CN112649799A - MIMO radar amplitude-phase error correction method - Google Patents

Abstract

The invention discloses a method for correcting amplitude and phase errors of an MIMO radar, which applies a particle swarm optimization algorithm to the angular positioning and amplitude-phase error correction of the MIMO radar, and improves the particle swarm optimization algorithm by introducing a pollination algorithm and a Gaussian variation algorithm to easily fall into the defects of local optimization and insufficient searching capability, so that the improved method can more quickly converge to an optimal result, obtain an amplitude and phase error calibration matrix and finally realize accurate angular positioning.

Description

MIMO radar amplitude-phase error correction method

Technical Field

The invention relates to the field of MIMO radar signal processing, in particular to a method for correcting amplitude and phase errors of an MIMO radar.

Background

The MIMO radar technology proposed in recent years can effectively improve the aperture and the signal processing freedom of the radar, thereby improving the resolution and the parameter estimation performance of spatial spectrum estimation. Therefore, the MIMO radar imaging is applied to various working occasions such as unmanned technology, satellite positioning, accurate target striking in military and the like, and has good development prospect.

Although the array spatial spectrum estimation algorithm has been verified in practical application in many occasions, good effect is obtained. However, many non-ideal factors often exist in a multi-channel radar array system, array errors of transmitting and receiving channels change array manifold, and when the array manifold is not accurately known, accurate positioning cannot be achieved by the direction-finding algorithms. Therefore, array error estimation and correction are an important ring in array signal processing, and any high-resolution spatial spectrum estimation method cannot be practically used without array error correction. In order to improve the imaging precision of the MIMO radar and enable the MIMO radar to be effectively applied to actual life, the research on a joint algorithm of a direction finding algorithm and an amplitude-phase error correction algorithm is the current hot problem. And is closely related to the development and stability of society.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a method for correcting the amplitude-phase error of an MIMO radar, which has the following specific technical scheme:

a MIMO radar amplitude-phase error correction method is provided, wherein the MIMO radar is a single-base MIMO radar, a uniform linear array of the MIMO radar is provided with M transmitting arrays and N receiving arrays, and the transmitting arrays and the receiving arrays are arranged along a y axis; k different targets are arranged in the space, and the reflected signals of the different targets are mutually independent; the receiving end obtains MN virtual arrays; the t pulse received by the receiving array is X (t), and certain amplitude and phase errors exist between the transmitting array and the receiving array of the MIMO radar, W_TAnd W_RAmplitude-phase error matrices for the virtual array, the transmit array, and the receive array, respectively;

the method specifically comprises the following steps:

s1: the method for processing the MIMO radar multichannel receiving information to obtain the optimization function specifically comprises the following substeps:

s1.1: for each target, obtaining an orientation vector of the virtual array by a Kronecker product of the transmit array and receive array orientation vectors;

wherein, a_TAnd a_RRespectively representing the direction vectors of the transmitting array and the receiving array;

is a Kronecker product; theta_kRepresenting the angle of arrival of the kth target;

s1.2: the t-th pulse x (t) received by the receiving array is represented as:

X(t)＝WAS+n (2)

wherein diag (·) represents a diagonal matrix; a represents a target orientation vector matrix, and A ═ a (theta)₁)，a(θ₂)，...，a(θ_k)]^HH denotes the transpose of the conjugate matrix; s denotes a matrix of the magnitude of the received signal energy, S ═ S₁，s₂，...，s_k]，s_kIs the signal from the kth target; n represents a noise matrix;

s1.3: the covariance matrix R of the t-th pulse X (t) received by the receiving array is expressed as

Wherein, Λ_sRepresents a K x K diagonal matrix consisting of K maximum eigenvalues, and D_nRepresenting a diagonal matrix consisting of the other MN-K small eigenvalues; e_sRepresenting a signal subspace, E_nRepresenting a noise subspace;

s1.4: obtaining a noise subspace E according to the formulas (2) to (4)_n；

S1.5：Constructing a spectral peak search function based on MUSIC algorithm, and solving f_musicMaximum value of (theta)

S1.6: to solve f_music(theta) maximum value, constructing a joint estimation cost function F (theta, W) based on the target angle of MUSIC and self calibration of array amplitude-phase errors_T，W_R) Expressed as formula (6) and the objective function expressed as formula (7)

S2: pairing cost functions F (theta, W) using random weight particle swarm optimization_T，W_R) Local optimization to obtain the optimal position x of new particle_i(t +1), and recording the optimum x_iThe position of (t +1) is gbest;

s3: jumping out of the currently trapped local optimum according to a flower pollination algorithm to carry out deep optimization to obtain the optimum position x of a new particle_new，iAnd recording the optimum x_new，iThe position of (1) is gbest;

s4: carrying out mutation on the gbest through a mutation algorithm; when the result after mutation is better than the current gbest, updating the optimal result; when the result after mutation is not better than the gbest, the method is discarded.

Further, the S2 specifically includes:

let a particle in the particle swarm algorithm be x_iAnd is and

using a group of particles as a potential solution of a d-dimensional search space; setting initial parameters of the particle swarm algorithm, namely setting the number of the particles to be N1, setting the iteration number to be T, and setting the ith particle to be x_i＝[θ₁，...，θ_k，W_T，W_R]The velocity of the ith particle is v_iOf 1 atThe t-th iteration formula for the i particles is as follows:

v_i(t+1)＝ω*v_i(t)+c₁*r₁*(pbest_i(t)-x_i(t))+c₂*r₂*(gbest(t)-x_i(t)) (8)

x_i(t+1)＝x_i(t)+v_i(t+1) (9)

ω＝σ*r₃+μ (10)

μ＝ω_min+(ω_max-ω_min)*r₄ (11)

wherein, c₁And c₂Acceleration coefficients in a particle swarm algorithm are all adopted; r is₁And r₂Is [0,1 ]]Uniformly distributed random vectors therein; pbest_iIs the optimal solution in the iteration history of the ith particle; gbest is the optimal solution for all particles in the current iteration; ω is not a random inertial weight, σ is the standard deviation, r₃And r₄Is [0,1 ]]Random number between, ω_minAnd ω_maxRespectively represent the minimum value and the maximum value of omega;

in the optimizing process, the t +1 th particle velocity v is updated_i(t +1), and then v_i(t +1) updating the particle position x for t +1 iterations_i(t +1), and recording the optimum x_iThe position of (t +1) is gbest.

Further, the flower pollination algorithm in S3 is an integrated flower pollination algorithm, which is expressed as:

x_new，i＝(px_i+r₃(x_j(t)-x_k(t)))+((1-p)(x_i+L(gbest(t)-x_i(t)) (12)

wherein x is_new，iIndicating the position of the new particle, x_iRepresenting the position of the particle before update, p representing the transition probability parameter, r₃Is [0,1 ]]L represents the extent of pollination, and gbest (t) is the optimal position of the particle in the t-th iteration.

Further, the mutation algorithm in S4 is a gaussian mutation algorithm, and specifically includes:

b_new(t)＝N_gv_max (13)

gbest_new(t)＝gbest(t)+v_new(t) (14)

wherein N is_gIs a standard normal distribution with a mean value of 0, a variance value of 1, v_maxRepresenting the maximum velocity vector.

The invention has the following beneficial effects:

the method can effectively optimize the cost function of the MUSIC algorithm, obtain the amplitude-phase error correction matrix and the target arrival angle, and is favorable for radar target detection. The random inertia weight is used for improving the inertia weight in the particle swarm algorithm, so that the global searching capability of the particle swarm algorithm is improved; and further, the particle updating algorithm has more possibility by using the integrated flower pollination algorithm, and the accuracy of the result is improved. And finally, the Gaussian variation operation can enable the optimal result to jump out of the local optimal, so that the minimum value of the optimizing function is further searched deeply, and the precision of the final result is improved.

Drawings

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

FIG. 2 is a graph comparing the cost function optimization results estimated by the method of the present invention (deployed), random inertial particle swarm (RNW-PSO) and the flower pollination method (FPA), respectively.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments, and the objects and effects of the present invention will become more apparent, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

As shown in fig. 1, in the MIMO radar amplitude-phase error correction method of the present invention, the MIMO radar is a single-ground MIMO radar, the uniform linear array of the MIMO radar has M transmit arrays and N receive arrays, and both the transmit arrays and the receive arrays are disposed along the y-axis; k different targets are arranged in the space, and the reflected signals of the different targets are mutually independent; the receiving end obtains MN virtual arrays; the t pulse received by the receiving array is X (t), and the transmitting array and the receiving array of the MIMO radar have certain amplitude and phaseError, W_TAnd W_RAmplitude-phase error matrices for the virtual array, the transmit array, and the receive array, respectively;

the method specifically comprises the following steps:

s1: the method for processing the MIMO radar multichannel receiving information to obtain the optimization function specifically comprises the following substeps:

s1.1: for each target, obtaining an orientation vector of the virtual array by a Kronecker product of the transmit array and receive array orientation vectors;

wherein, a_TAnd a_RRespectively representing the direction vectors of the transmitting array and the receiving array;

is a Kronecker product; theta_kRepresenting the angle of arrival of the kth target;

s1.2: the t-th pulse x (t) received by the receiving array is represented as:

X(t)＝WAS+n (2)

wherein diag (·) represents a diagonal matrix; a represents a target orientation vector matrix, and A ═ a (theta)₁)，a(θ₂)，...，a(θ_k)]^HH denotes the transpose of the conjugate matrix; s denotes a matrix of the magnitude of the received signal energy, S ═ S₁，s₂，...，s_k]，s_kIs the signal from the kth target; n represents a noise matrix;

s1.3: the covariance matrix R of the t-th pulse X (t) received by the receiving array is expressed as

Wherein, Λ_sRepresents a K x K diagonal matrix consisting of K maximum eigenvalues, and D_nRepresenting a diagonal matrix consisting of the other MN-K small eigenvalues; e_sRepresenting a signal subspace, E_nRepresenting a noise subspace;

s1.4: obtaining a noise subspace E according to the formulas (2) to (4)_n；

S1.5: constructing a spectral peak search function based on MUSIC algorithm, and solving f_musicMaximum value of (theta)

S1.6: to solve f_music(theta) maximum value, constructing a joint estimation cost function F (theta, W) based on the target angle of MUSIC and self calibration of array amplitude-phase errors_T，W_R) Expressed as formula (6) and the objective function expressed as formula (7)

S2: pairing cost functions F (theta, W) using random weight particle swarm optimization_T，W_R) Local optimization to obtain the optimal position x of new particle_i(t +1), and recording the optimum x_iThe position of (t +1) is gbest.

The use of random inertia factors effectively improves the global search capability because the inertia weight factors can determine the convergence speed of the particles and how they deviate from their original course.

The S2 specifically includes:

let a particle in the particle swarm algorithm be x_iAnd is and

using a group of particles as a potential solution of a d-dimensional search space; setting initial parameters of the particle swarm algorithm, namely setting the number of the particles to be N1, setting the iteration number to be T, and setting the ith particle to be x_i＝[θ₁，...，θ_k，W_T，W_R]The velocity of the ith particle is v_iThe formula for the t iteration of the ith particle is as follows:

v_i(t+1)＝ω*v_i(t)+c₁*r₁*(pbest_i(t)-x_i(t))+c₂*r₂*(gbest(t)-x_i(t)) (8)

x_i(t+1)＝x_i(t)+v_i(t+1) (9)

ω＝σ*r₃+μ (10)

μ＝ω_min+(ω_max-ω_min)*r₄ (11)

wherein, c₁And c₂Acceleration coefficients in a particle swarm algorithm are all adopted; r is₁And r₂Is [0,1 ]]Uniformly distributed random vectors therein; pbest_iIs the optimal solution in the iteration history of the ith particle; gbest is the optimal solution for all particles in the current iteration; ω is not a random inertial weight, σ is the standard deviation, r and r₄Is [0,1 ]]Random number between, ω_minAnd ω_maxRespectively represent the minimum value and the maximum value of omega;

in the optimizing process, the t +1 th particle velocity v is updated_i(t +1), and then v_i(t +1) updating the particle position x for t +1 iterations_i(t +1), and recording the optimum x_iThe position of (t +1) is gbest.

S3: jumping out of the currently trapped local optimum according to a flower pollination algorithm to carry out deep optimization to obtain the optimum position x of a new particle_new，iAnd recording the optimum x_new，iThe position of (1) is gbest.

The flower pollination algorithm is preferably an integrated flower pollination algorithm, and the global search capability of the RNW-PSO is improved by adopting FPA. The method of cross pollination is adopted to improve the searching speed and obtain better solution in the searching space as soon as possible. The specific iterative formula is as follows:

x_new，i＝(px_i+r₃(x_j(t)-x_k(t)))+((1-p)(x_i+L(gbest(t)-x_i(t)) (12)

wherein x is_new，iIndicating the position of the new particle, x_iRepresenting the position of the particle before update, p representing the transition probability parameter, r₃Is [0,1 ]]L represents the extent of pollination, and gbest (t) is the optimal position of the particle in the t-th iteration.

S4: carrying out mutation on the gbest through a mutation algorithm; when the result after mutation is better than the current gbest, updating the optimal result; when the result after mutation is not better than the gbest, the method is discarded.

The variation algorithm is preferably a gaussian variation algorithm, and specifically comprises the following steps:

v_new(t)＝N_gv_max (13)

gbest_new(t)＝gbest(t)+v_new(t) (14)

wherein N is_gIs a standard normal distribution with a mean value of 0, a variance value of 1, v_maxRepresenting the maximum velocity vector. When the iterative process falls into a locally optimal solution, the gaussian variation operation can make the result jump out of the locally optimal solution.

To validate the method of the present invention, SNR is set to 10db, transmit array M to 6, and receive array N to 8. Assume three target sources are located at (θ)₁，θ₂，θ₃) The number of snapshots is 128 (-5 °, 10 °, 30 °), and the transmit array amplitude-phase error matrix and the receive array error matrix are:

W_T＝[1，0.8e^j0.85，0.92e^j0.78，0.8e^j0.85，1.1e^j1.09，0.88e^j2.0] (15)

W_R＝[1，1.12e^j1.85，1.08e^j0.8，1.25e^j0.9，0.78e^j1.6，0.95e^j1.0，0.87e^j1.7，1.15e^j1.14] (16)

for comparison, the cost functions estimated by the method (deployed), the random inertial particle swarm optimization (RNW-PSO) and the pollination method (FPA) are adopted for optimization, and the optimization result is shown in FIG. 2.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and although the invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that various changes in the form and details of the embodiments may be made and equivalents may be substituted for elements thereof. All modifications, equivalents and the like which come within the spirit and principle of the invention are intended to be included within the scope of the invention.

Claims (4)

1. The MIMO radar amplitude-phase error correction method is characterized in that the MIMO radar is a single-base MIMO radar, a uniform linear array of the MIMO radar is provided with M transmitting arrays and N receiving arrays, and the transmitting arrays and the receiving arrays are arranged along the y axis; k different targets are arranged in the space, and the reflected signals of the different targets are mutually independent; the receiving end obtains MN virtual arrays; the t pulse received by the receiving array is X (t), and certain amplitude and phase errors exist between the transmitting array and the receiving array of the MIMO radar, W_TAnd W_RThe amplitude-phase error matrices for the virtual array, the transmit array, and the receive array, respectively.

The method specifically comprises the following steps:

s1: the method for processing the MIMO radar multichannel receiving information to obtain the optimization function specifically comprises the following substeps:

s1.1: for each target, obtaining an orientation vector of the virtual array by a Kronecker product of the transmit array and receive array orientation vectors;

wherein, a_TAnd a_RRespectively representing the direction vectors of the transmitting array and the receiving array;

is a Kronecker product; theta_kRepresenting the angle of arrival of the kth target;

s1.2: the t-th pulse x (t) received by the receiving array is represented as:

X(t)＝WAS+n (2)

wherein diag (·) represents a diagonal matrix; a represents a target orientation vector matrix, and A ═ a (theta)₁)，a(θ₂)，...，a(θ_k)]^HH denotes the transpose of the conjugate matrix; s denotes a matrix of the magnitude of the received signal energy, S ═ S₁，s₂，...，s_k]，s_kIs the signal from the kth target; n represents a noise matrix;

s1.3: the covariance matrix R of the t-th pulse X (t) received by the receiving array is expressed as

Wherein, Λ_sRepresents a K x K diagonal matrix consisting of K maximum eigenvalues, and D_nRepresenting a diagonal matrix consisting of the other MN-K small eigenvalues; e_sRepresenting a signal subspace, E_nRepresenting a noise subspace;

s1.4: obtaining a noise subspace E according to the formulas (2) to (4)_n；

S1.5: constructing a spectral peak search function based on MUSIC algorithm, and solving f_musicMaximum value of (theta)

S1.6: to solve f_music(theta) maximum value, constructing a joint estimation cost function F (theta, W) based on the target angle of MUSIC and self calibration of array amplitude-phase errors_T，W_R) Expressed as formula (6) and the objective function expressed as formula (7)

S2: pairing cost functions F (theta, W) using random weight particle swarm optimization_T，W_R) Local optimization to obtain the optimal position x of new particle_i(t +1), and recording the optimum x_iThe position of (t +1) is gbest;

s3: jumping out of the currently trapped local optimum according to a flower pollination algorithm to carry out deep optimization to obtain the optimum position x of a new particle_new，iAnd recording the optimum x_new，iThe position of (1) is gbest;

s4: carrying out mutation on the gbest through a mutation algorithm; when the result after mutation is better than the current gbest, updating the optimal result; when the result after mutation is not better than the gbest, the method is discarded.

2. The MIMO radar amplitude-phase error correction method according to claim 1, wherein S2 specifically is:

let a particle in the particle swarm algorithm be x_iAnd is and

using a group of particles as a d-dimension search spacePotential solutions in between; setting initial parameters of the particle swarm algorithm, namely setting the number of the particles to be N1, setting the iteration number to be T, and setting the ith particle to be x_i＝[θ₁，...，θ_k，W_T，W_R]The velocity of the ith particle is v_iThe formula for the t iteration of the ith particle is as follows:

v_i(t+1)＝ω*v_i(t)+c₁*r₁*(pbest_i(t)-x_i(t))+c₂*r₂*(gbest(t)-x_i(t)) (8)

x_i(t+1)＝x_i(t)+v_i(t+1) (9)

ω＝σ*r₃+μ (10)

μ＝ω_min+(ω_max-ω_min)*r₄ (11)

wherein, c₁And c₂Acceleration coefficients in a particle swarm algorithm are all adopted; r is₁And r₂Is [0,1 ]]Uniformly distributed random vectors therein; pbest_iIs the optimal solution in the iteration history of the ith particle; gbest is the optimal solution for all particles in the current iteration; ω is not a random inertial weight, σ is the standard deviation, r₃And r₄Is [0,1 ]]Random number between, ω_minAnd ω_maxRespectively represent the minimum value and the maximum value of omega;

in the optimizing process, the t +1 th particle velocity v is updated_i(t +1), and then v_i(t +1) updating the particle position x for t +1 iterations_i(t +1), and recording the optimum x_iThe position of (t +1) is gbest.

3. The MIMO radar amplitude-phase error correction method of claim 1, wherein the flower pollination algorithm in S3 is an integrated flower pollination algorithm expressed as:

x_new，i＝(px_i+r₃(x_j(t)-x_k(t)))+((1-p)(x_i+L(gbest(t)-x_i(t)) (12)

wherein x is_new，iTo indicate new grainsPosition of son, x_iRepresenting the position of the particle before update, p representing the transition probability parameter, r₃Is [0,1 ]]L represents the extent of pollination, and gbest (t) is the optimal position of the particle in the t-th iteration.

4. The MIMO radar amplitude-phase error correction method according to claim 1, wherein the variation algorithm in S4 is a gaussian variation algorithm, and specifically includes:

v_new(t)＝N_gv_max (13)

gbest_new(t)＝gbest(t)+v_new(t) (14)

wherein N is_gIs a standard normal distribution with a mean value of 0, a variance value of 1, v_maxRepresenting the maximum velocity vector.

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