CN107290732B - Single-base MIMO radar direction finding method for large-quantum explosion - Google Patents

Single-base MIMO radar direction finding method for large-quantum explosion Download PDF

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CN107290732B
CN107290732B CN201710562238.7A CN201710562238A CN107290732B CN 107290732 B CN107290732 B CN 107290732B CN 201710562238 A CN201710562238 A CN 201710562238A CN 107290732 B CN107290732 B CN 107290732B
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CN107290732A (en
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高洪元
杜亚男
刘丹丹
刁鸣
梁炎松
苏雨萌
池鹏飞
刘子奇
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Harbin Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention provides a single-base MIMO radar direction finding method for large-quantum explosion. (1) Establishing a transmitting and receiving co-located narrow-band single-ground MIMO radar system direction-finding model; (2) determining all quantum fragments in a quantum explosion algorithm, and uniformly distributing the quantum fragments to two subsets; (3) calculating the fitness of each quantum fragment, and determining the initial optimal quantum position of the 1 st quantum fragment set, the initial optimal solution quantum centroid and the uniform solution quantum centroid of the 2 nd quantum fragment set; (4) updating the quantum position of each quantum fragment; (5) mapping the quantum position of each quantum fragment to the position of a defined interval, and calculating a fitness value; (6) updating the global optimal quantum position; (7) and outputting the global optimal quantum position, and mapping the global optimal quantum position into a position, wherein the position corresponds to the direction of arrival to be estimated. The invention can realize rapid and high-precision direction finding under complex environments such as impact noise and the like, and has excellent direction finding performance.

Description

Single-base MIMO radar direction finding method for large-quantum explosion
Technical Field
The invention relates to a single-base MIMO radar direction finding method.
Background
The multiple-Input multiple-Output (MIMO) radar is a radar of a new system, and the MIMO radar can greatly improve the anti-interference capability of a radar system by emitting mutually orthogonal low-gain wide beams in space. Another important advantage of MIMO radar is that since its transmit beam is fixed and does not need to scan the space, the time during which the same target is illuminated within the beam is greatly increased, which provides sufficient time for long coherent accumulation. The MIMO radar has many advantages by using the MIMO technology in the communication system, and has become a research hotspot today. The monostatic MIMO radar can obtain a virtual aperture larger than that of the traditional phased array radar due to the virtual expansion capability, and has obvious performance advantage in the direction finding aspect.
Through the search of the prior art documents, it is found that "Direction of Arrival Estimation for single-dimensional MIMO radar Reduced-Dimension RISR Algorithm" published by Dang Xiao ang et al in 201611 th International Symposium on Antennas, Propagation and EM Theory (ISAPE) (2016, pp.607-611) provides a single-based MIMO radar Direction finding method based on Dimension-reducing RISR Algorithm, which can better estimate the Direction of Arrival, but has low Direction finding precision and high calculation complexity. "evaluation of dimension reduction DOA of cross-shaped array MIMO radar based on ESPRIT algorithm" published by shanghao et al in "report on electronics and informatics" (2016, vol.38, No.1, pp.80-89) provides a dimension reduction DOA estimation algorithm based on ESPRIT algorithm, which converts high-dimensional echo data into low-dimensional signal space through the design of dimension reduction matrix and the dimension reduction transformation of echo data, removes all redundant data to the maximum extent, has good direction-finding performance under gaussian noise background, but has serious direction-finding performance deterioration under complex background such as impact noise. The existing literature indicates that the existing research on the direction finding method of the monostatic MIMO radar has low direction finding precision and higher calculation complexity, and the existing direction finding method of the monostatic MIMO radar is mostly suitable for direction finding under the background of Gaussian noise, and the performance of the direction finding method is seriously deteriorated under the complex environments of impact noise and the like.
Disclosure of Invention
The invention aims to provide a single-ground MIMO radar direction finding method with small calculation amount, high direction finding precision and capability of ensuring large quantum explosion of direction finding performance under complex noise backgrounds such as impact noise.
The purpose of the invention is realized as follows:
the method comprises the following steps that firstly, a transmitting antenna of a transmitting-receiving co-located narrow-band single-ground MIMO radar system is a uniform linear array composed of M omnidirectional array elements, and a receiving antenna is a uniform linear array composed of N omnidirectional array elements; supposing that M orthogonal waveforms with the same carrier frequency and bandwidth are transmitted by a transmitting end at the same time, a radar echo is processed by a matched filter bank of each receiving channel to separate the M waveforms, P signal sources are arranged at the same distance, the distance of the signal sources is greater than the aperture of a transmitting antenna and a receiving antenna, and the signals pass through a matched filterAfter processing of the group, the output of the mth matched filter at the nth receiving array element is taken as ynm(l) N is 1,2, and N, M is 1,2, and M, the echoes received by the whole receiving antenna array are written as follows: y (l) ═ a (θ) s (l) + n (l), where y (l) ═ y1(l),y2(l),...,yNM(l)]T，A(θ)＝[a(θ1),a(θ2),...,a(θP)]Is a steering matrix of dimension MN multiplied by P,
Figure GDA0001390319880000021
for the p-th steering vector, the steering vector,
Figure GDA0001390319880000022
is the product of Kronecker, ar(θp) To receive steering vectors, at(θp) To transmit steering vectors, thetapDirection of arrival of the pth target, s (l) ═ s1(l),s2(l),...,sP(l)]TThe complex amplitude of the output of the received signal after matched filtering, n (l) is an impact noise vector of MN multiplied by 1 dimension; received data is normalized to using an infinite norm
Figure GDA0001390319880000023
max represents a function of maximum, and the covariance matrix of the multiple snapshot samples is
Figure GDA0001390319880000024
E represents a function for solving mathematical expectation, superscript H represents conjugate transposition, and feature decomposition is carried out on the covariance matrix to obtain a signal subspace and a noise subspace which are respectively UsAnd Un，ΛsAnd ΛnThe diagonal matrix composed of large eigenvalues and the diagonal matrix composed of small eigenvalues respectively, the weighted signal subspace fits the direction-finding equation into
Figure GDA0001390319880000025
Figure GDA0001390319880000026
Is when taking the maximum value of the functionThe value of the corresponding variable theta is selected,
Figure GDA0001390319880000027
for optimal estimation, PA(θ)＝A(θ)(AH(θ)A(θ))-1AH(θ) is a mapping matrix, θ ═ θ1,θ2,...,θP]Is a direction vector constituted by the direction of arrival, W represents a weighting matrix, trace [ ]]Trace-solving operation of the expression matrix;
step two, generating all initial quantum fragments in the quantum explosion method,
a quantum solution space composed of 2H quantum fragments, wherein the 2H quantum fragments are uniformly distributed to two subsets, each quantum fragment moves in a P-dimensional search space, the positions of the quantum fragments represent potential solutions of a single-base MIMO radar direction-finding problem, and the quantum positions of the ith quantum fragment in the kth quantum fragment set are defined as follows in the t-th iteration:
Figure GDA0001390319880000028
wherein i 1, 2., H; k is 1, 2;
Figure GDA0001390319880000029
a pth qubit, P ═ 1,2,.., P, representing the quantum position of the ith quantum fragment; mapping the quantum position of the ith quantum fragment to a defined interval, namely the position of the quantum fragment
Figure GDA00013903198800000210
The mapping relation is
Figure GDA00013903198800000211
p＝1,2,...,P，upAnd lpThe upper limit and the lower limit of the p-dimensional angle search interval are respectively, the rotation step corresponding to the ith quantum chip of the 1 st set is
Figure GDA00013903198800000212
Representing the p-dimension rotation step of the ith quantum fragment with quantum position in the defined quantum domain [0,1]Random initialization with rotation steps of-0.2, 0.2]Randomly initializing, wherein the initial time t is 0;
step three, calculating the fitness of each quantum fragment,
determining an initial optimal quantum position of a 1 st quantum chip set, an initial optimal solution quantum centroid and a uniform solution quantum centroid of a 2 nd quantum chip set, an ith quantum chip position
Figure GDA0001390319880000031
The fitness value of the infinite norm weighted signal subspace fitting direction-finding equation is
Figure GDA0001390319880000032
The optimal quantum position experienced by the 1 st set of the ith quantum fragments up to now is defined as the locally optimal quantum position of the quantum fragment and is denoted as
Figure GDA0001390319880000033
Figure GDA0001390319880000034
For the ith quantum fragment of the 1 st set, the P-dimension optimal quantum bit is experienced until the t iteration, P is 1,2
Figure GDA0001390319880000035
Figure GDA0001390319880000036
For the p-dimension optimal quantum bit experienced by all quantum fragments till the t-th iteration, selecting the optimal quantum bit in the 2 quantum fragment sets as the optimal solution quantum centroid
Figure GDA0001390319880000037
The uniform solution quantum centroid of the 2 nd quantum chip set is
Figure GDA0001390319880000038
Wherein
Figure GDA0001390319880000039
Step four, updating the quantum position of each quantum fragment, updating each quantum fragment set according to different rules,
for the 1 st quantum chip set, the p-dimensional rotation step of the i-th quantum chip is updated to
Figure GDA00013903198800000310
Weight wtGradually decreasing as the number of iterations increases, i 1, 2., H, P1, 2., P; r is1And r2Are all [0,1 ]]A uniform random number in between, c1And c2Is a weighting constant; for the
Figure GDA00013903198800000311
If the boundary value is exceeded, it is limited to the boundary, and the new quantum position of the ith quantum fragment is
Figure GDA00013903198800000312
1,2, H, wherein
Figure GDA00013903198800000313
P1, 2.. the P, abs () represents the function of taking the absolute value,
for the 2 nd quantum chip set, the p-dimension explosion step size of the ith quantum chip is as follows in the realization of large explosion
Figure GDA00013903198800000314
i 1,2, P is a contraction factor,
Figure GDA00013903198800000315
is [ -1,1 [ ]]Uniform random number in between, produces [0,1 ]]When gamma is less than or equal to 0.5, all quantum positions of the 2 nd quantum chip set are updated to be regular
Figure GDA0001390319880000041
Wherein
Figure GDA0001390319880000042
For the optimal solution of quantum centroid
Figure GDA0001390319880000043
P-dimension, P1, 2, P; otherwise, all quantum positions of the 2 nd quantum chip set are updated to rule
Figure GDA0001390319880000044
Wherein the content of the first and second substances,
Figure GDA0001390319880000045
to solve the quantum centroid uniformly
Figure GDA0001390319880000046
The p-th dimension of (a);
step five, quantum positions of the ith quantum chip of the kth quantum chip set
Figure GDA0001390319880000047
Mapping to a position of a defined interval
Figure GDA0001390319880000048
k is 1 and 2, and the fitness value of all quantum fragments is calculated, wherein the fitness function is
Figure GDA0001390319880000049
i＝1,2,...,H；
Step six, updating the global optimal quantum position, updating the local optimal quantum position of each quantum fragment in the 1 st quantum fragment set, updating the optimal solution quantum centroid and the uniform solution quantum centroid of the 2 nd quantum fragment set,
Figure GDA00013903198800000410
for the global optimal quantum positions experienced by all quantum fragments in the two quantum fragment sets so far, i is 1,2, for the ith quantum fragment of the 1 st quantum fragment set
Figure GDA00013903198800000411
Then order
Figure GDA00013903198800000412
Figure GDA00013903198800000413
Is a quantum position
Figure GDA00013903198800000414
The mapping position of (2); if not, then,
Figure GDA00013903198800000415
the 2 nd set of quantum chips is updated to
Figure GDA00013903198800000416
P1, 2, P, optimal solution quantum centroid for the 2 nd set of quantum chips
Figure GDA00013903198800000417
Replacing with the current global optimal quantum position;
step seven, judging whether the maximum iteration times is reached, if so, finishing the iteration, outputting a global optimal quantum position, and mapping the global optimal quantum position into a position, wherein the position corresponds to the direction of arrival to be estimated; otherwise, let t be t +1, return to step four.
In order to solve the problems, the invention firstly designs a quantum explosion method, and then designs a single-base MIMO radar direction finding method based on quantum explosion searching method and infinite norm weighted signal subspace fitting under the background of impact noise.
The invention provides a direction finding method for a single-base MIMO radar in an impulsive noise environment, and particularly relates to a direction finding method for the single-base MIMO radar by using quantum large explosion and infinite norm weighted subspace fitting in the impulsive noise environment.
The invention provides a single-ground MIMO radar direction finding method capable of quickly and accurately finding directions under the background of impact noise, aiming at the defects and shortcomings that the existing single-ground MIMO radar direction finding method is large in calculation amount and low in direction finding accuracy, and direction finding performance is seriously deteriorated and even fails under the background of complex noises such as impact noise. The method firstly designs a quantum large explosion method capable of fast solving with high precision, and then designs a single-base MIMO radar direction finding method using a quantum large explosion searching method and infinite norm weighting signal subspace fitting under the background of impact noise.
The invention considers a quantum explosion monostatic MIMO radar direction finding method under the background of impact noise, can simultaneously consider the direction finding speed and the direction finding precision, solves the infinite norm weighting signal subspace fitting direction finding equation by using the quantum explosion method, and obtains the optimal direction finding performance.
Compared with the prior art, the invention fully considers the requirements of convergence speed, direction finding precision and direction finding performance encountered by the monostatic MIMO radar direction finding under the impact noise environment, and has the following advantages:
(1) the invention is suitable for the impact noise environment, simultaneously adapts to Gaussian noise and strong impact noise environment, and has wide application range.
(2) The designed direction finding method of the monostatic MIMO radar well solves the problem of robust high-precision direction finding of a coherent receiving information source and an incoherent receiving information source in an impulse noise environment, and has excellent direction finding performance.
(3) The designed quantum explosion method can be used for quickly solving the subspace fitting direction-finding equation of the signal added with the infinite norm weight with high precision.
Drawings
FIG. 1 is a schematic diagram of a direction finding method of a monostatic MIMO radar based on quantum explosion.
Fig. 2 shows the direction of arrival of the independent incoming waves.
FIG. 3 is a direction of arrival estimation of coherent incoming waves.
Figure 4 estimates the success probability versus characteristic index.
Detailed Description
The invention will be further described below by way of example with reference to the accompanying drawings.
With reference to fig. 1, the present invention mainly comprises the following steps:
step one, a narrow-band single-ground MIMO radar system with co-location of transmitting and receiving is considered, wherein a transmitting antenna is a uniform linear array composed of M omnidirectional array elements, and a receiving antenna is a uniform linear array composed of N omnidirectional array elements. Assuming that the transmitting end simultaneously transmits M orthogonal waveforms with the same carrier frequency and bandwidth, the radar echo is processed by the matched filter banks of each receiving channel to separate the M waveforms. Meanwhile, P signal sources are assumed to be located at the same distance, and the distance of the signal sources is far greater than the aperture of the transmitting antenna and the aperture of the receiving antenna. After the processing of the matched filter bank, the output of the mth matched filter (corresponding to the mth signal of the transmitting antenna) of the nth receiving array element is taken as y at l snapshotsnm(l) N1, 2, and N, M1, 2, and M, the echoes received by the entire receiving antenna array can be written as follows: y (l) ═ a (θ) s (l) + n (l). Wherein y (l) ═ y1(l),y2(l),...,yNM(l)]T，A(θ)＝[a(θ1),a(θ2),...,a(θP)]Is a steering matrix of dimension MN multiplied by P,
Figure GDA0001390319880000051
for the p-th steering vector, the steering vector,
Figure GDA0001390319880000052
is the product of Kronecker, ar(θp) To receive steering vectors, at(θp) To transmit steering vectors, thetapDirection of arrival of the pth target, s (l) ═ s1(l),s2(l),...,sP(l)]TN (l) is an impulse noise vector of MN × 1 dimension, which is the complex amplitude of the output of the matched and filtered received signal. The received data may be normalized to using an infinite norm
Figure GDA0001390319880000061
max represents the function of taking the maximum value. The covariance matrix of the multiple snapshot samples is
Figure GDA0001390319880000062
E represents the math solving periodThe function of expectation, superscript H, represents the conjugate transpose. Performing characteristic decomposition on the covariance matrix to obtain a signal subspace and a noise subspace which are respectively UsAnd Un，ΛsAnd ΛnThe diagonal matrix composed of large eigenvalue and the diagonal matrix composed of small eigenvalue are respectively. Then the weighted signal subspace is fitted with a direction-finding equation of
Figure GDA0001390319880000063
Figure GDA0001390319880000064
Is the value of the variable theta corresponding to the function taking the maximum value,
Figure GDA0001390319880000065
for optimal estimation, PA(θ)＝A(θ)(AH(θ)A(θ))-1AH(θ) is a mapping matrix, θ ═ θ1,θ2,...,θP]Is a direction vector constituted by the direction of arrival, W represents a weighting matrix, trace [ ]]Indicating the tracing operation of the matrix.
And step two, generating all initial quantum fragments in the quantum explosion method. Considering a quantum solution space composed of 2H quantum chips, the 2H quantum chips are uniformly distributed into two subsets, each quantum chip moves in a P-dimensional search space, and the positions of the quantum chips represent potential solutions of the monostatic MIMO radar direction finding problem. At the t-th iteration, the quantum position of the ith quantum fragment of the kth quantum fragment set is defined as follows:
Figure GDA0001390319880000066
wherein i 1, 2., H; k is 1, 2;
Figure GDA0001390319880000067
a pth qubit, P ═ 1,2,.., P, representing the quantum position of the ith quantum fragment; mapping the quantum position of the ith quantum fragment to a defined interval, namely the position of the quantum fragment
Figure GDA0001390319880000068
The mapping relation is
Figure GDA0001390319880000069
p＝1,2,...,P，upAnd lpRespectively an upper limit value and a lower limit value of the angle search interval of the p-th dimension. The 1 st set of i quantum chips corresponds to a rotation step of
Figure GDA00013903198800000610
Representing the p-dimensional rotation step of the ith quantum chip. In order to make the initial position have certain dispersivity and uniform distribution, the quantum position is in the defined quantum domain [0, 1%]Random initialization with rotation steps of-0.2, 0.2]And (4) randomly initializing, wherein t is 0 initially.
And thirdly, calculating the fitness of each quantum fragment, and determining the initial optimal quantum position of the 1 st quantum fragment set, the initial optimal solution quantum centroid and the uniform solution quantum centroid of the 2 nd quantum fragment set. Ith quantum chip position
Figure GDA00013903198800000611
The fitness value of the infinite norm weighted signal subspace fitting direction-finding equation is
Figure GDA00013903198800000612
The larger the fitness value, the more excellent the quantum position and position of the quantum fragment, and the more accurate the estimated angle. The optimal quantum position experienced by the 1 st set of the ith quantum fragments up to now is defined as the locally optimal quantum position of the quantum fragment and is denoted as
Figure GDA00013903198800000613
Figure GDA00013903198800000614
The P-dimensional optimal qubit, P1, 2, P, is experienced for the ith quantum fragment of the 1 st set until the t-th iteration. The optimal quantum position experienced by all quantum fragments at present is recorded as the global optimal quantum position, namely the quantum position with the maximum fitness value is recorded as the quantum position with the maximum fitness value
Figure GDA0001390319880000071
Figure GDA0001390319880000072
P-dimension optimal qubits, P1, 2, P, for all quantum fragments experienced until the t-th iteration. Selecting the optimal quantum position in the 2 quantum chip sets as the optimal solution quantum centroid
Figure GDA0001390319880000073
The uniform solution quantum centroid of the 2 nd quantum chip set is
Figure GDA0001390319880000074
Wherein
Figure GDA0001390319880000075
p＝1,2,...,P。
And step four, updating the quantum position of each quantum fragment. Each quantum shard set is updated according to a different rule.
For the 1 st quantum chip set, the p-dimensional rotation step of the i-th quantum chip is updated to
Figure GDA0001390319880000076
Weight wtGradually decreasing as the number of iterations increases, i 1, 2., H, P1, 2., P; r is1And r2Are all [0,1 ]]A uniform random number in between, c1And c2Is a weighting constant; for the
Figure GDA0001390319880000077
If the boundary value is exceeded, it is limited to the boundary. The new qubit of the ith quantum chip is
Figure GDA0001390319880000078
1,2, H, wherein
Figure GDA0001390319880000079
P1, 2.. the P, abs () represents an absolute value function.
For the 2 nd quantum chip set, the p-dimension explosion step size of the ith quantum chip is as follows in the realization of large explosion
Figure GDA00013903198800000710
i 1,2, P is a contraction factor,
Figure GDA00013903198800000711
is [ -1,1 [ ]]A uniform random number in between. Produce [0,1]When gamma is less than or equal to 0.5, all quantum positions of the 2 nd quantum chip set are updated to be regular
Figure GDA00013903198800000712
Wherein
Figure GDA00013903198800000713
For the optimal solution of quantum centroid
Figure GDA00013903198800000714
P-dimension, P1, 2, P; otherwise, all quantum positions of the 2 nd quantum chip set are updated to rule
Figure GDA00013903198800000715
Wherein the content of the first and second substances,
Figure GDA00013903198800000716
to solve the quantum centroid uniformly
Figure GDA00013903198800000717
The p-th dimension of (a).
Step five, quantum positions of the ith quantum chip of the kth quantum chip set
Figure GDA00013903198800000718
Mapping to a position of a defined interval
Figure GDA0001390319880000081
k is 1, 2. Calculating the fitness value of all quantum fragments, wherein the fitness function is
Figure GDA0001390319880000082
i＝1,2,...,H。
And step six, updating the global optimal quantum position, updating the local optimal quantum position of each quantum fragment in the 1 st quantum fragment set, and updating the optimal solution quantum centroid and the uniform solution quantum centroid of the 2 nd quantum fragment set.
Figure GDA0001390319880000083
The global optimal quantum position experienced so far for all quantum fragments in the two quantum fragment sets. For the ith quantum chip of the 1 st quantum chip set, i is 1,2
Figure GDA0001390319880000084
Then order
Figure GDA0001390319880000085
Figure GDA0001390319880000086
Is a quantum position
Figure GDA0001390319880000087
The mapping position of (2); if not, then,
Figure GDA0001390319880000088
the 2 nd set of quantum chips is updated to
Figure GDA0001390319880000089
P1, 2. Optimal solution quantum centroid for the 2 nd set of quantum chips
Figure GDA00013903198800000810
The current globally optimal quantum position substitution is used.
Step seven, judging whether the maximum iteration times is reached, if so, finishing the iteration, outputting a global optimal quantum position, and mapping the global optimal quantum position into a position, wherein the position corresponds to the direction of arrival to be estimated; otherwise, let t be t +1, return to step four.
In a single-base MIMO radar system under the impact noise environment, the number of transmitting and receiving array elements is 5, the transmitting and receiving arrays are uniform linear arrays with the array element spacing of half wavelength, and the fast beat number is 200. The direction finding method of the single-base MIMO radar based on Infinite Norm (IN) Weighted Signal Subspace Fitting (WSSF) of quantum detonation (QBB) is marked as QBB-IN-WSSF, and the main parameters are set as follows: w is atMonotonically decreasing from 0.9 to 0.1, c1＝c 22, ρ 1, the limit of the rotation step in the 1 st quantum chip set is [ -0.2,0.2]. The comparison method comprises a fractional low-order moment-based MUSIC method (FLOM-MUSIC) and a fractional low-order moment maximum likelihood method (PSO-FLOM-ML) based on a particle swarm algorithm, wherein some simulation parameter settings and processes of the particle swarm algorithm can be referred to in the literature of dynamic DOA tracking under the background of impact noise, and the FLOM-MUSIC method refers to the most original literature. The number of quantum fragments in the quantum large explosion and the number of particles in the particle swarm optimization are both set to be 100, and the number of termination iterations is both 100.
Fig. 2 shows the relationship between the estimated value of the arrival direction and the true value IN 50 experimental simulations when the characteristic index is α ═ 1.30, the generalized signal-to-noise ratio is 10dB, and the directions of arrival of 3 independent narrow-band received signals are 5 °, 15 ° and 25 °, respectively, and it can be seen that the designed QBB-IN-WSSF method is far superior to the FLOM-MUSIC, and many values of the FLOM-MUSIC are estimated to fail close to the true value.
Fig. 3 shows the relationship between the estimated value of the direction of arrival and the true value of 50 experimental simulations when the characteristic index is α ═ 1.30, the generalized signal-to-noise ratio is 5dB, the directions of arrival of 3 coherent narrowband received signals are 5 °, 15 ° and 25 °, respectively, and 50 experimental simulations show that the designed QBB-IN-WSSF method is far better than PSO-FLOM-ML, and close to the true value, many values of FLOM-MUSIC are estimated to fail.
As can be seen from FIGS. 2 and 3, under the impact noise environment, the direction-finding performance of the designed direction-finding method of the single-base MIMO radar with the quantum explosion is far better than that of FLOM-MUSIC and PSO-FLOM-ML, and the designed method has strong impact noise resistance. The smaller the characteristic index is, the more severe the impulse noise tailing is, and the more severe the influence on the direction-finding performance is. When the characteristic index is 1, the estimated success probability is 0.985, and the other two algorithms are less than 0.2; when the eigen index is 1.2, the success probability is estimated to be 1 when the designed method is larger than 1.2, while the success probability reaches 1 in the case of 1.8 and 1.9, respectively, for the other two methods.
Fig. 4 shows the relationship between the probability of successful estimation and the characteristic index of 3 single-base MIMO radar direction finding methods, in which the directions of arrival of 2 independent narrow-band received target signals are respectively 10 ° and 18 °, the generalized signal-to-noise ratio is set to 10dB, and the estimation success is assumed to be within one degree. Simulation results show that the single-base MIMO radar direction finding method based on quantum large explosion can effectively find directions of independent and coherent sources in an impact noise environment, and has excellent performance in different impact noise environments.

Claims (1)

1. A single-base MIMO radar direction finding method for large-quantum explosion is characterized by comprising the following steps:
the method comprises the following steps that firstly, a transmitting antenna of a transmitting-receiving co-located narrow-band single-ground MIMO radar system is a uniform linear array composed of M omnidirectional array elements, and a receiving antenna is a uniform linear array composed of N omnidirectional array elements; supposing that M orthogonal waveforms with the same carrier frequency and bandwidth are transmitted by a transmitting end at the same time, a radar echo is processed by a matched filter bank of each receiving channel to separate the M waveforms, P signal sources are arranged at the same distance, the distance of the signal sources is greater than the aperture of a transmitting antenna and a receiving antenna, and after the processing of the matched filter bank, the output of an mth matched filter of an nth receiving array element is taken as ynm(l) N is 1,2, and N, M is 1,2, and M, the echoes received by the whole receiving antenna array are written as follows: y (l) ═ a (θ) s (l) + n (l), where y (l) ═ y1(l),y2(l),...,yNM(l)]T，A(θ)＝[a(θ1),a(θ2),...,a(θP)]Is a steering matrix of dimension MN multiplied by P,
Figure FDA0001390319870000011
for the p-th steering vector, the steering vector,
Figure FDA0001390319870000012
is the product of Kronecker, ar(θp) To receive steering vectors, at(θp) To transmit steering vectors, thetapDirection of arrival of the pth target, s (l) ═ s1(l),s2(l),...,sP(l)]TThe complex amplitude of the output of the received signal after matched filtering, n (l) is an impact noise vector of MN multiplied by 1 dimension; received data is normalized to using an infinite norm
Figure FDA0001390319870000013
max represents a function of maximum, and the covariance matrix of the multiple snapshot samples is
Figure FDA0001390319870000014
E represents a function for solving mathematical expectation, superscript H represents conjugate transposition, and feature decomposition is carried out on the covariance matrix to obtain a signal subspace and a noise subspace which are respectively UsAnd Un，ΛsAnd ΛnThe diagonal matrix composed of large eigenvalues and the diagonal matrix composed of small eigenvalues respectively, the weighted signal subspace fits the direction-finding equation into
Figure FDA0001390319870000015
Figure FDA0001390319870000016
Is the value of the variable theta corresponding to the function taking the maximum value,
Figure FDA0001390319870000017
for optimal estimation, PA(θ)＝A(θ)(AH(θ)A(θ))-1AH(θ) is a mapping matrix, θ ═ θ1,θ2,...,θP]Is a direction vector formed by the directions of arrival, W representsWeight matrix, trace [ [ alpha ] ]]Trace-solving operation of the expression matrix;
step two, generating all initial quantum fragments in the quantum explosion method,
a quantum solution space composed of 2H quantum fragments, wherein the 2H quantum fragments are uniformly distributed to two subsets, each quantum fragment moves in a P-dimensional search space, the positions of the quantum fragments represent potential solutions of a single-base MIMO radar direction-finding problem, and the quantum positions of the ith quantum fragment in the kth quantum fragment set are defined as follows in the t-th iteration:
Figure FDA0001390319870000018
wherein i 1, 2., H; k is 1, 2;
Figure FDA0001390319870000019
a pth qubit, P ═ 1,2,.., P, representing the quantum position of the ith quantum fragment; mapping the quantum position of the ith quantum fragment to a defined interval, namely the position of the quantum fragment
Figure FDA00013903198700000110
The mapping relation is
Figure FDA00013903198700000111
upAnd lpThe upper limit and the lower limit of the p-dimensional angle search interval are respectively, the rotation step corresponding to the ith quantum chip of the 1 st set is
Figure FDA0001390319870000021
Figure FDA0001390319870000022
Representing the p-dimension rotation step of the ith quantum fragment with quantum position in the defined quantum domain [0,1]Random initialization with rotation steps of-0.2, 0.2]Randomly initializing, wherein the initial time t is 0;
step three, calculating the fitness of each quantum fragment,
determining a 1 st set of quantum chipsInitial optimal quantum position, initial optimal solution quantum centroid and uniform solution quantum centroid of the 2 nd set of quantum chips, the ith quantum chip position
Figure FDA0001390319870000023
The fitness value of the infinite norm weighted signal subspace fitting direction-finding equation is
Figure FDA0001390319870000024
The optimal quantum position experienced by the 1 st set of the ith quantum fragments up to now is defined as the locally optimal quantum position of the quantum fragment and is denoted as
Figure FDA0001390319870000025
Figure FDA0001390319870000026
For the p-dimension optimal quantum bit experienced by the ith quantum fragment of the 1 st set till the t iteration, the optimal quantum position experienced by all the quantum fragments till now is recorded as the global optimal quantum position, namely the quantum position with the maximum fitness value is recorded as the quantum position with the maximum fitness value
Figure FDA0001390319870000027
Figure FDA0001390319870000028
For the p-dimension optimal quantum bit experienced by all quantum fragments till the t-th iteration, selecting the optimal quantum bit in the 2 quantum fragment sets as the optimal solution quantum centroid
Figure FDA0001390319870000029
The uniform solution quantum centroid of the 2 nd quantum chip set is
Figure FDA00013903198700000210
Wherein
Figure FDA00013903198700000211
Step four, updating the quantum position of each quantum fragment, updating each quantum fragment set according to different rules,
for the 1 st quantum chip set, the p-dimensional rotation step of the i-th quantum chip is updated to
Figure FDA00013903198700000212
Weight wtGradually decreasing with the increase of the iteration times; r is1And r2Are all [0,1 ]]A uniform random number in between, c1And c2Is a weighting constant; for the
Figure FDA00013903198700000213
If the boundary value is exceeded, it is limited to the boundary, and the new quantum position of the ith quantum fragment is
Figure FDA00013903198700000214
Wherein
Figure FDA00013903198700000215
abs () represents the absolute value function,
for the 2 nd quantum chip set, the p-dimension explosion step size of the ith quantum chip is as follows in the realization of large explosion
Figure FDA00013903198700000216
P is the contraction factor and is the ratio of the contraction factor,
Figure FDA00013903198700000217
is [ -1,1 [ ]]Uniform random number in between, produces [0,1 ]]When gamma is less than or equal to 0.5, all quantum positions of the 2 nd quantum chip set are updated to be regular
Figure FDA0001390319870000031
Wherein
Figure FDA0001390319870000032
For the optimal solution of quantum centroid
Figure FDA0001390319870000033
The p-th dimension of (a); otherwise, all quantum positions of the 2 nd quantum chip set are updated to rule
Figure FDA0001390319870000034
Wherein the content of the first and second substances,
Figure FDA0001390319870000035
to solve the quantum centroid uniformly
Figure FDA0001390319870000036
The p-th dimension of (a);
step five, quantum positions of the ith quantum chip of the kth quantum chip set
Figure FDA0001390319870000037
Mapping to a position of a defined interval
Figure FDA0001390319870000038
Calculating the fitness value of all quantum fragments, wherein the fitness function is
Figure FDA0001390319870000039
Step six, updating the global optimal quantum position, updating the local optimal quantum position of each quantum fragment in the 1 st quantum fragment set, updating the optimal solution quantum centroid and the uniform solution quantum centroid of the 2 nd quantum fragment set,
Figure FDA00013903198700000310
for the global optimal quantum positions experienced so far by all quantum fragments in the two quantum fragment sets, for the ith quantum fragment of the 1 st quantum fragment set, if
Figure FDA00013903198700000311
Then order
Figure FDA00013903198700000312
Figure FDA00013903198700000313
Is a quantum position
Figure FDA00013903198700000314
The mapping position of (2); if not, then,
Figure FDA00013903198700000315
the 2 nd set of quantum chips is updated to
Figure FDA00013903198700000316
Optimal solution quantum centroid for the 2 nd set of quantum chips
Figure FDA00013903198700000317
Replacing with the current global optimal quantum position;
step seven, judging whether the maximum iteration times is reached, if so, finishing the iteration, outputting a global optimal quantum position, and mapping the global optimal quantum position into a position, wherein the position corresponds to the direction of arrival to be estimated; otherwise, let t be t +1, return to step four.
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