CN103257344A

CN103257344A - Iteration-adaptive-algorithm-based method for detecting coherent MIMO radar target

Info

Publication number: CN103257344A
Application number: CN2013101624794A
Authority: CN
Inventors: 王婧; 曹宁; 鹿浩
Original assignee: Hohai University HHU
Current assignee: Hohai University HHU
Priority date: 2013-05-03
Filing date: 2013-05-03
Publication date: 2013-08-21
Anticipated expiration: 2033-05-03
Also published as: CN103257344B

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

Coherent MIMO Radar Target Detection Method Based on Iterative Adaptive Algorithm

技术领域technical field

本发明涉及一种MIMO雷达目标检测方法，更具体地说是一种基于迭代自适应算法的相干MIMO雷达目标检测方法。The invention relates to a MIMO radar target detection method, in particular to a coherent MIMO radar target detection method based on an iterative adaptive algorithm.

背景技术Background technique

多输入多输出（MIMO）雷达相比相控阵雷达具有对弱目标更高的检测性能、良好的反隐身效果及良好的抗摧毁能力，吸引了越来越多的学者对其进行研究。MIMO雷达一般可以分为两类：第一类为统计MIMO雷达或非相干MIMO雷达，即天线阵元空间稀布，从而可获得空间分集增益，有效的克服目标RCS起伏对雷达检测性能的影响；第二类为相干MIMO,采用较少的天线阵列就可形成很大的虚拟阵列孔径，提高了雷达角度分辨率和干扰抑制能力。Compared with phased array radar, multiple-input multiple-output (MIMO) radar has higher detection performance for weak targets, good anti-stealth effect and good anti-destruction ability, which has attracted more and more scholars to study it. MIMO radar can generally be divided into two categories: the first category is statistical MIMO radar or incoherent MIMO radar, that is, the antenna elements are sparsely distributed in space, so that space diversity gain can be obtained, and the influence of target RCS fluctuation on radar detection performance can be effectively overcome; The second type is coherent MIMO, which can form a large virtual array aperture with fewer antenna arrays, which improves the radar angular resolution and interference suppression capability.

空时自适应（STAP）是一种动目标检测方法，具有杂波抑制能力强，稳健性好、干扰抑制能力强的优势。杂波抑制能力强是因为STAP技术具有空时二维滤波特性。稳健性好是因为STAP技术通过自适应特性，可实现与复杂外界环境的有效匹配；同时，它还可一定程度地补偿多种不可避免的系统误差。干扰抑制能力强是因为STAP可实现对复杂电磁环境下的多种干扰的抑制。将STAP技术与相干MIMO雷达相结合，可以使系统即具有MIMO性能的优越性又具有STAP的优越性，更好的提高对杂波抑制性能，从而可以使的雷达系统获得较高的目标检测、动目标的跟踪性能、弱目标检测的性能及更强的信号截获的能力。Space-time adaptive (STAP) is a moving target detection method, which has the advantages of strong clutter suppression ability, good robustness, and strong interference suppression ability. The strong clutter suppression ability is due to the space-time two-dimensional filtering characteristics of STAP technology. The reason for the good robustness is that the STAP technology can achieve effective matching with the complex external environment through self-adaptive features; at the same time, it can also compensate various inevitable system errors to a certain extent. The strong interference suppression ability is because STAP can suppress various interferences in complex electromagnetic environments. Combining STAP technology with coherent MIMO radar can make the system not only have the advantages of MIMO performance but also have the advantages of STAP, better improve the performance of clutter suppression, so that the radar system can achieve higher target detection, Moving target tracking performance, weak target detection performance and stronger signal interception capability.

无论对于动目标还是静目标，只要得到目标的反射系数则可以知道动目标的位置参数（复幅度、距离、角度、多普勒）、静目标的位置参数（复幅度，距离、角度）。Regardless of whether it is a moving target or a static target, as long as the reflection coefficient of the target is obtained, the position parameters of the moving target (complex amplitude, distance, angle, Doppler) and the position parameters of the static target (complex amplitude, distance, angle) can be known.

现有技术中相干MIMO雷达空时自适应处理方法在复杂的电磁环境下由于压制性干扰造成了杂波自由度急剧增加，传统的自适应处理算法（STAP）的自由度无法满足杂波抑制要求；欺骗性干扰导致杂波的分布的严重非均匀，使得STAP算法无法获得足够的满足独立同分布条件的训练样本。另外，现存的STAP需要辅助数据去估计杂波和噪声谐波矩阵的基本数据，但是具有较高准确度的辅助数据是很难得到的，尤其对于非均匀的杂波环境。为了减少对于辅助数据的依赖，提出了不需要辅助数据的空时自适应算法，例如DAS法，但此类方法却面领着分辨率低高旁瓣的问题。因此本专利拟在现有空时自适应方法的基础上提出改进算法，克服现有STAP和DAS的缺点，更好的发挥相干MIMO雷达以及空时自适应方法的优点。The coherent MIMO radar space-time adaptive processing method in the prior art has a sharp increase in the degree of freedom of clutter due to suppressive interference in a complex electromagnetic environment, and the degree of freedom of the traditional adaptive processing algorithm (STAP) cannot meet the requirements of clutter suppression ; Deceptive interference leads to severe non-uniform distribution of clutter, making it impossible for the STAP algorithm to obtain enough training samples that satisfy the independent and identical distribution conditions. In addition, the existing STAP needs auxiliary data to estimate the basic data of the clutter and noise harmonic matrix, but the auxiliary data with high accuracy is difficult to obtain, especially for the non-uniform clutter environment. In order to reduce the dependence on auxiliary data, space-time adaptive algorithms without auxiliary data are proposed, such as DAS method, but these methods face the problem of low resolution and high side lobes. Therefore, this patent intends to propose an improved algorithm based on the existing space-time adaptive method, overcome the shortcomings of the existing STAP and DAS, and better utilize the advantages of the coherent MIMO radar and the space-time adaptive method.

发明内容Contents of the invention

本发明的目的在于提出一种基于迭代自适应算的相干MIMO雷达动目标检测方法，此方法通过分别对动目标和静目标的反射系数进行优化来获得其位置参数，具体为：The purpose of the present invention is to propose a coherent MIMO radar moving target detection method based on iterative adaptive calculation, this method obtains its position parameter by respectively optimizing the reflection coefficient of the moving target and the static target, specifically:

A、当观测目标为静目标时，不考虑多普勒效果A. When the observation target is a static target, the Doppler effect is not considered

A1、确定第n个观测点观测到的第一个回波信号与发射信号、目标的反射系数和噪声干扰之间关系模型如下：A1. Determine the relationship model between the first echo signal observed at the nth observation point and the transmitted signal, the reflection coefficient of the target and noise interference as follows:

${Y Y}^{H h} ((n no)) = = {Σ Σ}_{r r = = 11}^{P P} {Σ Σ}_{a a = = 11}^{K K} {α α}_{r r,, a a} {b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {{\overset{~ ~}{S S}}^{H h} J J}_{r r} + + {E E.}^{H h} ((n no))$

式中，Y(n)为第n个观测点观测到的第一个回波信号,其中

为观测点的数目；Y^H(n)表示将Y(n)进行共轭转置运算；P表示雷达回波信号处理中沿射线方向按距离分成的最小的距离单元即距离量化单元的数目，r=1,2，…P；K表示存在目标的角度间隔量化单元数目，a=1,.....K；α_r,a表示目标所在区域内目标的反射系数；b_a(n)为第n个观测点的接收阵列引导矢量；a_a(n)为第n个观测点的发射阵列引导矢量；

表示将a_a(n)做转置运算；E(n)表示第n个观测点接收信号的加性噪声，E^H(n)表示将E(n)进行共轭转置运算；

表示将

进行共轭转置运算，

\tilde{S} = {[\begin{matrix} S \\ 0_{(P - 1) \times M_{t}} \end{matrix}]}_{(L + P - 1) \times M_{t}}

为补零处理后得到的发射信号波形矩阵，

S = {[\begin{matrix} s_{1} & s_{2} & \cdot \cdot \cdot s_{m} \cdot \cdot \cdot & s_{M_{t}} \end{matrix}]}_{L \times M_{t}}

为发射信号波形矩阵，其中，s_m表示第m条发射天线发射的正交波形，m=1,...M_t；M_t为发射天线的数目，L为发射信号子脉冲的数目；In the formula, Y(n) is the first echo signal observed at the nth observation point, where

is the number of observation points; Y ^H (n) represents the conjugate transposition operation of Y(n); P represents the number of the smallest distance unit divided by distance along the ray direction in the radar echo signal processing, that is, the number of distance quantization units, r=1,2,...P; K represents the number of angular interval quantization units where the target exists, a=1,...K; α _{r, a} represents the reflection coefficient of the target in the area where the target is located; b _a (n) is the receiving array steering vector of the nth observation point; a _a (n) is the transmitting array steering vector of the nth observation point;

Indicates that a _a (n) is transposed; E(n) indicates the additive noise of the received signal at the nth observation point, and E ^H (n) indicates that E(n) is conjugated and transposed;

express will

Perform the conjugate transpose operation,

\tilde{S} = {[\begin{matrix} S \\ 0_{(P - 1) \times m_{t}} \end{matrix}]}_{(L + P - 1) \times m_{t}}

is the transmitted signal waveform matrix obtained after zero padding,

S = {[\begin{matrix} {the s}_{1} & {the s}_{2} & &Center Dot; &Center Dot; \cdot {the s}_{m} &Center Dot; \cdot \cdot & {the s}_{m_{t}} \end{matrix}]}_{L \times m_{t}}

Be the transmit signal waveform matrix, wherein, s _m represents the orthogonal waveform transmitted by the m transmit antenna, m=1,...M _t ; M _t is the number of transmit antennas, and L is the number of transmit signal sub-pulses;

J_r∈C^{(L+P-1)×(L+P-1)}为变换矩阵，用来描述不同距离量化段接收到的信号，其表达式为：J _r ∈ C ^{(L+P-1)×(L+P-1)} is a transformation matrix, which is used to describe the signals received by different distance quantization sections, and its expression is:

${b b}_{a a} ((n no)) = = {[[{e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no})) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))} \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no} + + (({M m}_{r r} - - 11)) dr dr)) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))}]]}^{T T};;$

$a_{a} (n) = {[e^{- (j 2 π ((n - 1) d_{n}) \sin (θ_{a}) / λ_{0})} \cdot \cdot \cdot e^{- (j 2 π ((n - 1) d_{n} + (M_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T},$ 其中 $n = 1,2, \cdot \cdot \cdot \tilde{N},$ d_n表示信号收集点间的距离;θ_a表示目标在第a个角度间隔量化单元的反射角;λ₀表示雷达系统载波波长;dr表示接受天线间的距离;dt表示发射天线间的距离;M_r表示接收天线的个数； $a_{a} (no) = {[e^{- (j 2 π ((no - 1) d_{no}) \sin (θ_{a}) / λ_{0})} \cdot \cdot \cdot e^{- (j 2 π ((no - 1) d_{no} + (m_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T},$ in $no = 1,2, \cdot \cdot \cdot \tilde{N},$ d _n represents the distance between signal collection points; θ _a represents the reflection angle of the target at the ath angular interval quantization unit; λ ₀ represents the carrier wavelength of the radar system; dr represents the distance between receiving antennas; dt represents the distance between transmitting antennas; M _r represents the number of receiving antennas;

A2、对上述关系模型线性化；A2. Linearize the above relational model;

A3、利用延时叠加DAS算法初始化目标的反射系数，如下：A3. Use the delay superposition DAS algorithm to initialize the reflection coefficient of the target, as follows:

${\overset{^^}{α α}}_{r r,, a a} = = \frac{{v v}_{r r,, a a}^{H h} y the y}{{v v}_{r r,, a a}^{H h} {v v}_{r r,, a a}};;$

其中：in:

$\begin{matrix} {v v}_{r r,, a a} = = [\begin{matrix} {\overset{~ ~}{v v}}_{r r,, a a} ((11)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {\overset{~ ~}{v v}}_{r r,, a a} ((\overset{~ ~}{N N})) \end{matrix}] &Element; &Element; {C C}^{\overset{~ ~}{N N} {M m}_{r r} ((L L + + P P - - 11)) \times \times 11} \end{matrix}$ ${\overset{~ ~}{v v}}_{r r,, a a} ((n no)) = = vec vec [[{b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {\overset{~ ~}{S S}}^{H h} {J J}_{r r}]] &Element; &Element; {C C}^{{M m}_{r r} ((L L + + P P - - 11)) \times \times 11},,$ $n no = = 11,, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; \overset{~ ~}{N N},,$

r=1,...P,a=1,...K； $y = [\begin{matrix} vec (Y^{H} (1)) \\ \cdot \\ \cdot \\ \cdot \\ vec (Y^{H} (\tilde{N})) \end{matrix}]$ 其中

表示初始化的目标反射系数，

表示将V_r,a进行共轭转置运算；M_r表示接收天线的个数；vec表示将矩阵进行向量化操作，即将矩阵按矩阵列的次序依次排为一列；r=1,...P,a=1,...K;

the y = [\begin{matrix} vec (Y^{h} (1)) \\ \cdot \\ \cdot \\ \cdot \\ vec (Y^{h} (\tilde{N})) \end{matrix}]

in

represents the initial target reflection coefficient,

Indicates that V _{r and a} are conjugated and transposed; M _r indicates the number of receiving antennas; vec indicates that the matrix is vectorized, that is, the matrix is arranged in a row in the order of the matrix columns;

A4、利用贝叶斯模型阶数选择工具来优化目标的反射系数，具体为：将延时叠加DAS初始的目标反射系数，带入（1）式得到初始值的贝叶斯BIC值，迭代目标的反射系数并更新贝叶斯BIC值，比较前后两次贝叶斯BIC值，当贝叶斯BIC值不再减少时，则停止迭代得到目标的反射系数；A4. Use the Bayesian model order selection tool to optimize the reflection coefficient of the target, specifically: put the initial target reflection coefficient of the delayed superposition DAS into formula (1) to obtain the Bayesian BIC value of the initial value, and iterate the target and update the Bayesian BIC value, compare the two Bayesian BIC values before and after, when the Bayesian BIC value no longer decreases, stop iterating to get the reflection coefficient of the target;

${BIC BIC}_{\overset{~ ~}{r r},, \overset{~ ~}{a a}} ((η η)) = = {22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)) \times \times In In [[{| | | | y the y - - \underset{((r r,, a a)) &Element; &Element; {{J J ((η η)) \cup \cup ((\overset{~ ~}{r r},, \overset{~ ~}{a a}))}}}{Σ Σ} {V V}_{r r,, a a} {\overset{^^}{a a}}_{r r,, a a} | | | |}_{22}^{22}]] + + 44 ηIn ηIn (({22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)))) - - - - - - ((11))$

式中，||.||₂表示欧几里得范数，

表示欧几里得范数的平方，η表示当前选择的目标个数；4代表每个目标要估计的参数个数；J(η)表示已经选择的目标序号集合。当进行第一次迭代时

此时假设没有目标存在；

表示一个未确定的目标序号，其中

表示未确定的目标在距离量化单元的位置，

表示未确定目标在角间隔量化单元的位置，

迭代结束后，J(η)以外部分的反射系数被设为0，被认为没有目标存在；其中，反射系数的迭代公式如下：In the formula, ||.|| ₂ represents the Euclidean norm,

Represents the square of the Euclidean norm, η represents the number of currently selected targets; 4 represents the number of parameters to be estimated for each target; J(η) represents the set of selected target numbers. when doing the first iteration

At this time, it is assumed that no target exists;

Indicates an undetermined target sequence number, where

Indicates the position of the undetermined target in the distance quantization unit,

Indicates the position of the undetermined target in the angular interval quantization unit,

After the iteration, the reflection coefficient of the part other than J(η) is set to 0, and it is considered that there is no target; the iteration formula of the reflection coefficient is as follows:

${\overset{^^}{α α}}_{r r,, a a} = = \frac{{v v}_{r r,, a a}^{H h} {R R}^{- - 11} y the y}{{v v}_{r r,, a a}^{H h} {R R}^{- - 11} {v v}_{r r,, a a}}$

式中，

其中R中的表示表示上一次迭代得到的目标的反射系数，当第一次迭代时，R中的表示初始的目标反射系数；In the formula,

where in R Indicates the reflection coefficient of the target obtained in the previous iteration. When the first iteration is performed, the Indicates the initial target reflection coefficient;

B、当目标为动目标时，考虑到多普勒效果B. When the target is a moving target, consider the Doppler effect

B1、确定第n个观测点观测到的第一个回波信号与发射信号、目标的反射B1. Determine the first echo signal observed at the nth observation point, the transmitted signal, and the reflection of the target

系数和噪声干扰之间关系模型如下：The relationship model between coefficients and noise interference is as follows:

${Y Y}^{H h} ((n no)) = = {Σ Σ}_{r r = = 11}^{P P} {Σ Σ}_{a a = = 11}^{K K} {Σ Σ}_{d d = = 11}^{G G} {α α}_{r r,, a a,, d d} {b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {\overset{~ ~}{S S}}^{H h} (({ω ω}_{d d})) {J J}_{r r} + + {E E.}^{H h} ((n no))$

式中，Y(n)为第n个观测点接收到的第一个回波信号，其中

P表示雷达回波信号处理中沿射线方向按距离分成的最小的距离单元即距离量化单元的数目，r=1,…P；K表示存在目标的角度间隔量化单元数目，a=1,.....K；G表示存在目标的多普勒间隔量化单元数目，d=1,…G；α_r,a,d表示目标所在区域内目标的反射系数；b_a(n)为第n个观测点的接收阵列引导矢量；a_a(n)为第n个观测点的发射阵列引导矢量；

表示将a_a(n)进行转置运算，

是将

共轭转置运算，其中

\tilde{S} (ω_{d}) = {[\begin{matrix} S (ω_{d}) \\ 0_{(P - 1) \times M_{t}} \end{matrix}]}_{(L + P - 1) \times M_{t}}

为补零处理后得到的引入多普勒的发射信号波形矩阵，

S (ω_{d}) = [\begin{matrix} {\tilde{s}}_{1} (ω_{d}) & {\tilde{s}}_{2} (ω_{d}) & \cdot \cdot \cdot {\tilde{s}}_{m} (ω_{d}) \cdot \cdot \cdot & {\tilde{s}}_{M_{t}} (ω_{d}) \end{matrix}],

其中：m=1,...M_t,d=1,...G；

d (ω_{d}) = {[\begin{matrix} 1 & e^{{jω}_{d}} & \cdot \cdot \cdot & e^{{jω}_{d} (L - 1)} \end{matrix}]}^{T},

s_m表示第m个发射天线发射正交信号的波形；ω_d是第d个多普勒量化单元的角多普勒频率；M_t为发射天线的数目；L为发射信号子脉冲的数目；

运算表示矩阵的Hadamard乘积；E(n)表示第n个观测点接收信号中的加性噪声，E^H(n)表示将E(n)进行共轭转置运算；In the formula, Y(n) is the first echo signal received by the nth observation point, where

P represents the number of the smallest distance units divided by distance along the ray direction in the radar echo signal processing, that is, the number of distance quantization units, r=1,...P; K represents the number of angular interval quantization units with targets, a=1,... ...K; G represents the number of Doppler interval quantization units where the target exists, d=1,...G; α _{r, a, d} represent the reflection coefficient of the target in the area where the target is located; b _a (n) is the nth The receiving array steering vector of the observation point; a _a (n) is the transmitting array steering vector of the nth observation point;

Indicates that a _a (n) is transposed,

will be

Conjugate transpose operation, where

\tilde{S} (ω_{d}) = {[\begin{matrix} S (ω_{d}) \\ 0_{(P - 1) \times m_{t}} \end{matrix}]}_{(L + P - 1) \times m_{t}}

is the transmitted signal waveform matrix introduced into Doppler obtained after zero padding,

S (ω_{d}) = [\begin{matrix} {\tilde{the s}}_{1} (ω_{d}) & {\tilde{the s}}_{2} (ω_{d}) & &Center Dot; \cdot &Center Dot; {\tilde{the s}}_{m} (ω_{d}) &Center Dot; &Center Dot; &Center Dot; & {\tilde{the s}}_{m_{t}} (ω_{d}) \end{matrix}],

in: m=1,...M _t ,d=1,...G;

d (ω_{d}) = {[\begin{matrix} 1 & e^{{jω}_{d}} & \cdot \cdot &Center Dot; & e^{{jω}_{d} (L - 1)} \end{matrix}]}^{T},

s _m represents the waveform of the orthogonal signal transmitted by the m-th transmit antenna; ω _d is the angular Doppler frequency of the d-th Doppler quantization unit; M _t is the number of transmit antennas; L is the number of sub-pulses of the transmit signal;

The operation represents the Hadamard product of the matrix; E(n) represents the additive noise in the received signal of the nth observation point, and E ^H (n) represents the conjugate transposition operation of E(n);

$a_{a} (n) = {[e^{- (j 2 π ((n - 1) d_{n}) \sin (θ_{a}) / λ_{0})} \cdot \cdot \cdot e^{- (j 2 π ((n - 1) d_{n} + (M_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T};$ $n = 1,2, \cdot \cdot \cdot \tilde{N},$ d_n表示信号收集点间的距离;θ_a表示目标在第a个角度间隔量化单元的反射角;λ₀表示雷达系统载波波长;dr表示接受天线间的距离;dt表示发射天线间的距离;M_r表示接收天线的个数； $a_{a} (no) = {[e^{- (j 2 π ((no - 1) d_{no}) \sin (θ_{a}) / λ_{0})} \cdot \cdot \cdot e^{- (j 2 π ((no - 1) d_{no} + (m_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T};$ $no = 1,2, &Center Dot; &Center Dot; &Center Dot; \tilde{N},$ d _n represents the distance between signal collection points; θ _a represents the reflection angle of the target at the ath angle interval quantization unit; λ ₀ represents the carrier wavelength of the radar system; dr represents the distance between receiving antennas; dt represents the distance between transmitting antennas; M _r represents the number of receiving antennas;

B2、对上述关系模型线性化；B2. Linearize the above relational model;

B3、利用延时叠加DAS算法初始化目标的反射系数，如下：B3. Use the delayed superposition DAS algorithm to initialize the reflection coefficient of the target, as follows:

${\overset{^^}{α α}}_{r r,, a a,, d d} = = \frac{{v v}_{r r,, a a,, d d}^{H h} y the y}{{v v}_{r r,, a a,, d d}^{H h} {v v}_{r r,, a a,, d d}}$

其中：in:

$\begin{matrix} {v v}_{r r,, a a,, d d} = = [\begin{matrix} {\overset{~ ~}{v v}}_{r r,, a a,, d d} ((11)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {\overset{~ ~}{v v}}_{r r,, a a,, d d} ((\overset{~ ~}{N N})) \end{matrix}] &Element; &Element; {C C}^{\overset{~ ~}{N N} {M m}_{r r} ((L L + + P P - - 11)) \times \times 11} \end{matrix}$

${\overset{~ ~}{v v}}_{r r,, a a,, d d} ((n no)) = = vec vec [[{b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {\overset{~ ~}{S S}}^{H h} (({ω ω}_{d d})) {J J}_{r r}]] &Element; &Element; {C C}^{{M m}_{r r} ((L L + + P P - - 11)) \times \times 11}$

$y the y = = [\begin{matrix} vec vec (({Y Y}^{H h} ((11)))) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ vec vec (({Y Y}^{H h} ((\overset{~ ~}{N N})))) \end{matrix}]$

其中

表示初始化的目标反射系数，

表示将v_r,a,d进行共轭转置运算；vec表示将矩阵进行向量化操作，即将矩阵按矩阵列的次序依次排为一列；in

represents the initial target reflection coefficient,

Indicates that v _{r, a, and d} are conjugated and transposed; vec indicates that the matrix is vectorized, that is, the matrix is arranged in a row in the order of the matrix columns;

B4、利用贝叶斯模型阶数选择工具来优化目标的反射系数，具体为：将延时叠加DAS初始的目标反射系数，带入（2）式得到初始值的贝叶斯BIC值，迭代目标的反射系数并更新贝叶斯BIC值，比较前后两次贝叶斯BIC值，当贝叶斯BIC值不再减少时，则停止迭代得到目标的反射系数；B4. Use the Bayesian model order selection tool to optimize the reflection coefficient of the target, specifically: put the initial target reflection coefficient of the delayed superimposition DAS into (2) to obtain the initial Bayesian BIC value, and iterate the target and update the Bayesian BIC value, compare the two Bayesian BIC values before and after, when the Bayesian BIC value no longer decreases, stop iterating to get the reflection coefficient of the target;

${BIC BIC}_{\overset{~ ~}{r r},, \overset{~ ~}{a a},, \overset{~ ~}{d d}} ((η η)) = = {22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)) \times \times In In [[{| | | | y the y - - \underset{((r r,, a a,, d d)) &Element; &Element; {{J J ((η η)) \cup \cup ((\overset{~ ~}{r r},, \overset{~ ~}{a a,,} \overset{~ ~}{d d}))}}}{Σ Σ} {V V}_{r r,, a a,, d d} {\overset{^^}{a a}}_{r r,, a a,, d d} | | | |}_{22}^{22}]] + + 55 ηIn ηIn (({22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)))) - - - - - - ((22))$

式中，||·||₂表示欧几里得范数，

表示欧几里得范数的平方，η表示当前选择的目标个数；5代表每个目标要估计的参数个数；J(η)表示已经选择的目标序号集合。当进行第一次迭代时

此时假设没有目标存在；

表示一个未确定的目标序号，其中

表示未确定的目标在距离量化单元的位置，

表示未确定目标在角间隔量化单元的位置，

表示未确定目标在多普勒量化单元的位置，

迭代结束后，J(η)以外部分的反射系数被设为0，被认为没有目标存在；where ||·|| ₂ represents the Euclidean norm,

Represents the square of the Euclidean norm, η represents the number of currently selected targets; 5 represents the number of parameters to be estimated for each target; J(η) represents the set of selected target numbers. when doing the first iteration

At this time, it is assumed that no target exists;

Indicates an undetermined target sequence number, where

Indicates the position of the undetermined target in the Doppler quantization unit,

After the iteration, the reflection coefficient of the part other than J(η) is set to 0, and it is considered that there is no target;

其中，反射系数的迭代公式如下：Among them, the iterative formula of the reflection coefficient is as follows:

${\overset{^^}{α α}}_{r r,, a a,, d d} = = \frac{{v v}_{r r,, a a,, d d}^{H h} {R R}^{- - 11} y the y}{{v v}_{r r,, a a,, d d}^{H h} {{R R}^{- - 11} v v}_{r r,, a a . . d d}};;$

式中， $R = Σ_{r = 1}^{P} Σ_{a = 1}^{K} Σ_{d = 1}^{G} {| {\hat{α}}_{r, a . d} |}^{2} v_{r, a, d} v_{r, a, d}^{H}$ r=1,...P,a=1,...K,d=1,...GIn the formula, $R = Σ_{r = 1}^{P} Σ_{a = 1}^{K} Σ_{d = 1}^{G} {| {\hat{α}}_{r, a . d} |}^{2} v_{r, a, d} v_{r, a, d}^{h}$ r=1,...P,a=1,...K,d=1,...G

其中R中的

表示上一次迭代得到的目标的反射系数;当第一次迭代时，R中的

表示初始的目标反射系数。where in R

Indicates the reflection coefficient of the target obtained in the previous iteration; when the first iteration is performed, the

Indicates the initial target reflection coefficient.

本发明与现有技术相比具有以下显著的进步：Compared with the prior art, the present invention has the following remarkable progress:

（1）本发明的方法不需要辅助数据，只需要通过接受到的y和变换后得到的v去得到目标的目标参数，从而解决了现有空时自适应算法需要辅助数据去估计杂波和噪声谐波矩阵的基本数据，在非均匀杂波环境下，无法得到满足条件的辅助数据的问题。(1) The method of the present invention does not require auxiliary data, and only needs to obtain the target parameters of the target through the received y and the transformed v, thereby solving the problem that the existing space-time adaptive algorithm needs auxiliary data to estimate clutter and The basic data of the noise harmonic matrix cannot obtain the auxiliary data that meets the conditions in the non-uniform clutter environment.

（2）现存的自适应算法，例如Capon法和幅度相位估计算法（APES）可以减少杂波的影响。但当接受到的信号处于低信噪比的情况下，如果在快照的数目不够多的情况下，MIMO目标检测性能将会大大的减弱，但迭代自适应算法是用户参数自由和非参数的自适应算法，可以在几个甚至只有一个快照的情况，仍可以较为准确的得到目标的参数。(2) Existing adaptive algorithms, such as Capon method and amplitude phase estimation algorithm (APES) can reduce the influence of clutter. But when the received signal is in the case of low signal-to-noise ratio, if the number of snapshots is not enough, the performance of MIMO target detection will be greatly weakened, but the iterative adaptive algorithm is user parameter free and non-parametric The adaptive algorithm can obtain the parameters of the target more accurately even in the case of several or even only one snapshot.

（3）本方法进一步改善了DAS估计分辨率低和高旁瓣的性能。将DAS法做为目标参数估计的初始化方法，采用BIC模型阶数选择工具来改善目标参数估计的准确性。(3) This method further improves the performance of DAS estimation with low resolution and high sidelobes. The DAS method is used as the initialization method of the target parameter estimation, and the BIC model order selection tool is used to improve the accuracy of the target parameter estimation.

（4）现存的空时自适应算法运算量高，但此算法具有收敛速度快、性能稳定运算量低的特点。(4) Existing space-time adaptive algorithms have high computational complexity, but this algorithm has the characteristics of fast convergence speed, stable performance and low computational complexity.

下面结合附图和具体实施方式对本发明作进一步详细的描述；Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail;

附图说明Description of drawings

图1是本发明的相干MIMO目标检测系统的流程图；Fig. 1 is the flowchart of coherent MIMO target detection system of the present invention;

图2是DAS法动目标检测仿真图；Figure 2 is a simulation diagram of DAS method moving target detection;

图3是迭代自适应算法（IAA）动目标检测仿真图。Fig. 3 is a simulation diagram of moving target detection by Iterative Adaptive Algorithm (IAA).

具体实施方式Detailed ways

如图1所示，本发明一种基于迭代自适应算法的相干MIMO雷达目标检测方法，该方法通过分别对动目标和静目标的反射系数进行优化来获得其位置参数，具体为：As shown in Figure 1, a coherent MIMO radar target detection method based on an iterative adaptive algorithm of the present invention, the method obtains its position parameters by optimizing the reflection coefficients of moving targets and static targets respectively, specifically:

A当观测目标为静目标时，不考虑多普勒效果A When the observation target is a static target, the Doppler effect is not considered

式中，Y(n)为第n个观测点接收到的第一个回波信号,其中

表示将

进行共轭转置运算，

\tilde{S} = {[\begin{matrix} S \\ 0_{(P - 1) \times M_{t}} \end{matrix}]}_{(L + P - 1) \times M_{t}}

为补零处理后得到的发射信号波形矩阵，

S {= [\begin{matrix} s_{1} & s_{2} & \cdot \cdot \cdot s_{m} \cdot \cdot \cdot & s_{M_{t}} \end{matrix}]}_{L \times M_{t}}

为发射信号波形矩阵，其中，s_m表示第m条发射天线发射的正交波形，m=1,...M_t；M_t为发射天线的数目，L为发射信号子脉冲的数目；J_r∈C^{(L+P-1)×(L+P-1)}为变换矩阵，用来描述不同距离量化段接收到的信号，其表达式为：In the formula, Y(n) is the first echo signal received by the nth observation point, where

express will

Perform the conjugate transpose operation,

\tilde{S} = {[\begin{matrix} S \\ 0_{(P - 1) \times m_{t}} \end{matrix}]}_{(L + P - 1) \times m_{t}}

is the transmitted signal waveform matrix obtained after zero padding,

S {= [\begin{matrix} {the s}_{1} & {the s}_{2} & \cdot \cdot &Center Dot; {the s}_{m} &Center Dot; &Center Dot; &Center Dot; & {the s}_{m_{t}} \end{matrix}]}_{L \times m_{t}}

is the transmit signal waveform matrix, where s _m represents the orthogonal waveform transmitted by the mth transmit antenna, m=1,...M _t ; M _t is the number of transmit antennas, and L is the number of transmit signal sub-pulses; J _r ∈ C ^{(L+P-1)×(L+P-1)} is a transformation matrix, which is used to describe the signals received by different distance quantization sections, and its expression is:

${b b}_{a a} ((n no)) = = {[[{e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no})) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))} \cdot \cdot \cdot \cdot \cdot \cdot {e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no} + + (({M m}_{r r} - - 11)) dr dr)) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))}]]}^{T T};;$

$a_{a} (n) = {[e^{- (j 2 π ((n - 1) d_{n}) \sin (θ_{a}) / λ_{0})} \cdot \cdot \cdot e^{- (j 2 π ((n - 1) d_{n} + (M_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T},$ 其中 $n = 1,2, \cdot \cdot \cdot \tilde{N},$ d_n表示信号收集点间的距离;θ_a表示目标在第a个角度间隔量化单元的反射角;λ₀表示雷达系统载波波长;dr表示接受天线间的距离;dt表示发射天线间的距离;M_r表示接收天线的数目； $a_{a} (no) = {[e^{- (j 2 π ((no - 1) d_{no}) \sin (θ_{a}) / λ_{0})} &Center Dot; &Center Dot; &Center Dot; e^{- (j 2 π ((no - 1) d_{no} + (m_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T},$ in $no = 1,2, &Center Dot; &Center Dot; &Center Dot; \tilde{N},$ d _n represents the distance between signal collection points; θ _a represents the reflection angle of the target at the ath angular interval quantization unit; λ ₀ represents the carrier wavelength of the radar system; dr represents the distance between receiving antennas; dt represents the distance between transmitting antennas; M _r represents the number of receiving antennas;

A2、对上述关系模型线性化，

其中

A = [\begin{matrix} v_{1,1} & v_{1,2} & {\cdot \cdot \cdot v}_{r, a} \cdot \cdot \cdot & v_{P, K} \end{matrix}] &Element; C^{\tilde{N} M_{r} (L + P - 1) \times PK}

x=[α_1,1 α_1,2 …α_r,a… α_P,K]^T∈C^PK×1

v_{r, a} = [\begin{matrix} {\tilde{v}}_{r, a} (1) \\ \cdot \\ \cdot \\ \cdot \\ {\tilde{v}}_{r, a} (n) \\ \cdot \\ \cdot \\ \cdot \\ {\tilde{v}}_{r, a} (\tilde{N}) \end{matrix}] &Element; C^{\tilde{N} M_{r} (L + P - 1) \times 1}

{\tilde{v}}_{r, a} (n) = vec [b_{a} (n) a_{a}^{T} (n) {\tilde{S}}^{H} J_{r}] &Element; C^{M_{r} (L + P - 1) \times 1},

n = 1, \cdot \cdot \cdot \tilde{N}

r=1,...P,a=1,...K；

e = [\begin{matrix} vec (E^{H} (1)) \\ \cdot \\ \cdot \\ \cdot \\ vec (E^{H} (\tilde{N})) \end{matrix}],

y = [\begin{matrix} vec (Y^{H} (1)) \\ \cdot \\ \cdot \\ \cdot \\ vec (Y^{H} (\tilde{N})) \end{matrix}];

M_r表示接收天线的数目；α_r,a表示目标所在区域内目标的反射系数;vec表示将矩阵进行向量化操作，即将矩阵按矩阵列的次序依次排为一列；A2. Linearize the above relational model,

in

A = [\begin{matrix} v_{1,1} & v_{1,2} & {&Center Dot; &Center Dot; &Center Dot; v}_{r, a} \cdot \cdot &Center Dot; & v_{P, K} \end{matrix}] &Element; C^{\tilde{N} m_{r} (L + P - 1) \times PK}

x=[α _1,1 α _1,2 …α _r,a … α _P,K ] ^T ∈ ^{C PK×1}

v_{r, a} = [\begin{matrix} {\tilde{v}}_{r, a} (1) \\ &Center Dot; \\ &Center Dot; \\ &Center Dot; \\ {\tilde{v}}_{r, a} (no) \\ \cdot \\ \cdot \\ \cdot \\ {\tilde{v}}_{r, a} (\tilde{N}) \end{matrix}] &Element; C^{\tilde{N} m_{r} (L + P - 1) \times 1}

{\tilde{v}}_{r, a} (no) = vec [b_{a} (no) a_{a}^{T} (no) {\tilde{S}}^{h} J_{r}] &Element; C^{m_{r} (L + P - 1) \times 1},

no = 1, &Center Dot; &Center Dot; \cdot \tilde{N}

r=1,...P,a=1,...K;

e = [\begin{matrix} vec ({E.}^{h} (1)) \\ &Center Dot; \\ &Center Dot; \\ &Center Dot; \\ vec ({E.}^{h} (\tilde{N})) \end{matrix}],

the y = [\begin{matrix} vec (Y^{h} (1)) \\ \cdot \\ \cdot \\ \cdot \\ vec (Y^{h} (\tilde{N})) \end{matrix}];

M _r represents the number of receiving antennas; α _{r, a} represents the reflection coefficient of the target in the area where the target is located; vec represents the vectorization operation of the matrix, that is, the matrix is arranged in a row in the order of the matrix columns;

A3、利用延时叠加DAS算法初始化目标的反射系数，如下：A3. Use the delayed superposition DAS algorithm to initialize the reflection coefficient of the target, as follows:

其中

表示初始化的目标反射系数，

表示将V_r,a进行共轭转置运算；in

represents the initial target reflection coefficient,

Indicates that V _{r, a} is subjected to a conjugate transpose operation;

式中，||.||₂表示欧几里得范数，

此时假设没有目标存在；

表示一个未确定的目标序号，其中

表示未确定的目标在距离量化单元的位置，表示未确定目标在角间隔量化单元的位置，

迭代结束后，J(η)以外部分的反射系数被设为0，被认为没有目标存在；In the formula, ||.|| ₂ represents the Euclidean norm,

At this time, it is assumed that no target exists;

Indicates an undetermined target sequence number, where

Indicates the position of the undetermined target in the distance quantization unit, Indicates the position of the undetermined target in the angular interval quantization unit,

式中，

其中R中的

表示表示上一次迭代得到的目标的反射系数，当第一次迭代时，R中的

表示初始的目标反射系数；通过

计算得到新的

更新贝叶斯BIC值，比较前后两次贝叶斯BIC值，当贝叶斯BIC值不再减少时得到满足条件的

In the formula,

where in R

Indicates the reflection coefficient of the target obtained in the previous iteration. When the first iteration is performed, the

Indicates the initial target reflection coefficient; by

calculate the new

Update the Bayesian BIC value, compare the two Bayesian BIC values before and after, and get the satisfying condition when the Bayesian BIC value no longer decreases

B1、确定第n个观测点接收到的第一个回波信号与发射信号、目标的反射系数和噪声干扰之间关系模型如下：B1. Determine the relationship model between the first echo signal received by the nth observation point and the transmitted signal, the reflection coefficient of the target and noise interference as follows:

式中，Y(n)为第n个观测点接收到的第一个回波信号，其中

P表示雷达回波信号处理中沿射线方向按距离分成的最小的距离单元即距离量化单元的数目，r=1,…P；K表示存在目标的角度间隔量化单元数目，a=1,.....K；G表示存在目标的多普勒间隔量化单元数目，d=1,…G；α_r,a,d表示目标所在区域内目标的反射系数；b_a(n)为第n个观测点的接收阵列引导矢量；a_a(n)为第n个观测点的发射阵列引导矢量；表示将a_a(n)进行转置运算，

是将

共轭转置运算，其中

\tilde{S} (ω_{d}) = {[\begin{matrix} S (ω_{d}) \\ 0_{(P - 1) \times M_{t}} \end{matrix}]}_{(L + P - 1) \times M_{t}}

为补零处理后得到的引入多普勒的发射信号波形矩阵，

S (ω_{d}) = [\begin{matrix} {\tilde{s}}_{1} (ω_{d}) & {\tilde{s}}_{2} (ω_{d}) & \cdot \cdot \cdot {\tilde{s}}_{m} (ω_{d}) \cdot \cdot \cdot & {\tilde{s}}_{M_{t}} (ω_{d}) \end{matrix}],

其中：

m=1,...M_t,d=1,...G；

d (ω_{d}) = {[\begin{matrix} 1 & e^{{jω}_{d}} & \cdot \cdot \cdot & e^{{jω}_{d} (L - 1)} \end{matrix}]}^{T},

P indicates the number of the smallest distance units divided by distance along the ray direction in the radar echo signal processing, that is, the number of distance quantization units, r=1,...P; K indicates the number of angular interval quantization units with targets, a=1,... ...K; G represents the number of Doppler interval quantization units where there is a target, d=1,...G; α _{r, a, d} represent the reflection coefficient of the target in the area where the target is located; b _a (n) is the nth The receiving array steering vector of the observation point; a _a (n) is the transmitting array steering vector of the nth observation point; Indicates that a _a (n) is transposed,

will be

Conjugate transpose operation, where

\tilde{S} (ω_{d}) = {[\begin{matrix} S (ω_{d}) \\ 0_{(P - 1) \times m_{t}} \end{matrix}]}_{(L + P - 1) \times m_{t}}

S (ω_{d}) = [\begin{matrix} {\tilde{the s}}_{1} (ω_{d}) & {\tilde{the s}}_{2} (ω_{d}) & &Center Dot; &Center Dot; &Center Dot; {\tilde{the s}}_{m} (ω_{d}) &Center Dot; \cdot &Center Dot; & {\tilde{the s}}_{m_{t}} (ω_{d}) \end{matrix}],

in:

m=1,...M _t ,d=1,...G;

d (ω_{d}) = {[\begin{matrix} 1 & e^{{jω}_{d}} & &Center Dot; &Center Dot; \cdot & e^{{jω}_{d} (L - 1)} \end{matrix}]}^{T},

$a_{a} (n) = {[e^{- (j 2 π ((n - 1) d_{n}) \sin (θ_{a}) / λ_{0})} \cdot \cdot \cdot e^{- (j 2 π ((n - 1) d_{n} + (M_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T};$ $n = 1,2, \cdot \cdot \cdot \tilde{N},$ d_n表示信号收集点间的距离;θ_a表示目标在第a个角度间隔量化单元的反射角;λ₀表示雷达系统载波波长;dr表示接受天线间的距离;dt表示发射天线间的距离;M_t表示发射天线的个数； $a_{a} (no) = {[e^{- (j 2 π ((no - 1) d_{no}) \sin (θ_{a}) / λ_{0})} \cdot &Center Dot; &Center Dot; e^{- (j 2 π ((no - 1) d_{no} + (m_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T};$ $no = 1,2, \cdot &Center Dot; &Center Dot; \tilde{N},$ d _n represents the distance between signal collection points; θ _a represents the reflection angle of the target at the ath angle interval quantization unit; λ ₀ represents the carrier wavelength of the radar system; dr represents the distance between receiving antennas; dt represents the distance between transmitting antennas; M _t represents the number of transmitting antennas;

B2、对上述关系模型线性化，如下：B2. Linearize the above relational model, as follows:

y=Ax+ey=Ax+e

其中，A=[v_1,1,1 v_1,1,2 …v_r,a,d… v_P,K,G] x=[α_1,1,1 α_1,1,2 …α_r,a,d… α_P,K,G]^T Among them, A=[v _1,1,1 v _1,1,2 ...v _r,a,d ... v _P,K,G ] x=[α _1,1,1 α _1,1,2 ...α _{r ,a,d} … α _P,K,G ] ^T

${v v}_{r r,, a a,, d d} = = [\begin{matrix} {\overset{~ ~}{v v}}_{r r,, a a,, d d} ((11)) \\ \cdot &Center Dot; \\ \cdot \cdot \\ \cdot &Center Dot; \\ {\overset{~ ~}{v v}}_{r r,, a a,, d d} ((n no)) \\ \cdot \cdot \\ \cdot &Center Dot; \\ \cdot \cdot \\ {\overset{~ ~}{v v}}_{r r,, a a,, d d} ((\overset{~ ~}{N N})) \end{matrix}] &Element; &Element; {C C}^{\overset{~ ~}{N N} {M m}_{r r} ((L L + + P P - - 11)) \times \times 11};;$ ${\overset{~ ~}{v v}}_{r r,, a a,, d d} ((n no)) = = vec vec [[{b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {\overset{~ ~}{S S}}^{H h} (({ω ω}_{d d})) {J J}_{r r}]] &Element; &Element; {C C}^{{M m}_{r r} ((L L + + P P - - 11)) \times \times 11},,$

$n no = = 11,, \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; \overset{~ ~}{N N};; e e = = [\begin{matrix} vec vec (({E E.}^{H h} ((11)))) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ vec vec (({E E.}^{H h} ((\overset{~ ~}{N N})))) \end{matrix}],,$ $y the y = = [\begin{matrix} vec vec (({Y Y}^{H h} ((11)))) \\ \cdot \cdot \\ \cdot \cdot \\ \cdot &Center Dot; \\ vec vec (({Y Y}^{H h} ((\overset{~ ~}{N N})))) \end{matrix}];;$

M_r表示接收天线的个数；α_r,a,d表示目标所在区域内目标的反射系数;vec表示将矩阵进行向量化操作，即将矩阵按矩阵列的次序依次排为一列；M _r represents the number of receiving antennas; α _{r, a, d} represent the reflection coefficient of the target in the area where the target is located; vec represents the vectorization operation of the matrix, that is, the matrix is arranged in a row in the order of the matrix columns;

其中表示初始化的目标反射系数，

表示将v_r,a,d进行共轭转置运算；in represents the initial target reflection coefficient,

Indicates that v _{r, a, d} are conjugated and transposed;

式中，||.||₂表示欧几里得范数，

此时假设没有目标存在；

表示一个未确定的目标序号，其中

表示未确定的目标在距离量化单元的位置，

表示未确定目标在角间隔量化单元的位置，

表示未确定目标在多普勒量化单元的位置，迭代结束后，J(η)以外部分的反射系数被设为0，被认为没有目标存在；In the formula, ||.|| ₂ represents the Euclidean norm,

At this time, it is assumed that no target exists;

Indicates an undetermined target sequence number, where

Indicates the position of the undetermined target in the Doppler quantization unit, After the iteration, the reflection coefficient of the part other than J(η) is set to 0, and it is considered that there is no target;

${\overset{^^}{α α}}_{r r,, a a,, d d} = = \frac{{v v}_{r r,, a a,, d d}^{H h} {R R}^{- - 11} y the y}{{v v}_{r r,, a a,, d d}^{H h} {R R}^{- - 11} {v v}_{r r,, a a . . d d}};;$

式中， $R = Σ_{r = 1}^{P} Σ_{a = 1}^{K} Σ_{d = 1}^{G} {| {\hat{α}}_{r, a . d} |}^{2} v_{r, a, d} v_{r, a, d}^{H}$ r=1,...P,a=1,...K,d=1,...G其中R中的

为初始的目标反射系数。In the formula,

R = Σ_{r = 1}^{P} Σ_{a = 1}^{K} Σ_{d = 1}^{G} {| {\hat{α}}_{r, a . d} |}^{2} v_{r, a, d} v_{r, a, d}^{h}

r=1,...P,a=1,...K,d=1,...G where in R

is the initial target reflection coefficient.

本发明的效果可以通过以下仿真说明：Effect of the present invention can be illustrated by following simulation:

1、仿真条件与内容1. Simulation conditions and content

由于不可忽略多普勒的情况较为复杂且我们研究的主要内容是相干MIMO雷达的动目标检测，因此本发明进行当目标是动目标时参数的检测仿真，随机产生4个运动的目标，假设所有的目标都位于多普勒数为1的位置，我们所关心的区域为角度为从-30度到30度，多普勒角度为从-30度到30度。发射天线Mt=5、接受天线Mr=5、子脉冲的数目为L=32，载波的工作频率为1.24GHz，发射天线间的距离dt=2.5*载波的波长，接受天线间的距离dr=0.5*载波的波长，性噪比SNA=20，其中SNA=10log(tr(S^HS)/Lσ²)、tr表示矩阵的迹、噪声

为M_r行L+P-1列的高斯白噪声、σ²为高斯噪声的方差；将距离划为12个频带即P=12、角度划分为7个频带即K=7、多普勒角度划分为5个频带即H=5。观测点

即只有一个观测点。采用迭代自适应算法对目标定位进行仿真。Since the situation of non-negligible Doppler is more complicated and the main content of our research is the moving target detection of coherent MIMO radar, so the present invention carries out the detection simulation of the parameter when the target is a moving target, randomly generates 4 moving targets, assuming all The targets are all located at the position where the Doppler number is 1, the area we care about is the angle from -30 degrees to 30 degrees, and the Doppler angle is from -30 degrees to 30 degrees. The transmitting antenna Mt=5, the receiving antenna Mr=5, the number of sub-pulses is L=32, the operating frequency of the carrier is 1.24GHz, the distance between the transmitting antennas dt=2.5*the wavelength of the carrier, the distance between the receiving antennas dr=0.5 *The wavelength of the carrier, the sex-to-noise ratio SNA=20, where SNA=10log(tr(S ^H S)/Lσ ² ), tr represents the trace and noise of the matrix

Gaussian white noise of M _r row L+P-1 column, σ ² is the variance of Gaussian noise; the distance is divided into 12 frequency bands, that is, P=12, the angle is divided into 7 frequency bands, that is, K=7, and the Doppler angle It is divided into 5 frequency bands, that is, H=5. Observation point

That is, there is only one observation point. The iterative adaptive algorithm is used to simulate the target location.

2、仿真的结果如图2及图3所示，当采用DAS法对目标进行参数估计时，具有较低的分辨率和较弱的干扰抑制，很难估计出准确的目标，会产生很多的错误如将不是目标的地方，估计为目标，当采用迭代自适应算法（IAA）对其进行动目标检测时，在同样的情况下可以较为准确的定位出目标的参数。再者由于本方法是用户参数自由和非参数的自适应算法，所以在快照数目缺少的情况甚至只有一个快照的情况下仍可以很准确的定位出目标。另外，此方法不需要辅助数据。只需要通过接受到的y和变换后得到的v去得到目标的目标参数，从而解决了现有空时自适应算法需要辅助数据去估计杂波和噪声谐波矩阵的基本数据，但在非均匀杂波环境下，无法得到满足条件的辅助数据的问题。且此算法与DAS法相比，在提高分辨率和降低旁瓣的情况下，此法运算的时间与DAS几乎相等，相比于需要辅助数据的空时自适应算法，由于此法不需要辅助算法因此在一定程度上提高了运算速度。且此方法具有收敛速度快、性能稳定的特点。2. The simulation results are shown in Figure 2 and Figure 3. When the DAS method is used to estimate the parameters of the target, it has low resolution and weak interference suppression, it is difficult to estimate the accurate target, and a lot of noise will be generated. If the error is not the target, it is estimated to be the target. When the iterative adaptive algorithm (IAA) is used to detect the moving target, the parameters of the target can be located more accurately under the same circumstances. Furthermore, since this method is a user-parameter-free and non-parametric adaptive algorithm, it can still locate the target very accurately when the number of snapshots is insufficient or even there is only one snapshot. Also, this method does not require auxiliary data. It only needs to obtain the target parameters of the target through the received y and the transformed v, thus solving the problem that the existing space-time adaptive algorithm needs auxiliary data to estimate the basic data of the clutter and noise harmonic matrix, but in the non-uniform In the clutter environment, the auxiliary data that meets the conditions cannot be obtained. Moreover, compared with the DAS method, the calculation time of this method is almost equal to that of DAS in the case of improving the resolution and reducing the side lobe. Compared with the space-time adaptive algorithm that requires auxiliary data, since this method does not require auxiliary algorithms Therefore, the operation speed is improved to a certain extent. And this method has the characteristics of fast convergence and stable performance.

综上，本发明采用迭代自适应算法能有效的克服现存的动目标参数检测所遇到的问题，极大的提高了相干MIMO雷达动目标检测的准确性。To sum up, the present invention adopts an iterative adaptive algorithm, which can effectively overcome the existing problems encountered in the detection of moving target parameters, and greatly improves the accuracy of coherent MIMO radar moving target detection.

Claims

1. A coherent MIMO radar target detection method based on iterative adaptive algorithm obtains its position parameters by optimizing the reflection coefficients of moving targets and static targets respectively. The method is specifically:

A. When the observation target is a static target, the Doppler effect is not considered

A1. Determine the first echo signal observed at the nth observation point, the transmitted signal, and the reflection of the target

The relationship model between coefficients and noise interference is as follows:

{Y Y}^{H h} ((n no)) = = {Σ Σ}_{r r = = 11}^{P P} {Σ Σ}_{a a = = 11}^{K K} {α α}_{r r,, a a} {b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {{\overset{~ ~}{S S}}^{H h} J J}_{r r} + + {E E.}^{H h} ((n no))

In the formula, Y(n) is the first echo signal observed at the nth observation point, where

express will

Perform the conjugate transpose operation,

\tilde{S} {= [\begin{matrix} S \\ 0_{(P - 1) \times m_{t}} \end{matrix}]}_{(L + P - 1) \times m_{t}}

is the transmitted signal waveform matrix obtained after zero padding,

S = {[\begin{matrix} {the s}_{1} & {the s}_{2} & &Center Dot; &Center Dot; &Center Dot; {the s}_{m} &Center Dot; &Center Dot; &Center Dot; & {the s}_{m_{t}} \end{matrix}]}_{L \times m_{t}}

J _r ∈ C ^{(L+P-1)×(L+P-1)} is a transformation matrix, which is used to describe the signals received by different distance quantization sections, and its expression is:

{b b}_{a a} ((n no)) = = {[[{e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no})) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))} \cdot \cdot \cdot \cdot \cdot \cdot {e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no} + + (({M m}_{r r} - - 11)) dr dr)) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))}]]}^{T T};;

a_{a} (no) = {[e^{- (j 2 π ((no - 1) d_{no}) \sin (θ_{a}) / λ_{0})} &Center Dot; &Center Dot; \cdot e^{- (j 2 π ((no - 1) d_{no} + (m_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T},

in d _n represents the distance between signal collection points; θ _a represents the reflection angle of the target at the ath angular interval quantization unit; λ ₀ represents the carrier wavelength of the radar system; dr represents the distance between receiving antennas; dt represents the distance between transmitting antennas; M _r represents the number of receiving antennas;

A2. Linearize the above relational model;

A3. Use the delayed superposition DAS algorithm to initialize the reflection coefficient of the target, as follows:

{\overset{^^}{α α}}_{r r,, a a} = = \frac{{v v}_{r r,, a a}^{H h} y the y}{{v v}_{r r,, a a}^{H h} {v v}_{r r,, a a}};;

in:

\begin{matrix} {v v}_{r r,, a a} = = [\begin{matrix} {\overset{~ ~}{v v}}_{r r,, a a} ((11)) \\ \cdot \cdot \\ \cdot \cdot \\ \cdot \cdot \\ {\overset{~ ~}{v v}}_{r r,, a a} ((\overset{~ ~}{N N})) \end{matrix}] &Element; &Element; {C C}^{\overset{~ ~}{N N} {M m}_{r r} ((L L + + P P - - 11)) \times \times 11} \end{matrix}

{\overset{~ ~}{v v}}_{r r,, a a} ((n no)) = = vec vec [[{b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {\overset{~ ~}{S S}}^{H h} {J J}_{r r}]] &Element; &Element; {C C}^{{M m}_{r r} ((L L + + P P - - 11)) \times \times 11},,

n no = = 11,, \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot \overset{~ ~}{N N},,

r=1,...P,a=1,...K;

the y = [\begin{matrix} vec (Y^{h} (1)) \\ \cdot \\ &Center Dot; \\ &Center Dot; \\ vec (Y^{h} (\tilde{N})) \end{matrix}]

in represents the initial target reflection coefficient,

A4. Use the Bayesian model order selection tool to optimize the reflection coefficient of the target, specifically: put the initial target reflection coefficient of the delayed superposition DAS into formula (1) to obtain the Bayesian BIC value of the initial value, and iterate the target and update the Bayesian BIC value, compare the two Bayesian BIC values before and after, when the Bayesian BIC value no longer decreases, stop iterating to get the reflection coefficient of the target;

{BIC BIC}_{\overset{~ ~}{r r},, \overset{~ ~}{a a}} ((η η)) = = {22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)) \times \times In In [[{| | | | y the y - - \underset{((r r,, a a)) &Element; &Element; {{J J ((η η)) \cup \cup ((\overset{~ ~}{r r},, \overset{~ ~}{a a}))}}}{Σ Σ} {V V}_{r r,, a a} {\overset{^^}{a a}}_{r r,, a a} | | | |}_{22}^{22}]] + + 44 ηIn ηIn (({22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)))) - - - - - - ((11))

In the formula, ||.|| ₂ represents the Euclidean norm,

Represents the square of the Euclidean norm, η represents the number of currently selected targets; 4 represents the number of parameters to be estimated for each target; J(η) represents the set of target serial numbers selected during this iteration, when the first during an iteration

At this time, it is assumed that no target exists;

Indicates an undetermined target sequence number, where

勭 represents the position of the undetermined target in the distance quantization unit,

Among them, the iterative formula of the reflection coefficient is as follows:

{\overset{^^}{α α}}_{r r,, a a} = = \frac{{v v}_{r r,, a a}^{H h} {R R}^{- - 11} y the y}{{v v}_{r r,, a a}^{H h} {R R}^{- - 11} {v v}_{r r,, a a}}

In the formula, where in R Indicates the reflection coefficient of the target obtained in the previous iteration. When the first iteration is performed, the

Indicates the initial target reflection coefficient;

B. When the target is a moving target, consider the Doppler effect

B1. Determine the relationship model between the first echo signal observed at the nth observation point and the transmitted signal, the reflection coefficient of the target and noise interference as follows:

{Y Y}^{H h} ((n no)) = = {Σ Σ}_{r r = = 11}^{P P} {Σ Σ}_{a a = = 11}^{K K} {Σ Σ}_{d d = = 11}^{G G} {α α}_{r r,, a a,, d d} {b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {{\overset{~ ~}{S S}}^{H h} (({ω ω}_{d d})) J J}_{r r} + + {E E.}^{H h} ((n no))

Indicates that a _a (n) is transposed, will be Conjugate transpose operation, where

\tilde{S} (ω_{d}) = {[\begin{matrix} S (ω_{d}) \\ 0_{(P - 1) \times m_{t}} \end{matrix}]}_{(L + P - 1) \times m_{t}}

S = (ω_{d}) = [\begin{matrix} {\tilde{the s}}_{1} (ω_{d}) & {\tilde{the s}}_{2} (ω_{d}) & \cdot \cdot \cdot {\tilde{the s}}_{m} (ω_{d}) &Center Dot; &Center Dot; &Center Dot; & {\tilde{the s}}_{m_{t}} \end{matrix} (ω_{d})],

in:

m=1,...M _t ,d=1,...G;

d (ω_{d}) = {[\begin{matrix} 1 & e^{{jω}_{d}} & &Center Dot; &Center Dot; &Center Dot; & e^{{jω}_{d} (L - 1)} \end{matrix}]}^{T},

{b b}_{a a} ((n no)) = = {[[{e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no})) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))} \cdot \cdot \cdot &Center Dot; \cdot &Center Dot; {e e}^{- - ((j j 22 π π ((((n no - - 11)) {d d}_{n no} + + (({M m}_{r r} - - 11)) dr dr)) sin sin (({θ θ}_{a a})) / / {λ λ}_{00}))}]]}^{T T};;

a_{a} (no) = {[e^{- (j 2 π ((no - 1) d_{no}) \sin (θ_{a}) / λ_{0})} \cdot \cdot &Center Dot; e^{- (j 2 π ((no - 1) d_{no} + (m_{t} - 1) dt) \sin (θ_{a}) / λ_{0})}]}^{T};

no = 1,2, &Center Dot; &Center Dot; &Center Dot; \tilde{N},

d _n represents the distance between signal collection points; θ _a represents the reflection angle of the target at the ath angle interval quantization unit; λ ₀ represents the carrier wavelength of the radar system; dr represents the distance between receiving antennas; dt represents the distance between transmitting antennas; M _r represents the number of receiving antennas;

B2. Linearize the above relational model;

B3. Use the delayed superposition DAS algorithm to initialize the reflection coefficient of the target, as follows:

{\overset{^^}{α α}}_{r r,, a a,, d d} = = \frac{{v v}_{r r,, a a,, d d}^{H h} y the y}{{v v}_{r r,, a a,, d d}^{H h} {v v}_{r r,, a a,, d d}}

in:

\begin{matrix} {v v}_{r r,, a a,, d d} = = [\begin{matrix} {\overset{~ ~}{v v}}_{r r,, a a,, d d} ((11)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {\overset{~ ~}{v v}}_{r r,, a a,, d d} ((\overset{~ ~}{N N})) \end{matrix}] &Element; &Element; {C C}^{\overset{~ ~}{N N} {M m}_{r r} ((L L + + P P - - 11)) \times \times 11} \end{matrix}

{\overset{~ ~}{v v}}_{r r,, a a,, d d} ((n no)) = = vec vec [[{b b}_{a a} ((n no)) {a a}_{a a}^{T T} ((n no)) {\overset{~ ~}{S S}}^{H h} (({ω ω}_{d d})) {J J}_{r r}]] &Element; &Element; {C C}^{{M m}_{r r} ((L L + + P P - - 11)) \times \times 11}

y the y = = [\begin{matrix} vec vec (({Y Y}^{H h} ((11)))) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ vec vec (({Y Y}^{H h} ((\overset{~ ~}{N N})))) \end{matrix}]

in

represents the initial target reflection coefficient,

B4. Use the Bayesian model order selection tool to optimize the reflection coefficient of the target, specifically: put the initial target reflection coefficient of the delayed superimposition DAS into (2) to obtain the initial Bayesian BIC value, and iterate the target and update the Bayesian BIC value, compare the two Bayesian BIC values before and after, when the Bayesian BIC value no longer decreases, stop iterating to get the reflection coefficient of the target;

{BIC BIC}_{\overset{~ ~}{r r},, \overset{~ ~}{a a},, \overset{~ ~}{d d}} ((η η)) = = {22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)) \times \times In In [[{| | | | y the y - - \underset{((r r,, a a,, d d)) &Element; &Element; {{J J ((η η)) \cup \cup ((\overset{~ ~}{r r},, \overset{~ ~}{a a,,} \overset{~ ~}{d d}))}}}{Σ Σ} {V V}_{r r,, a a,, d d} {\overset{^^}{a a}}_{r r,, a a,, d d} | | | |}_{22}^{22}]] + + 55 ηIn ηIn (({22 M m}_{r r} \overset{~ ~}{N N} ((L L + + P P - - 11)))) - - - - - - ((22))

In the formula, ||.|| ₂ represents the Euclidean norm,

Represents the square of the Euclidean norm, η represents the number of targets currently selected; 5 represents the number of parameters to be estimated for each target; J(η) represents the set of target serial numbers that have been selected; when performing the first iteration

At this time, it is assumed that no target exists; Indicates an undetermined target sequence number, where

Among them, the iterative formula of the reflection coefficient is as follows:

{\overset{~ ~}{α α}}_{r r,, a a,, d d} = = \frac{{v v}_{r r,, a a,, d d}^{H h} {R R}^{- - 11} y the y}{{v v}_{r r,, a a,, d d}^{H h} {R R}^{- - 11} {v v}_{r r,, a a . . d d}};;

In the formula,

R = Σ_{r = 1}^{P} Σ_{a = 1}^{K} Σ_{d = 1}^{G} {| {\hat{α}}_{r, a . d} |}^{2} v_{r, a, d} v_{r, a, d}^{h}

r=1,...P,a=1,...K,d=1,...G

where in R

Indicates the initial target reflection coefficient.