to the transmit array_i) Is the transmitted steering vector of the target airspace,a mapped angle value representing the ith sample point within the angular region of the target relative to the transmit array,and theta_iThe method comprises the following steps of one-to-one correspondence, wherein I is 1, I is the number of sampling points of a target relative to an angle area of an emission array;

(9) calculating the signal mode in (7) according to the mapping relation obtained in (8)Form corresponding to the departure angle

2. The method of claim 1, wherein the transmit beam domain matrix W in (2) is designed by using a convex optimization method according to the position of the spatial sector where the target is located, and the method is implemented as follows:

(2a) when the array structure of the transmitting antenna and the receiving antenna is a half-wavelength uniform linear array ULA with equal intervals, an Lx 1 virtual transmitting guide vector can be guidedExpressed as: wherein ,[·]^TRepresenting the transposition of the vector, theta representing the departure angle of the target;

(2b) and (3) obtaining a transmitting beam domain matrix W by solving the following convex optimization problem according to the parameters designed in the step (2 a):

wherein ,[·]^HRepresents the conjugate transpose of the matrix, | | · | | | represents the 2-norm of the matrix, θ_iE Θ, I ═ 1,2, I, Θ denotes the angular region of the target relative to the transmit array, I denotes the total number of sample points of Θ, representing the complement angular region of Θ, J representsThe total number of sampling points of (a), [·]^Trepresenting the transpose of the matrix, α represents the maximum acceptable W in Θ^Ha(θ_i) and the error between.

3. The method of claim 1, wherein the echo signal matrix X ═ X is obtained in (3)₁,X₂,...,X_q,...,X_Q]It is implemented as follows:

(3a) when the transmitting and receiving array is a half-wavelength uniform linear array ULA with equal interval, the departure angle and arrival angle of the kth target are respectively theta_kAndindicating that k is 1,2, …, G, the transmit steering matrix a and the receive steering matrix B can be represented as:

A＝[a(θ₁),a(θ₂),...a(θ_k),...,a(θ_G)]

wherein ,a transmit steering vector representing the kth target,a received steering vector representing a kth target;

(3b) reflection coefficient diagonal matrix Lambda of G targets at q-th echo pulse_qCan be expressed as:

Λ_q＝diag(c_q)

wherein diag (. circle.) represents the diagonalization operation, c_q＝[α_1,q,α_2,q,...α_k,q,...,α_G,q]^TVector of reflection coefficients representing the q-th echo pulse of G targets, α_k,qRepresenting the reflection coefficient of the kth target in the qth echo pulse;

(3c) calculating an echo signal matrix X of the q-th received pulse according to the transmitting waveform and the parameters in (3a) and (3b)_q：

(3d) to X_qTaking Q values from 1 to Q in sequence to obtain an echo signal matrix X ═ X₁,X₂,...,X_q,...,X_Q]。

4. The method of claim 1, wherein the new echo signal matrix Y constructed in (4) is implemented as follows:

(4a) signal matrix X for the q-th echo pulse_qRight riding S^HPerforming matched filtering to obtain a signal matrix Y of the q pulse after matched filtering_q：

wherein ,[·]^TRepresenting a matrix transposition [ ·]^HRepresenting a matrix conjugate transpose; s is L mutually orthogonal waveforms transmitted by a bistatic MIMO radar transmitting array;representing a noise matrix matching the filtered q-th pulse,Λ_qa reflection coefficient diagonal matrix representing the q-th echo pulse of the G targets; a is a transmitting guide matrix; b is a receiving steering matrix;

(4b) according to the formula in (4a), Y is_qObtaining a signal column vector y of the q pulse after matched filtering according to column arrangement_q：

(4c) taking Q values from 1 to Q, according to the formula in (4b), the following matrixes are obtained respectively:

matching the filtered signal column vector y of the 1 st pulse₁Signal column vector y to the Q-th pulse after matched filtering_QNote as new echo signal matrix: y ═ Y₁,y₂,...,y_q,...,y_Q]；

Reflection coefficient vector c of G targets at 1 st pulse₁Vector c of reflection coefficients of the Q-th pulse of the G targets_QAnd is recorded as a reflection coefficient matrix: c ═ C₁,c₂,...,c_q,...,c_Q]；

Noise matrix matching the filtered 1 st pulseNoise matrix to the Q-th pulse after matched filteringAnd (3) recording as a noise matrix after matched filtering:

(4d) substituting the formula in (4b) into Y ═ Y₁,y₂,...,y_q,...,y_Q]And according to the parameters in the step (4c), obtaining a new echo signal matrix Y as follows:

5. the method of claim 1, wherein the autocorrelation matrix R in (5) is calculated as follows:

6. The method of claim 1, wherein the signal subspace E in (5) is_sIt is determined as follows:

(5a) and (3) carrying out eigenvalue decomposition on the autocorrelation matrix R to obtain:

wherein ,u_kK-th eigenvalue, v, representing the autocorrelation matrix R_kK-th eigenvalue u representing the autocorrelation matrix R_kCorresponding feature vector, σ²Representing the noise power, I_LNRepresenting an LN order unit matrix;

(5b) the 1 st eigenvalue u of the autocorrelation matrix R in (5a)₁Corresponding feature vector v₁To the G-th eigenvalue u of the covariance matrix R_GCorresponding feature vector v_GForming an MN G dimensional matrix by columns, and recording the matrix as a signal subspace E_s。

7. The method of claim 1, wherein the target departure angle estimate is calculated in (6)Sum angle of arrival estimateThe method is realized as follows:

(6a) when the transmitting and receiving array is a half-wavelength uniform linear array ULA with equal interval, the departure angle and arrival angle of the kth target are respectively theta_kAndmeaning that k is 1,2, …, G, the transmit angle matrixΨ_tAnd the reception angle matrix Ψ_rCan be respectively expressed as:

Ψ_t＝T^-1Φ_tT

Ψ_r＝T^-1Φ_rT

wherein ,Φ_tIs Ψ_tThe matrix of eigenvalues of (a),

Φ_ris Ψ_rThe matrix of eigenvalues of (a),

t is a specific non-singular matrix of GXG;

(6b) according to the properties of the signal subspace and the radar array structure, the following two equations are obtained:

(6c) substituting (6a) into the equation in (6b) to solve the transmit angle matrix Ψ_tAnd angle of receptionMatrix Ψ_r：

wherein ,representing a pseudo-inverse of the matrix;

(6d) to the transmit angle matrix Ψ_tAnd the reception angle matrix Ψ_rPerforming feature decomposition

(6e) obtaining an estimated value of the divergence angle of the kth target according to the parameters in (6d) by using the following formulaAnd angle of arrival estimate for kth target

Wherein, angle () represents the phase taking operation.