CN103257344B - Iteration-adaptive-algorithm-based method for detecting coherent MIMO radar target - Google Patents

Abstract

The invention discloses an iteration-adaptive-algorithm-based method for detecting a coherent MIMO radar target. First, a relation model among a first echo signal, a transmitting signal reflection coefficients and noise interference of the target is confirmed, wherein the relation model is observed on the n<th> observation point, secondly, the relation model is linearized, further the reflection coefficients of the target are initialized through a delayed superposition DAS algorithm, and finally, a bayesian model order selecting tool is used for optimizing the reflection coefficients of the target. An iteration adaptive algorithm can effectively solve existing encountered problems of moving target parameter detection and greatly improves accuracy of detecting of the coherent MIMO radar moving target.

Description

Based on the relevant MIMO radar object detection method of iteration self-adapting algorithm

Technical field

The present invention relates to a kind of MIMO radar object detection method, is more particularly a kind of relevant MIMO radar object detection method based on iteration self-adapting algorithm.

Background technology

Multiple-input and multiple-output (MIMO) radar is compared phased-array radar and is had detection perform, good anti-stealthy effect and the good anti-lethality higher to weak signal target, has attracted increasing scholar to study it.MIMO radar generally can be divided into two classes: the first kind is statistics MIMO radar or incoherent MIMO radar, the i.e. bare cloth of bay space, thus can obtain space diversity gain, effectively overcomes the impact that target RCS rises and falls on Studies of Radar Detection performance; Equations of The Second Kind is relevant MIMO, adopts less aerial array just can form very large virtual array aperture, improves radar angular resolution and interference rejection capability.

Space-time adaptive (STAP) is a kind of moving target detection method, has clutter suppression capability strong, the advantage that robustness is good, interference rejection capability is strong.Clutter suppression capability is by force because STAP technology has space-time two-dimensional filtering characteristic.Robustness is well because STAP technology, by adaptive characteristic, can realize mating with the effective of complicated external environment; Meanwhile, it also can compensate multiple inevitable systematic error to a certain extent.Interference rejection capability is by force because STAP can realize the suppression to the multiple interference under complex electromagnetic environment.STAP technology is combined with relevant MIMO radar, not only system can be made to have the superiority of MIMO performance but also have the superiority of STAP, better raising is to clutter recognition performance, thus the radar system that can make obtains the ability of higher target detection, the tracking performance of moving-target, the performance of Faint target detection and stronger signal interception.

No matter for moving-target or quiet target, as long as the reflection coefficient obtaining target then can know the location parameter (complex magnitude, distance, angle) of the location parameter (complex magnitude, distance, angle, Doppler) of moving-target, quiet target.

In prior art, relevant MIMO radar space-time adaptive processing method sharply increases because suppression jamming causes Clutter Degrees of Freedom under the electromagnetic environment of complexity, and the degree of freedom of traditional self-adaptive processing algorithm (STAP) cannot meet clutter recognition requirement; Duplicity interference causes the seriously non-homogeneous of the distribution of clutter, makes STAP algorithm cannot obtain enough training samples meeting independent same distribution condition.In addition, existing STAP needs auxiliary data to go to estimate the master data of clutter and noise harmonics matrix, but the auxiliary data with high accuracy is very un-come-at-able, especially for clutter environment heterogeneous.In order to reduce the dependence for auxiliary data, propose the space-time adaptive algorithm not needing auxiliary data, such as DAS method, but the problem of the low high secondary lobe of resolution is led in this class methods face.Therefore this patent is intended proposing innovatory algorithm on the basis of existing space-time adaptive method, overcomes the shortcoming of existing STAP and DAS, better plays the advantage of relevant MIMO radar and space-time adaptive method.

Summary of the invention

The object of the invention is to propose a kind of relevant MIMO radar moving target detection method calculated based on iteration self-adapting, the method obtains its location parameter by being optimized the reflection coefficient of moving-target and quiet target respectively, is specially:

A, when observed object is quiet target, do not consider Doppler's effect

A1, determine first echoed signal that the n-th observation station observes and transmit, between the reflection coefficient of target and noise, relational model is as follows:

$Y^H\left(n\right)=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{r,a}{b}_a\left(n\right)a_a^T\left(n\right){{\tilde{S}}^{H}J}_r+E^H\left(n\right)$

In formula, Y (n) is first echoed signal that the n-th observation station observes, wherein for the number of observation station; Y ^hn Y (n) is carried out conjugate transpose operation by () expression; P represents along the minimum range unit i.e. number of distance quantifying unit that directions of rays is divided into by distance in radar echo signal process, r=1,2 ... P; K represents that the angle intervals that there is target quantizes number of unit, a=1 ... ..K; α _r,arepresent the reflection coefficient of target region internal object; b _an () is that the receiving array of the n-th observation station guides vector; a _an () is that the emission array of the n-th observation station guides vector; represent a _an () does transpose operation; E (n) represents the additive noise of the n-th observation station Received signal strength, E ^hn E (n) is carried out conjugate transpose operation by () expression; representing will carry out conjugate transpose operation, $\tilde{S}={\left[\begin{array}{c}S\\ 0_{(P-1)\&times;M_t}\end{array}\right]}_{(L+P-1)\&times;M_t}$ For the waveform matrix that transmits obtained after zero padding process, $S={\left[\begin{array}{cccc}{s}_1& s_2& \&CenterDot;\&CenterDot;\&CenterDot;s_m\&CenterDot;\&CenterDot;\&CenterDot;& s_{M_t}\end{array}\right]}_{L\&times;M_t}$ For the waveform matrix that transmits, wherein, s _mrepresent the orthogonal waveforms of m article of transmission antennas transmit, m=1 ... M _t; M _tfor the number of emitting antenna, L is the number of subpulse of transmitting;

J _r∈ C ^{(L+P-1) × (L+P-1)}for transformation matrix, be used for describing different distance and quantize the signal that receives of section, its expression formula is:

$b_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_r-1)\mathrm{dr})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$

$a_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_t-1)\mathrm{dt})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T,$ Wherein $n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N},$ D _nrepresent the distance between signal collection point; θ _arepresent that target quantizes the reflection angle of unit a angle intervals; λ ₀represent radar system carrier wavelength; Dr represents the distance accepted between antenna; Dt represents the distance between emitting antenna; M _rrepresent the number of receiving antenna;

A2, to above-mentioned relation model linearization;

A3, time delay is utilized to superpose the reflection coefficient of DAS algorithm initialization target, as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a}=\frac{v_{r,a}^{H}y}{v_{r,a}^H{v}_{r,a}};$

Wherein:

$\begin{array}{c}{v}_{r,a}=\left[\begin{array}{c}{\tilde{v}}_{r,a}\left(1\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a}\left(\tilde{N}\right)\end{array}\right]\&Element;C^{\tilde{N}{M}_r(L+P-1)\&times;1}\end{array}$ ${\tilde{v}}_{r,a}\left(n\right)=\mathrm{vec}\left[b_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H{J}_r\right]\&Element;C^{M_r(L+P-1)\&times;1},$ $n=1,\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N},$

r=1,...P,a=1,...K； $y=\left[\begin{array}{c}\mathrm{vec}\left(Y^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(Y^H\left(\tilde{N}\right)\right)\end{array}\right]$ Wherein represent initialized target reflection factor, represent V _r,acarry out conjugate transpose operation; M _rrepresent the number of receiving antenna; Vec represents matrix is carried out vectorization operation, and arranging successively by the order of rectangular array by matrix is row;

A4, Bayesian model exponent number selection tool is utilized to carry out the reflection coefficient of optimization aim, be specially: time delay is superposed the target reflection factor that DAS is initial, (1) formula of bringing into obtains the Bayes BIC value of initial value, the reflection coefficient of iterative target also upgrades Bayes BIC value, twice Bayes BIC value relatively, when Bayes BIC value no longer reduces, then iteration is stopped to obtain the reflection coefficient of target;

${\mathrm{BIC}}_{\tilde{r},\tilde{a}}\left(\mathrm{\&eta;}\right)={2M}_r\tilde{N}(L+P-1)\&times;\mathrm{In}\left[{\left|\right|y-\underset{(r,a)\&Element;\{J\left(\mathrm{\&eta;}\right)\&cup;(\tilde{r},\tilde{a})\}}{\mathrm{\&Sigma;}}{V}_{r,a}{\hat{a}}_{r,a}\left|\right|}_2^2\right]+4\mathrm{\&eta;In}\left({2M}_r\tilde{N}(L+P-1)\right)---\left(1\right)$

In formula, || .|| ₂represent Euclid norm, represent Euclid norm square, η represents the target number of current selection; 4 represent the number of parameters that each target will estimate; J (η) represents the target sequence number set selected.When carrying out first time iteration now hypothesis does not have target; represent a undetermined target sequence number, wherein represent the position of undetermined target in distance quantifying unit, represent and do not determine the position of target in angular spacing quantifying unit, after iteration terminates, beyond J (η), the reflection coefficient of part is set as 0, is considered to do not have target; Wherein, the iterative formula of reflection coefficient is as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a}=\frac{v_{r,a}^H{R}^{-1}y}{v_{r,a}^H{R}^{-1}{v}_{r,a}}$

In formula, wherein in R represent the reflection coefficient of the target that last iteration obtains, when first time iteration, in R represent initial target reflection factor;

B, when target is moving-target, consider Doppler's effect

B1, determine first echoed signal that the n-th observation station observes and transmit, the reflection of target

Between coefficient and noise, relational model is as follows:

$Y^H\left(n\right)=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{d=1}{\overset{G}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{r,a,d}{b}_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H\left({\mathrm{\&omega;}}_d\right)J_r+E^H\left(n\right)$

In formula, Y (n) is first echoed signal that the n-th observation station receives, wherein p represents along the minimum range unit i.e. number of distance quantifying unit that directions of rays is divided into by distance in radar echo signal process, r=1 ... P; K represents that the angle intervals that there is target quantizes number of unit, a=1 ... ..K; G represents the interval quantizing number of unit of the Doppler that there is target, d=1 ... G; α _{r, a, d}represent the reflection coefficient of target region internal object; b _an () is that the receiving array of the n-th observation station guides vector; a _an () is that the emission array of the n-th observation station guides vector; represent a _an () carries out transpose operation, will conjugate transpose operation, wherein $\tilde{S}\left({\mathrm{\&omega;}}_d\right)={\left[\begin{array}{c}S\left({\mathrm{\&omega;}}_d\right)\\ 0_{(P-1)\&times;M_t}\end{array}\right]}_{(L+P-1)\&times;M_t}$ For the waveform matrix that transmits of introducing Doppler obtained after zero padding process, $S\left({\mathrm{\&omega;}}_d\right)=\left[\begin{array}{cccc}{\tilde{s}}_1\left({\mathrm{\&omega;}}_d\right)& {\tilde{s}}_2\left({\mathrm{\&omega;}}_d\right)& \&CenterDot;\&CenterDot;\&CenterDot;{\tilde{s}}_m\left({\mathrm{\&omega;}}_d\right)\&CenterDot;\&CenterDot;\&CenterDot;& {\tilde{s}}_{M_t}\left({\mathrm{\&omega;}}_d\right)\end{array}\right],$ Wherein: m=1 ... M _t, d=1 ... G; $d\left({\mathrm{\&omega;}}_d\right)={\left[\begin{array}{cccc}1& e^{{\mathrm{j\&omega;}}_d}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{{\mathrm{j\&omega;}}_d(L-1)}\end{array}\right]}^T,$ S _mrepresent the waveform of m transmission antennas transmit orthogonal signal; ω _dit is the angle Doppler frequency of d Doppler's quantifying unit; M _tfor the number of emitting antenna; L is the number of subpulse of transmitting; the Hadamard product of computing representing matrix; E (n) represents the additive noise in the n-th observation station Received signal strength, E ^hn E (n) is carried out conjugate transpose operation by () expression;

$b_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_r-1)\mathrm{dr})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$

$a_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_t-1)\mathrm{dt})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$ $n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N},$ D _nrepresent the distance between signal collection point; θ _arepresent that target quantizes the reflection angle of unit a angle intervals; λ ₀represent radar system carrier wavelength; Dr represents the distance accepted between antenna; Dt represents the distance between emitting antenna; M _rrepresent the number of receiving antenna;

B2, to above-mentioned relation model linearization;

B3, time delay is utilized to superpose the reflection coefficient of DAS algorithm initialization target, as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a,d}=\frac{v_{r,a,d}^{H}y}{v_{r,a,d}^H{v}_{r,a,d}}$

Wherein:

$\begin{array}{c}{v}_{r,a,d}=\left[\begin{array}{c}{\tilde{v}}_{r,a,d}\left(1\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a,d}\left(\tilde{N}\right)\end{array}\right]\&Element;C^{\tilde{N}{M}_r(L+P-1)\&times;1}\end{array}$

${\tilde{v}}_{r,a,d}\left(n\right)=\mathrm{vec}\left[b_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H\left({\mathrm{\&omega;}}_d\right)J_r\right]\&Element;C^{M_r(L+P-1)\&times;1}$

$y=\left[\begin{array}{c}\mathrm{vec}\left(Y^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(Y^H\left(\tilde{N}\right)\right)\end{array}\right]$

Wherein represent initialized target reflection factor, represent v _{r, a, d}carry out conjugate transpose operation; Vec represents matrix is carried out vectorization operation, and arranging successively by the order of rectangular array by matrix is row;

B4, Bayesian model exponent number selection tool is utilized to carry out the reflection coefficient of optimization aim, be specially: time delay is superposed the target reflection factor that DAS is initial, (2) formula of bringing into obtains the Bayes BIC value of initial value, the reflection coefficient of iterative target also upgrades Bayes BIC value, twice Bayes BIC value relatively, when Bayes BIC value no longer reduces, then iteration is stopped to obtain the reflection coefficient of target;

${\mathrm{BIC}}_{\tilde{r},\tilde{a},\tilde{d}}\left(\mathrm{\&eta;}\right)={2M}_r\tilde{N}(L+P-1)\&times;\mathrm{In}\left[{\left|\right|y-\underset{(r,a,d)\&Element;\{J\left(\mathrm{\&eta;}\right)\&cup;(\tilde{r},\widetilde{a,}\tilde{d})\}}{\mathrm{\&Sigma;}}{V}_{r,a,d}{\hat{a}}_{r,a,d}\left|\right|}_2^2\right]+5\mathrm{\&eta;In}\left({2M}_r\tilde{N}(L+P-1)\right)---\left(2\right)$

In formula, || || ₂represent Euclid norm, represent Euclid norm square, η represents the target number of current selection; 5 represent the number of parameters that each target will estimate; J (η) represents the target sequence number set selected.When carrying out first time iteration now hypothesis does not have target; represent a undetermined target sequence number, wherein represent the position of undetermined target in distance quantifying unit, represent and do not determine the position of target in angular spacing quantifying unit, represent and do not determine the position of target in Doppler's quantifying unit, after iteration terminates, beyond J (η), the reflection coefficient of part is set as 0, is considered to do not have target;

Wherein, the iterative formula of reflection coefficient is as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a,d}=\frac{v_{r,a,d}^H{R}^{-1}y}{v_{r,a,d}^H{R^{-1}v}_{r,a.d}};$

In formula, $R=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{d=1}{\overset{G}{\mathrm{\&Sigma;}}}{\left|{\widehat{\mathrm{\&alpha;}}}_{r,a.d}\right|}^2{v}_{r,a,d}{v}_{r,a,d}^H$ r=1,...P,a=1,...K,d=1,...G

Wherein in R represent the reflection coefficient of the target that last iteration obtains; When first time iteration, in R represent initial target reflection factor.

The present invention compared with prior art has following significant progress:

(1) method of the present invention does not need auxiliary data, the v obtained after only needing the y by receiving and conversion goes to obtain the target component of target, thus solve existing space-time adaptive algorithm and need auxiliary data to go to estimate the master data of clutter and noise harmonics matrix, under non-homogeneous clutter environment, the problem of the auxiliary data of condition cannot be met.

(2) existing adaptive algorithm, such as Capon method and amplitude-phase algorithm for estimating (APES) can reduce the impact of clutter.But when the signal received is in low signal-to-noise ratio, if when the number of snapshot is insufficient, MIMO target detection performance will weaken greatly, but iteration self-adapting algorithm is customer parameter freedom and non-parametric adaptive algorithm, in several situation even only having a snapshot, still can obtain the parameter of target comparatively accurately.

(3) this method further improves the performance that DAS estimates the low and high secondary lobe of resolution.By the initial method that DAS method is estimated as target component, BIC model order selection tool is adopted to improve the accuracy of target component estimation.

(4) existing space-time adaptive algorithm operation quantity is high, but this algorithm has fast convergence rate, feature that stable performance operand is low.

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail;

Accompanying drawing explanation

Fig. 1 is the process flow diagram of relevant MIMO object detection system of the present invention;

Fig. 2 is DAS method moving target detect analogous diagram;

Fig. 3 is iteration self-adapting algorithm (IAA) moving target detect analogous diagram.

Embodiment

As shown in Figure 1, a kind of relevant MIMO radar object detection method based on iteration self-adapting algorithm of the present invention, the method obtains its location parameter by being optimized the reflection coefficient of moving-target and quiet target respectively, is specially:

A, when observed object is quiet target, does not consider Doppler's effect

A1, determine first echoed signal that the n-th observation station observes and transmit, between the reflection coefficient of target and noise, relational model is as follows:

$Y^H\left(n\right)=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{r,a}{b}_a\left(n\right)a_a^T\left(n\right){{\tilde{S}}^{H}J}_r+E^H\left(n\right)$

In formula, Y (n) is first echoed signal that the n-th observation station receives, wherein for the number of observation station; Y ^hn Y (n) is carried out conjugate transpose operation by () expression; P represents along the minimum range unit i.e. number of distance quantifying unit that directions of rays is divided into by distance in radar echo signal process, r=1,2 ... P; K represents that the angle intervals that there is target quantizes number of unit, a=1 ... ..K; α _r,arepresent the reflection coefficient of target region internal object; b _an () is that the receiving array of the n-th observation station guides vector; a _an () is that the emission array of the n-th observation station guides vector; represent a _an () does transpose operation; E (n) represents the additive noise of the n-th observation station Received signal strength, E ^hn E (n) is carried out conjugate transpose operation by () expression; representing will carry out conjugate transpose operation, $\tilde{S}={\left[\begin{array}{c}S\\ 0_{(P-1)\&times;M_t}\end{array}\right]}_{(L+P-1)\&times;M_t}$ For the waveform matrix that transmits obtained after zero padding process, $S{=\left[\begin{array}{cccc}{s}_1& s_2& \&CenterDot;\&CenterDot;\&CenterDot;s_m\&CenterDot;\&CenterDot;\&CenterDot;& s_{M_t}\end{array}\right]}_{L\&times;M_t}$ For the waveform matrix that transmits, wherein, s _mrepresent the orthogonal waveforms of m article of transmission antennas transmit, m=1 ... M _t; M _tfor the number of emitting antenna, L is the number of subpulse of transmitting; J _r∈ C ^{(L+P-1) × (L+P-1)}for transformation matrix, be used for describing different distance and quantize the signal that receives of section, its expression formula is:

$b_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_r-1)\mathrm{dr})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$

$a_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_t-1)\mathrm{dt})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T,$ Wherein $n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N},$ D _nrepresent the distance between signal collection point; θ _arepresent that target quantizes the reflection angle of unit a angle intervals; λ ₀represent radar system carrier wavelength; Dr represents the distance accepted between antenna; Dt represents the distance between emitting antenna; M _rrepresent the number of receiving antenna;

A2, to above-mentioned relation model linearization, wherein $A=\left[\begin{array}{cccc}{v}_{\mathrm{1,1}}& v_{\mathrm{1,2}}& {\&CenterDot;\&CenterDot;\&CenterDot;v}_{r,a}\&CenterDot;\&CenterDot;\&CenterDot;& v_{P,K}\end{array}\right]\&Element;C^{\tilde{N}{M}_r(L+P-1)\&times;\mathrm{PK}}$ x=[α _1,1?α _1,2?…α _r,a…?α _P,K] ^T∈C ^PK×1 $v_{r,a}=\left[\begin{array}{c}{\tilde{v}}_{r,a}\left(1\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a}\left(n\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a}\left(\tilde{N}\right)\end{array}\right]\&Element;C^{\tilde{N}{M}_r(L+P-1)\&times;1}$ ${\tilde{v}}_{r,a}\left(n\right)=\mathrm{vec}\left[b_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H{J}_r\right]\&Element;C^{M_r(L+P-1)\&times;1},$ $n=1,\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N}$ r=1,...P,a=1,...K； $e=\left[\begin{array}{c}\mathrm{vec}\left(E^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(E^H\left(\tilde{N}\right)\right)\end{array}\right],$ $y=\left[\begin{array}{c}\mathrm{vec}\left(Y^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(Y^H\left(\tilde{N}\right)\right)\end{array}\right];$ M _rrepresent the number of receiving antenna; α _r,arepresent the reflection coefficient of target region internal object; Vec represents matrix is carried out vectorization operation, and arranging successively by the order of rectangular array by matrix is row;

A3, time delay is utilized to superpose the reflection coefficient of DAS algorithm initialization target, as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a}=\frac{v_{r,a}^{H}y}{v_{r,a}^H{v}_{r,a}};$

Wherein represent initialized target reflection factor, represent V _r,acarry out conjugate transpose operation;

A4, Bayesian model exponent number selection tool is utilized to carry out the reflection coefficient of optimization aim, be specially: time delay is superposed the target reflection factor that DAS is initial, (1) formula of bringing into obtains the Bayes BIC value of initial value, the reflection coefficient of iterative target also upgrades Bayes BIC value, twice Bayes BIC value relatively, when Bayes BIC value no longer reduces, then iteration is stopped to obtain the reflection coefficient of target;

${\mathrm{BIC}}_{\tilde{r},\tilde{a}}\left(\mathrm{\&eta;}\right)={2M}_r\tilde{N}(L+P-1)\&times;\mathrm{In}\left[{\left|\right|y-\underset{(r,a)\&Element;\{J\left(\mathrm{\&eta;}\right)\&cup;(\tilde{r},\tilde{a})\}}{\mathrm{\&Sigma;}}{V}_{r,a}{\hat{a}}_{r,a}\left|\right|}_2^2\right]+4\mathrm{\&eta;In}\left({2M}_r\tilde{N}(L+P-1)\right)---\left(1\right)$

In formula, || .|| ₂represent Euclid norm, represent Euclid norm square, η represents the target number of current selection; 4 represent the number of parameters that each target will estimate; J (η) represents the target sequence number set selected.When carrying out first time iteration now hypothesis does not have target; represent a undetermined target sequence number, wherein represent the position of undetermined target in distance quantifying unit, represent and do not determine the position of target in angular spacing quantifying unit, after iteration terminates, beyond J (η), the reflection coefficient of part is set as 0, is considered to do not have target;

Wherein, the iterative formula of reflection coefficient is as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a}=\frac{v_{r,a}^H{R}^{-1}y}{v_{r,a}^H{R}^{-1}{v}_{r,a}}$

In formula, wherein in R represent the reflection coefficient of the target that last iteration obtains, when first time iteration, in R represent initial target reflection factor; Pass through calculate new upgrade Bayes BIC value, compare twice, front and back Bayes BIC value, be met condition when Bayes BIC value no longer reduces

B, when target is moving-target, consider Doppler's effect

B1, determine first echoed signal that the n-th observation station receives and transmit, between the reflection coefficient of target and noise, relational model is as follows:

$Y^H\left(n\right)=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{d=1}{\overset{G}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{r,a,d}{b}_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H\left({\mathrm{\&omega;}}_d\right)J_r+E^H\left(n\right)$

In formula, Y (n) is first echoed signal that the n-th observation station receives, wherein p represents along the minimum range unit i.e. number of distance quantifying unit that directions of rays is divided into by distance in radar echo signal process, r=1 ... P; K represents that the angle intervals that there is target quantizes number of unit, a=1 ... ..K; G represents the interval quantizing number of unit of the Doppler that there is target, d=1 ... G; α _{r, a, d}represent the reflection coefficient of target region internal object; b _an () is that the receiving array of the n-th observation station guides vector; a _an () is that the emission array of the n-th observation station guides vector; represent a _an () carries out transpose operation, will conjugate transpose operation, wherein $\tilde{S}\left({\mathrm{\&omega;}}_d\right)={\left[\begin{array}{c}S\left({\mathrm{\&omega;}}_d\right)\\ 0_{(P-1)\&times;M_t}\end{array}\right]}_{(L+P-1)\&times;M_t}$ For the waveform matrix that transmits of introducing Doppler obtained after zero padding process, $S\left({\mathrm{\&omega;}}_d\right)=\left[\begin{array}{cccc}{\tilde{s}}_1\left({\mathrm{\&omega;}}_d\right)& {\tilde{s}}_2\left({\mathrm{\&omega;}}_d\right)& \&CenterDot;\&CenterDot;\&CenterDot;{\tilde{s}}_m\left({\mathrm{\&omega;}}_d\right)\&CenterDot;\&CenterDot;\&CenterDot;& {\tilde{s}}_{M_t}\left({\mathrm{\&omega;}}_d\right)\end{array}\right],$ Wherein: m=1 ... M _t, d=1 ... G; $d\left({\mathrm{\&omega;}}_d\right)={\left[\begin{array}{cccc}1& e^{{\mathrm{j\&omega;}}_d}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{{\mathrm{j\&omega;}}_d(L-1)}\end{array}\right]}^T,$ S _mrepresent the waveform of m transmission antennas transmit orthogonal signal; ω _dit is the angle Doppler frequency of d Doppler's quantifying unit; M _tfor the number of emitting antenna; L is the number of subpulse of transmitting; the Hadamard product of computing representing matrix; E (n) represents the additive noise in the n-th observation station Received signal strength, E ^hn E (n) is carried out conjugate transpose operation by () expression;

$b_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_r-1)\mathrm{dr})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$

$a_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_t-1)\mathrm{dt})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$ $n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N},$ D _nrepresent the distance between signal collection point; θ _arepresent that target quantizes the reflection angle of unit a angle intervals; λ ₀represent radar system carrier wavelength; Dr represents the distance accepted between antenna; Dt represents the distance between emitting antenna; M _trepresent the number of emitting antenna;

B2, to above-mentioned relation model linearization, as follows:

y=Ax+e

Wherein, A=[v _1,1,1v _1,1,2v _{r, a, d}v _{p, K, G}] x=[α _1,1,1α _1,1,2α _{r, a, d}α _{p, K, G}] ^t

$v_{r,a,d}=\left[\begin{array}{c}{\tilde{v}}_{r,a,d}\left(1\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a,d}\left(n\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a,d}\left(\tilde{N}\right)\end{array}\right]\&Element;C^{\tilde{N}{M}_r(L+P-1)\&times;1};$ ${\tilde{v}}_{r,a,d}\left(n\right)=\mathrm{vec}\left[b_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H\left({\mathrm{\&omega;}}_d\right)J_r\right]\&Element;C^{M_r(L+P-1)\&times;1},$

$n=1,\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N};e=\left[\begin{array}{c}\mathrm{vec}\left(E^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(E^H\left(\tilde{N}\right)\right)\end{array}\right],$ $y=\left[\begin{array}{c}\mathrm{vec}\left(Y^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(Y^H\left(\tilde{N}\right)\right)\end{array}\right];$

M _rrepresent the number of receiving antenna; α _{r, a, d}represent the reflection coefficient of target region internal object; Vec represents matrix is carried out vectorization operation, and arranging successively by the order of rectangular array by matrix is row;

B3, time delay is utilized to superpose the reflection coefficient of DAS algorithm initialization target, as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a,d}=\frac{v_{r,a,d}^{H}y}{v_{r,a,d}^H{v}_{r,a,d}}$

Wherein represent initialized target reflection factor, represent v _{r, a, d}carry out conjugate transpose operation;

B4, Bayesian model exponent number selection tool is utilized to carry out the reflection coefficient of optimization aim, be specially: time delay is superposed the target reflection factor that DAS is initial, (2) formula of bringing into obtains the Bayes BIC value of initial value, the reflection coefficient of iterative target also upgrades Bayes BIC value, twice Bayes BIC value relatively, when Bayes BIC value no longer reduces, then iteration is stopped to obtain the reflection coefficient of target;

${\mathrm{BIC}}_{\tilde{r},\tilde{a},\tilde{d}}\left(\mathrm{\&eta;}\right)={2M}_r\tilde{N}(L+P-1)\&times;\mathrm{In}\left[{\left|\right|y-\underset{(r,a,d)\&Element;\{J\left(\mathrm{\&eta;}\right)\&cup;(\tilde{r},\widetilde{a,}\tilde{d})\}}{\mathrm{\&Sigma;}}{V}_{r,a,d}{\hat{a}}_{r,a,d}\left|\right|}_2^2\right]+5\mathrm{\&eta;In}\left({2M}_r\tilde{N}(L+P-1)\right)---\left(2\right)$

In formula, || .|| ₂represent Euclid norm, represent Euclid norm square, η represents the target number of current selection; 5 represent the number of parameters that each target will estimate; J (η) represents the target sequence number set selected.When carrying out first time iteration now hypothesis does not have target; represent a undetermined target sequence number, wherein represent the position of undetermined target in distance quantifying unit, represent and do not determine the position of target in angular spacing quantifying unit, represent and do not determine the position of target in Doppler's quantifying unit, after iteration terminates, beyond J (η), the reflection coefficient of part is set as 0, is considered to do not have target;

Wherein, the iterative formula of reflection coefficient is as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a,d}=\frac{v_{r,a,d}^H{R}^{-1}y}{v_{r,a,d}^H{R}^{-1}{v}_{r,a.d}};$

In formula, $R=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{d=1}{\overset{G}{\mathrm{\&Sigma;}}}{\left|{\widehat{\mathrm{\&alpha;}}}_{r,a.d}\right|}^2{v}_{r,a,d}{v}_{r,a,d}^H$ R=1 ... P, a=1 ... K, d=1 ... G is wherein in R represent the reflection coefficient of the target that last iteration obtains; When first time iteration, in R for initial target reflection factor.

Effect of the present invention can be illustrated by following emulation:

1, simulated conditions and content

And the moving target detect of the to the effect that relevant MIMO radar of our research comparatively complicated due to the situation of can not ignore Doppler, therefore the present invention carries out the detection simulation of the parameter when target is moving-target, the target of random generation 4 motion, suppose that all targets are all positioned at the position that Doppler's number is 1, the region that we are concerned about is angle is from-30 degree to 30 degree, and doppler angle is from-30 degree to 30 degree.Emitting antenna Mt=5, accept antenna Mr=5, the number of subpulse is L=32, the frequency of operation of carrier wave is 1.24GHz, the wavelength of the distance dt=2.5* carrier wave between emitting antenna, accept the wavelength of the distance dr=0.5* carrier wave between antenna, to-noise ratio SNA=20, wherein SNA=10log (tr (S ^hs)/L σ ²), the mark of tr representing matrix, noise for M _rwhite Gaussian noise, σ that row L+P-1 arranges ²for the variance of Gaussian noise; Distance is divided into 12 frequency bands and P=12, angular divisions is 7 frequency bands and K=7, doppler angle are divided into 5 frequency bands and H=5.Observation station namely an observation station is only had.Iteration self-adapting algorithm is adopted to emulate target localization.

2, the result of emulation as shown in Figures 2 and 3, when adopting DAS method to carry out parameter estimation to target, there is lower resolution and more weak AF panel, be difficult to estimate target accurately, a lot of mistakes can be produced as the place that will be target, being estimated as target, when adopting iteration self-adapting algorithm (IAA) to carry out moving target detect to it, the parameter of target can being oriented under similar circumstances comparatively accurately.Moreover due to this method be customer parameter freely and non-parametric adaptive algorithm, so still target can be oriented very accurately when the situation that snapshot number lacks even only has a snapshot.In addition, the method does not need auxiliary data.The v obtained after only needing the y by receiving and conversion goes to obtain the target component of target, thus solve existing space-time adaptive algorithm and need auxiliary data to go to estimate the master data of clutter and noise harmonics matrix, but under non-homogeneous clutter environment, the problem of the auxiliary data of condition cannot be met.And this algorithm is compared with DAS method, when improving resolution and reducing secondary lobe, time and the DAS of this method computing are almost equal, compared to the space-time adaptive algorithm needing auxiliary data, because this method does not need aided algorithm therefore to improve arithmetic speed to a certain extent.And the method has the feature of fast convergence rate, stable performance.

To sum up, the problem that the present invention adopts iteration self-adapting algorithm effectively can overcome existing moving-target parameter detecting to run into, greatly improves the accuracy of relevant MIMO radar moving target detect.

Claims (1)

1., based on a relevant MIMO radar object detection method for iteration self-adapting algorithm, obtain its location parameter by being optimized the reflection coefficient of moving-target and quiet target respectively, the method is specially:

A, when observed object is quiet target, do not consider Doppler's effect

A1, determine first echoed signal that the n-th observation station observes and transmit, the reflection of target

Between coefficient and noise, relational model is as follows:

$Y^H\left(n\right)=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{r,a}{b}_a\left(n\right)a_a^T\left(n\right){{\tilde{S}}^{H}J}_r+E^H\left(n\right)$

In formula, Y (n) is first echoed signal that the n-th observation station observes, wherein for the number of observation station; Y ^hn Y (n) is carried out conjugate transpose operation by () expression; P represents along the minimum range unit i.e. number of distance quantifying unit that directions of rays is divided into by distance in radar echo signal process, r=1,2 ... P; K represents that the angle intervals that there is target quantizes number of unit, a=1 ... ..K; α _r,arepresent the reflection coefficient of target region internal object; b _an () is that the receiving array of the n-th observation station guides vector; a _an () is that the emission array of the n-th observation station guides vector; represent a _an () does transpose operation; E (n) represents the additive noise of the n-th observation station Received signal strength, E ^hn E (n) is carried out conjugate transpose operation by () expression; representing will carry out conjugate transpose operation, $\tilde{S}{=\left[\begin{array}{c}S\\ 0_{(P-1)\&times;M_t}\end{array}\right]}_{(L+P-1)\&times;M_t}$ For the waveform matrix that transmits obtained after zero padding process, $S={\left[\begin{array}{cccc}{s}_1& s_2& \&CenterDot;\&CenterDot;\&CenterDot;s_m\&CenterDot;\&CenterDot;\&CenterDot;& s_{M_t}\end{array}\right]}_{L\&times;M_t}$ For the waveform matrix that transmits, wherein, s _mrepresent the orthogonal waveforms of m article of transmission antennas transmit, m=1 ... M _t; M _tfor the number of emitting antenna, L is the number of subpulse of transmitting;

J _r∈ C ^{(L+P-1) × (L+P-1)}for transformation matrix, be used for describing different distance and quantize the signal that receives of section, its expression formula is:

$b_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_r-1)\mathrm{dr})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$

$a_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_t-1)\mathrm{dt})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T,$ Wherein d _nrepresent the distance between signal collection point; θ _arepresent that target quantizes the reflection angle of unit a angle intervals; λ ₀represent radar system carrier wavelength; Dr represents the distance accepted between antenna; Dt represents the distance between emitting antenna; M _rrepresent the number of receiving antenna;

A2, to above-mentioned relation model linearization;

A3, time delay is utilized to superpose the reflection coefficient of DAS algorithm initialization target, as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a}=\frac{v_{r,a}^{H}y}{v_{r,a}^H{v}_{r,a}};$

Wherein:

$\begin{array}{c}{v}_{r,a}=\left[\begin{array}{c}{\tilde{v}}_{r,a}\left(1\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a}\left(\tilde{N}\right)\end{array}\right]\&Element;C^{\tilde{N}{M}_r(L+P-1)\&times;1}\end{array}$ ${\tilde{v}}_{r,a}\left(n\right)=\mathrm{vec}\left[b_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H{J}_r\right]\&Element;C^{M_r(L+P-1)\&times;1},$ $n=1,\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N},$

r=1,...P,a=1,...K； $y=\left[\begin{array}{c}\mathrm{vec}\left(Y^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(Y^H\left(\tilde{N}\right)\right)\end{array}\right]$

Wherein represent initialized target reflection factor, represent V _r,acarry out conjugate transpose operation; M _rrepresent the number of receiving antenna; Vec represents matrix is carried out vectorization operation, and arranging successively by the order of rectangular array by matrix is row;

A4, Bayesian model exponent number selection tool is utilized to carry out the reflection coefficient of optimization aim, be specially: time delay is superposed the target reflection factor that DAS is initial, (1) formula of bringing into obtains the Bayes BIC value of initial value, the reflection coefficient of iterative target also upgrades Bayes BIC value, twice Bayes BIC value relatively, when Bayes BIC value no longer reduces, then iteration is stopped to obtain the reflection coefficient of target;

${\mathrm{BIC}}_{\tilde{r},\tilde{a}}\left(\mathrm{\&eta;}\right)={2M}_r\tilde{N}(L+P-1)\&times;\mathrm{In}\left[{\left|\right|y-\underset{(r,a)\&Element;\{J\left(\mathrm{\&eta;}\right)\&cup;(\tilde{r},\tilde{a})\}}{\mathrm{\&Sigma;}}{V}_{r,a}{\hat{a}}_{r,a}\left|\right|}_2^2\right]+4\mathrm{\&eta;In}\left({2M}_r\tilde{N}(L+P-1)\right)---\left(1\right)$

In formula, || .|| ₂represent Euclid norm, represent Euclid norm square, η represents the target number of current selection; 4 represent the number of parameters that each target will estimate; J (η) represents the target sequence number set selected when this iteration, when carrying out first time iteration now hypothesis does not have target; represent a undetermined target sequence number, wherein dong represents the position of undetermined target in distance quantifying unit, represent and do not determine the position of target in angular spacing quantifying unit, after iteration terminates, beyond J (η), the reflection coefficient of part is set as 0, is considered to do not have target;

Wherein, the iterative formula of reflection coefficient is as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a}=\frac{v_{r,a}^H{R}^{-1}y}{v_{r,a}^H{R}^{-1}{v}_{r,a}}$

In formula, wherein in R represent the reflection coefficient of the target that last iteration obtains, when first time iteration, in R represent initial target reflection factor;

B, when target is moving-target, consider Doppler's effect

B1, determine first echoed signal that the n-th observation station observes and transmit, between the reflection coefficient of target and noise, relational model is as follows:

$Y^H\left(n\right)=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{d=1}{\overset{G}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{r,a,d}{b}_a\left(n\right)a_a^T\left(n\right){{\tilde{S}}^H\left({\mathrm{\&omega;}}_d\right)J}_r+E^H\left(n\right)$

In formula, Y (n) is first echoed signal that the n-th observation station observes, wherein p represents along the minimum range unit i.e. number of distance quantifying unit that directions of rays is divided into by distance in radar echo signal process, r=1 ... P; K represents that the angle intervals that there is target quantizes number of unit, a=1 ... ..K; G represents the interval quantizing number of unit of the Doppler that there is target, d=1 ... G; α _{r, a, d}represent the reflection coefficient of target region internal object; b _an () is that the receiving array of the n-th observation station guides vector; a _an () is that the emission array of the n-th observation station guides vector; represent a _an () carries out transpose operation, will conjugate transpose operation, wherein $\tilde{S}\left({\mathrm{\&omega;}}_d\right)={\left[\begin{array}{c}S\left({\mathrm{\&omega;}}_d\right)\\ 0_{(P-1)\&times;M_t}\end{array}\right]}_{(L+P-1)\&times;M_t}$ For the waveform matrix that transmits of introducing Doppler obtained after zero padding process, $S=\left({\mathrm{\&omega;}}_d\right)=\left[\begin{array}{cccc}{\tilde{s}}_1\left({\mathrm{\&omega;}}_d\right)& {\tilde{s}}_2\left({\mathrm{\&omega;}}_d\right)& \&CenterDot;\&CenterDot;\&CenterDot;{\tilde{s}}_m\left({\mathrm{\&omega;}}_d\right)\&CenterDot;\&CenterDot;\&CenterDot;& {\tilde{s}}_{M_t}\end{array}\left({\mathrm{\&omega;}}_d\right)\right],$ Wherein: m=1 ... M _t, d=1 ... G; $d\left({\mathrm{\&omega;}}_d\right)={\left[\begin{array}{cccc}1& e^{{\mathrm{j\&omega;}}_d}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{{\mathrm{j\&omega;}}_d(L-1)}\end{array}\right]}^T,$ S _mrepresent the waveform of m transmission antennas transmit orthogonal signal; ω _dit is the angle Doppler frequency of d Doppler's quantifying unit; M _tfor the number of emitting antenna; L is the number of subpulse of transmitting; the Hadamard product of computing representing matrix; E (n) represents the additive noise in the n-th observation station Received signal strength, E ^hn E (n) is carried out conjugate transpose operation by () expression;

$b_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_r-1)\mathrm{dr})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$

$a_a\left(n\right)={[e^{-(j2\mathrm{\&pi;}\left((n-1)d_n\right)\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}\&CenterDot;\&CenterDot;\&CenterDot;e^{-(j2\mathrm{\&pi;}((n-1)d_n+(M_t-1)\mathrm{dt})\sin \left({\mathrm{\&theta;}}_a\right)/{\mathrm{\&lambda;}}_0)}]}^T;$ $n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;\tilde{N},$ D _nrepresent the distance between signal collection point; θ _arepresent that target quantizes the reflection angle of unit a angle intervals; λ ₀represent radar system carrier wavelength; Dr represents the distance accepted between antenna; Dt represents the distance between emitting antenna; M _rrepresent receiving antenna number;

B2, to above-mentioned relation model linearization;

B3, time delay is utilized to superpose the reflection coefficient of DAS algorithm initialization target, as follows:

${\widehat{\mathrm{\&alpha;}}}_{r,a,d}=\frac{v_{r,a,d}^{H}y}{v_{r,a,d}^H{v}_{r,a,d}}$

Wherein:

$\begin{array}{c}{v}_{r,a,d}=\left[\begin{array}{c}{\tilde{v}}_{r,a,d}\left(1\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\tilde{v}}_{r,a,d}\left(\tilde{N}\right)\end{array}\right]\&Element;C^{\tilde{N}{M}_r(L+P-1)\&times;1}\end{array}$

${\tilde{v}}_{r,a,d}\left(n\right)=\mathrm{vec}\left[b_a\left(n\right)a_a^T\left(n\right){\tilde{S}}^H\left({\mathrm{\&omega;}}_d\right)J_r\right]\&Element;C^{M_r(L+P-1)\&times;1}$

$y=\left[\begin{array}{c}\mathrm{vec}\left(Y^H\left(1\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \mathrm{vec}\left(Y^H\left(\tilde{N}\right)\right)\end{array}\right]$

Wherein represent initialized target reflection factor, represent v _{r, a, d}carry out conjugate transpose operation; Vec represents matrix is carried out vectorization operation, and arranging successively by the order of rectangular array by matrix is row;

B4, Bayesian model exponent number selection tool is utilized to carry out the reflection coefficient of optimization aim, be specially: time delay is superposed the target reflection factor that DAS is initial, (2) formula of bringing into obtains the Bayes BIC value of initial value, the reflection coefficient of iterative target also upgrades Bayes BIC value, twice Bayes BIC value relatively, when Bayes BIC value no longer reduces, then iteration is stopped to obtain the reflection coefficient of target;

${\mathrm{BIC}}_{\tilde{r},\tilde{a},\tilde{d}}\left(\mathrm{\&eta;}\right)={2M}_r\tilde{N}(L+P-1)\&times;\mathrm{In}\left[{\left|\right|y-\underset{(r,a,d)\&Element;\{J\left(\mathrm{\&eta;}\right)\&cup;(\tilde{r},\widetilde{a,}\tilde{d})\}}{\mathrm{\&Sigma;}}{V}_{r,a,d}{\hat{a}}_{r,a,d}\left|\right|}_2^2\right]+5\mathrm{\&eta;In}\left({2M}_r\tilde{N}(L+P-1)\right)---\left(2\right)$

In formula, || .|| ₂represent Euclid norm, represent Euclid norm square, η represents the target number of current selection; 5 represent the number of parameters that each target will estimate; J (η) represents the target sequence number set selected; When carrying out first time iteration now hypothesis does not have target; represent a undetermined target sequence number, wherein represent the position of undetermined target in distance quantifying unit, represent and do not determine the position of target in angular spacing quantifying unit, represent and do not determine the position of target in Doppler's quantifying unit, after iteration terminates, beyond J (η), the reflection coefficient of part is set as 0, is considered to do not have target;

Wherein, the iterative formula of reflection coefficient is as follows:

${\widetilde{\mathrm{\&alpha;}}}_{r,a,d}=\frac{v_{r,a,d}^H{R}^{-1}y}{v_{r,a,d}^H{R}^{-1}{v}_{r,a.d}};$

In formula, $R=\underset{r=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{a=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{d=1}{\overset{G}{\mathrm{\&Sigma;}}}{\left|{\widehat{\mathrm{\&alpha;}}}_{r,a.d}\right|}^2{v}_{r,a,d}{v}_{r,a,d}^H$ r=1,...P,a=1,...K,d=1,...G

Wherein in R represent the reflection coefficient of the target that last iteration obtains; When first time iteration, in R represent initial target reflection factor.