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CN114609651A - Space domain anti-interference method of satellite navigation receiver based on small sample data - Google Patents

Space domain anti-interference method of satellite navigation receiver based on small sample data Download PDF

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CN114609651A
CN114609651A CN202210309726.8A CN202210309726A CN114609651A CN 114609651 A CN114609651 A CN 114609651A CN 202210309726 A CN202210309726 A CN 202210309726A CN 114609651 A CN114609651 A CN 114609651A
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滕云龙
宫大为
元硕成
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Higher Research Institute Of University Of Electronic Science And Technology Shenzhen
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    • G—PHYSICS
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Abstract

The invention discloses a small sample data-based space domain anti-interference method for a satellite navigation receiver, which comprises the following steps of: step 1, acquiring a sample covariance matrix through snapshot data obtained by sampling of a receiver; step 2, constructing a subspace orthogonal to the navigation signal guide vector; step 3, projecting the received signal to a constructed subspace to obtain an interference and noise covariance matrix; step 4, performing contraction estimation on the obtained interference and noise covariance matrix; and 5, estimating a navigation signal guide vector to obtain an optimal weight vector. The method can obtain better airspace anti-interference performance under the condition of small sample data no matter in a high signal-to-noise ratio environment or a low signal-to-noise ratio environment.

Description

基于小样本数据的卫星导航接收机空域抗干扰方法Airspace anti-jamming method of satellite navigation receiver based on small sample data

技术领域technical field

本发明属于卫星导航技术领域，具体应用于卫星导航接收机空域抗干扰技术中。The invention belongs to the technical field of satellite navigation, and is specifically applied to the airspace anti-jamming technology of satellite navigation receivers.

背景技术Background technique

随着我国北斗系统的不断完善，我国卫星导航事业得到了长足发展，相关技术的研究与应用也进入了一个新的阶段。由于卫星导航接收机的核心是一个阵列天线，系统功能对实时性的要求较高，且近年来大规模阵列逐渐得到了广泛应用与关注。因此在某些情况下，阵列接收数据的样本数，不仅无法远大于阵列阵元数，甚至小于阵元数，这会导致样本协方差矩阵与协方差矩阵的理论值偏差较大，甚至样本协方差矩阵为奇异矩阵，这时需要对样本协方差矩阵进行处理，以获得更加精确有效的协方差矩阵。With the continuous improvement of my country's Beidou system, my country's satellite navigation industry has made great progress, and the research and application of related technologies has also entered a new stage. Since the core of the satellite navigation receiver is an array antenna, the system functions have high requirements on real-time performance, and in recent years, large-scale arrays have gradually been widely used and concerned. Therefore, in some cases, the number of samples of data received by the array can not be much larger than the number of array elements, or even smaller than the number of array elements, which will lead to a large deviation between the theoretical value of the sample covariance matrix and the covariance matrix, and even the sample covariance matrix. The variance matrix is a singular matrix, and the sample covariance matrix needs to be processed to obtain a more accurate and effective covariance matrix.

目前，已有多种协方差矩阵估计理论，针对这种情况提出了有效估计方法，但此类方法由于没有对协方差矩阵进行预处理，因此无法直接适用于导航接收机的空域抗干扰方法。At present, there are a variety of covariance matrix estimation theories, and effective estimation methods are proposed for this situation, but these methods cannot be directly applied to the airspace anti-jamming method of navigation receivers because they do not preprocess the covariance matrix.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于克服现有技术的不足，提供一种能够在小样本数据情况下，无论是高信噪比环境还是低信噪比环境，都能取得较好的空域抗干扰性能的基于小样本数据的卫星导航接收机空域抗干扰方法。The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a small sample-based system that can achieve better airspace anti-jamming performance regardless of whether it is a high SNR environment or a low SNR environment. Airspace anti-jamming method for satellite navigation receivers with sample data.

本发明的目的是通过以下技术方案来实现的：基于小样本数据的卫星导航接收机空域抗干扰方法，包括以下步骤：The object of the present invention is to be achieved through the following technical solutions: a satellite navigation receiver airspace anti-jamming method based on small sample data, comprising the following steps:

步骤1、通过接收机采样得到的快拍数据获取样本协方差矩阵；Step 1. Obtain a sample covariance matrix from snapshot data sampled by the receiver;

步骤2、构造与导航信号导向矢量正交的子空间；Step 2. Construct a subspace orthogonal to the navigation signal steering vector;

步骤3、将接收信号投影到构造的子空间，得到干扰加噪声协方差矩阵；Step 3. Project the received signal to the constructed subspace to obtain the interference plus noise covariance matrix;

步骤4、对得到的干扰加噪声协方差矩阵进行收缩估计；Step 4. Perform shrinkage estimation on the obtained interference plus noise covariance matrix;

步骤5、估计导航信号导向矢量，获得最优权矢量。Step 5: Estimate the navigation signal steering vector to obtain the optimal weight vector.

进一步地，所述步骤1具体实现方法为：卫星导航接收设备的核心是一个天线阵列，假定其是一个均匀线阵，阵元数为M，则在t时刻，天线阵列接收到的信号表示为：Further, the specific implementation method of step 1 is: the core of the satellite navigation receiving device is an antenna array, assuming that it is a uniform linear array, and the number of array elements is M, then at time t, the signal received by the antenna array is expressed as: :

x(t)＝xs(t)+xi(t)+xn(t) (1)x(t)=x s (t)+x i (t)+x n (t) (1)

其中，xs(t)、xi(t)、xn(t)分别表示阵列接收的导航信号、干扰信号、噪声；Among them, x s (t), x i (t), x n (t) represent the navigation signal, interference signal, and noise received by the array, respectively;

xs(t)＝ss(t)as，其中ss(t)表示导航信号波形，as表示导航信号导向矢量；xi(t)＝si(t)ai， si(t)表示干扰信号波形，ai表示干扰信号导向矢量；x s (t)=s s (t)a s , where s s (t) represents the navigation signal waveform, and a s represents the navigation signal steering vector; x i (t)=s i (t)a i , s i ( t) represents the interference signal waveform, a i represents the interference signal steering vector;

接收机采样得到的样本协方差矩阵为：The sample covariance matrix obtained by the receiver sampling is:

Figure BDA0003567530350000021
Figure BDA0003567530350000021

其中，T为采样的快拍数。where T is the number of snapshots sampled.

进一步地，所述步骤2具体实现方法为：对导航信号所在空间角区域进行Capon功率谱积分，得到导航信号协方差矩阵：Further, the specific implementation method of step 2 is: performing Capon power spectrum integration on the spatial angle region where the navigation signal is located to obtain the covariance matrix of the navigation signal:

Figure BDA0003567530350000022
Figure BDA0003567530350000022

其中，Θs是导航信号空间角区域；对于从任意角度入射的信号，其导向矢量根据信号空间来向角度θ确定，表示为：Among them, Θ s is the space angle area of the navigation signal; for the signal incident from any angle, its steering vector is determined according to the signal space to the angle θ, which is expressed as:

Figure BDA0003567530350000023
Figure BDA0003567530350000023

其中，d代表相邻阵元间距离，λ代表信号波长，M表示阵元数；Among them, d represents the distance between adjacent array elements, λ represents the signal wavelength, and M represents the number of array elements;

对

Figure BDA0003567530350000024
进行特征值分解，得到：right
Figure BDA0003567530350000024
Perform eigenvalue decomposition to get:

Figure BDA0003567530350000025
Figure BDA0003567530350000025

其中，ηm是

Figure BDA0003567530350000026
特征值分解后得到的特征值，按大小降序排列，em是相应特征值对应的特征向量；将特征向量构成矩阵E＝[e1,e2,…,eM]表示为E＝[E1,E2]，其中E1包含最大的2～3个特征值对应的特征向量，E2包含其余特征值对应的特征向量；则导航信号子空间表示为
Figure BDA0003567530350000027
导航信号导向矢量as属于该子空间，且as正交于导航信号补子空间
Figure BDA0003567530350000028
其中I为单位矩阵。where ηm is
Figure BDA0003567530350000026
The eigenvalues obtained after the eigenvalues are decomposed are arranged in descending order of size, and em is the eigenvector corresponding to the corresponding eigenvalue; the eigenvectors constitute a matrix E=[e 1 ,e 2 ,...,e M ] is expressed as E=[E 1 , E 2 ], where E 1 contains the eigenvectors corresponding to the largest 2 to 3 eigenvalues, and E2 contains the eigenvectors corresponding to the remaining eigenvalues; then the navigation signal subspace is expressed as
Figure BDA0003567530350000027
The navigation signal steering vector a s belongs to this subspace, and a s is orthogonal to the complementary subspace of the navigation signal
Figure BDA0003567530350000028
where I is the identity matrix.

进一步地，所述步骤3具体实现方法为：将

Figure BDA0003567530350000029
表示为
Figure BDA00035675303500000210
导航信号导向矢量as和子空间B也正交；当阵列接收信号投影到子空间B时，得到的投影信号为：Further, the specific implementation method of step 3 is:
Figure BDA0003567530350000029
Expressed as
Figure BDA00035675303500000210
The navigation signal steering vector a s is also orthogonal to the subspace B; when the array received signal is projected to the subspace B, the resulting projected signal is:

Figure BDA00035675303500000211
Figure BDA00035675303500000211

投影后的信号对应的样本协方差矩阵为The sample covariance matrix corresponding to the projected signal is

Figure BDA0003567530350000031
Figure BDA0003567530350000031

还表示为：Also expressed as:

Figure BDA0003567530350000032
Figure BDA0003567530350000032

其中，

Figure BDA0003567530350000033
为噪声功率的估计值，取样本协方差矩阵
Figure BDA0003567530350000034
的最小特征值；并且通过实验可知，子空间B不会对非导航信号空间角区域的导向矢量产生影响，因此
Figure BDA0003567530350000035
从而得到：in,
Figure BDA0003567530350000033
is the estimated value of noise power, take the sample covariance matrix
Figure BDA0003567530350000034
The smallest eigenvalues of
Figure BDA0003567530350000035
which results in:

Figure BDA0003567530350000036
Figure BDA0003567530350000036

进而得到干扰加噪声协方差矩阵，具体表示为：Then the interference plus noise covariance matrix is obtained, which is specifically expressed as:

Figure BDA0003567530350000037
Figure BDA0003567530350000037

进一步地，所述步骤4具体实现方法为：信号协方差矩阵的理论值是Toeplitz矩阵，因此收缩估计的目标矩阵是一个Toeplitz矩阵，具体表示为：Further, the specific implementation method of step 4 is: the theoretical value of the signal covariance matrix is the Toeplitz matrix, so the target matrix of the shrinkage estimation is a Toeplitz matrix, which is specifically expressed as:

Figure BDA0003567530350000038
Figure BDA0003567530350000038

其中w为收缩因子，S为待估计的协方差矩阵，具体为步骤3得到的

Figure BDA0003567530350000039
T为具有Toeplitz结构的目标矩阵；收缩估计的关键是求得收缩因子w，而T具体表示为：where w is the shrinkage factor, and S is the covariance matrix to be estimated, specifically obtained in step 3
Figure BDA0003567530350000039
T is the target matrix with the Toeplitz structure; the key to shrinkage estimation is to obtain the shrinkage factor w, and T is specifically expressed as:

Figure BDA00035675303500000310
Figure BDA00035675303500000310

其中，tr(·)表示矩阵的迹，HM＝11T-IM，1为元素均为1的列向量，IM为单位矩阵；Wherein, tr( ) represents the trace of the matrix, H M =11 T -I M , 1 is a column vector whose elements are all 1, and IM is the identity matrix;

通过应用MSE准则和无偏估计获取收缩因子w，得到优化问题为：By applying the MSE criterion and unbiased estimation to obtain the shrinkage factor w, the optimization problem is obtained as:

Figure BDA00035675303500000311
Figure BDA00035675303500000311

其中，

Figure BDA00035675303500000312
Figure BDA0003567530350000041
Figure BDA0003567530350000042
cλ＝(1TS1)2-2(1TS21)+tr(S2)，
Figure BDA0003567530350000043
in,
Figure BDA00035675303500000312
Figure BDA0003567530350000041
Figure BDA0003567530350000042
c λ =(1 T S1) 2 -2(1 T S 2 1)+tr(S 2 ),
Figure BDA0003567530350000043

w的值通过求解如下优化问题获得The value of w is obtained by solving the following optimization problem

Figure BDA0003567530350000044
Figure BDA0003567530350000044

该优化问题的解为

Figure BDA0003567530350000045
其中m∨n表示取其中的较大值，m∧n表示取其中的较小值；则最终
Figure BDA0003567530350000046
的进一步估计值
Figure BDA0003567530350000047
The solution to this optimization problem is
Figure BDA0003567530350000045
Where m∨n means to take the larger value, m∧n means to take the smaller value; then the final
Figure BDA0003567530350000046
a further estimate of
Figure BDA0003567530350000047

进一步地，所述步骤5具体实现方法为：通过选取

Figure BDA0003567530350000048
中最大特征值对应的特征向量e1计算导航信号导向矢量的估计值
Figure BDA0003567530350000049
得到最终的最优权矢量
Figure BDA00035675303500000410
Further, the specific implementation method of the step 5 is: by selecting
Figure BDA0003567530350000048
The eigenvector e 1 corresponding to the largest eigenvalue in the calculation of the estimated value of the navigation signal steering vector
Figure BDA0003567530350000049
get the final optimal weight vector
Figure BDA00035675303500000410

本发明的有益效果是：本发明能够在小样本数据，即采样的快拍数较少情况下，无论是高信噪比环境还是低信噪比环境，都能取得较好的空域抗干扰性能。The beneficial effects of the present invention are: the present invention can achieve better airspace anti-jamming performance in the case of small sample data, that is, the number of sampled snapshots is small, regardless of whether it is a high signal-to-noise ratio environment or a low signal-to-noise ratio environment .

具体实施方式Detailed ways

下面进一步说明本发明的技术方案。The technical solutions of the present invention are further described below.

本发明的一种基于小样本数据的卫星导航接收机空域抗干扰方法，包括以下步骤：A kind of satellite navigation receiver airspace anti-jamming method based on small sample data of the present invention comprises the following steps:

步骤1、通过接收机采样得到的快拍数据获取样本协方差矩阵；具体实现方法为：卫星导航接收设备的核心是一个天线阵列，假定其是一个均匀线阵，阵元数为M，则在t时刻，天线阵列接收到的信号表示为：Step 1. Obtain the sample covariance matrix from the snapshot data sampled by the receiver; the specific implementation method is: the core of the satellite navigation receiving device is an antenna array, assuming that it is a uniform linear array and the number of array elements is M, then At time t, the signal received by the antenna array is expressed as:

x(t)＝xs(t)+xi(t)+xn(t) (15)x(t)=x s (t)+x i (t)+x n (t) (15)

其中，xs(t)、xi(t)、xn(t)分别表示阵列接收的导航信号(期望信号)、干扰信号、噪声；xs(t)＝ss(t)as，其中ss(t)表示导航信号波形，as表示导航信号导向矢量；xi(t)＝si(t)ai， si(t)表示干扰信号波形，ai表示干扰信号导向矢量；Among them, x s (t), x i (t), and x n (t) represent the navigation signal (desired signal), interference signal, and noise received by the array, respectively; x s (t)=s s (t)a s , where s s (t) represents the waveform of the navigation signal, and a s represents the steering vector of the navigation signal; x i (t)=s i (t)a i , s i (t) represents the waveform of the interference signal, and a i represents the steering vector of the interference signal ;

目前，导航接收机空域抗干扰技术大多基于波束形成技术，此类算法通常采用MVDR准则，即：At present, most of the airspace anti-jamming technologies of navigation receivers are based on beamforming technology. Such algorithms usually use the MVDR criterion, namely:

Figure BDA0003567530350000051
Figure BDA0003567530350000051

其中，w＝[w1,w2,…,wj,…,wM]T为阵列加权矢量，而Ri+n为干扰加噪声协方差矩阵，通过阵列权矢量加权后，阵列的输出为y＝wHx(t)，则阵列的输出功率为 P＝E{|y|2}＝wHRw。可见，如果去除掉信号协方差矩阵中导航信号成分，即可构成MVDR 波束形成器所需的干扰加噪声协方差矩阵Ri+n。MVDR准则的核心思想是在保证期望信号无失真通过波束形成器，即符合约束条件wHas＝1的同时，使干扰信号加噪声的总输出功率最小，最优权矢量

Figure BDA0003567530350000052
可最终通过求解上述最优化问题求得，由于在实际应用过程中无法直接获得干扰加噪声协方差矩阵的理论值，因此通常采用接收机采样得到的样本协方差矩阵代替，即：Among them, w=[w 1 ,w 2 ,...,w j ,...,w M ] T is the array weighting vector, and R i+n is the interference plus noise covariance matrix. After weighting by the array weight vector, the output of the array is y=w H x(t), then the output power of the array is P=E{|y| 2 }=w H Rw. It can be seen that if the navigation signal component in the signal covariance matrix is removed, the interference plus noise covariance matrix R i+n required by the MVDR beamformer can be formed. The core idea of the MVDR criterion is to ensure that the desired signal passes through the beamformer without distortion, that is, to meet the constraint condition w H a s =1, while minimizing the total output power of the interference signal plus noise, and the optimal weight vector
Figure BDA0003567530350000052
It can be finally obtained by solving the above optimization problem. Since the theoretical value of the interference plus noise covariance matrix cannot be directly obtained in the actual application process, the sample covariance matrix obtained by the receiver sampling is usually used instead, namely:

Figure BDA0003567530350000053
Figure BDA0003567530350000053

其中，T为采样的快拍数。当采样的快拍数没有远大于阵元数M，甚至小于阵元数M时，样本协方差矩阵相比于协方差矩阵理论值相差过大，甚至是奇异矩阵，无法求逆来计算最优权矢量，此外，如果不去除协方差矩阵中导航信号组成部分，当信噪比较高时，导航信号会被视为干扰信号而受到抑制，无法得到最优性能。where T is the number of snapshots sampled. When the number of snapshots sampled is not much larger than the number of array elements M, or even smaller than the number of array elements M, the difference between the sample covariance matrix and the theoretical value of the covariance matrix is too large, or even a singular matrix, and the inversion cannot be calculated to calculate the optimal value. In addition, if the component of the navigation signal in the covariance matrix is not removed, when the signal-to-noise ratio is high, the navigation signal will be regarded as an interference signal and be suppressed, and the optimal performance cannot be obtained.

步骤2、构造与导航信号导向矢量正交的子空间；Step 2. Construct a subspace orthogonal to the navigation signal steering vector;

本发明采用子空间投影的方法对样本协方差矩阵进行预处理，从而去除其中导航信号的组成部分。由于在实际应用中，导航信号和干扰信号在空间角度上不同，多种低分辨率方法结合星历信息可确定导航信号和干扰信号各自所在的空间角区域，因此角区域可视为先验信息。对导航信号所在空间角区域进行Capon功率谱积分，得到导航信号协方差矩阵：The invention adopts the method of subspace projection to preprocess the sample covariance matrix, so as to remove the components of the navigation signal. Since in practical applications, the navigation signal and the interference signal are different in spatial angle, a variety of low-resolution methods can combine the ephemeris information to determine the spatial angular region where the navigation signal and the interference signal are located respectively, so the angular region can be regarded as a priori information. . The Capon power spectrum integration is performed on the spatial angle region where the navigation signal is located, and the covariance matrix of the navigation signal is obtained:

Figure BDA0003567530350000061
Figure BDA0003567530350000061

其中，Θs是导航信号空间角区域；对于均匀线阵，由于天线阵列结构已知，对于从任意角度入射的信号，其导向矢量根据信号空间来向角度θ确定，表示为：Among them, Θs is the spatial angle area of the navigation signal; for a uniform linear array, since the structure of the antenna array is known, for a signal incident from any angle, its steering vector is determined according to the signal space to the angle θ, which is expressed as:

Figure BDA0003567530350000062
Figure BDA0003567530350000062

其中，d代表相邻阵元间距离，λ代表信号波长，M表示阵元数；Among them, d represents the distance between adjacent array elements, λ represents the signal wavelength, and M represents the number of array elements;

对

Figure BDA0003567530350000063
进行特征值分解，得到：right
Figure BDA0003567530350000063
Perform eigenvalue decomposition to get:

Figure BDA0003567530350000064
Figure BDA0003567530350000064

其中，ηm是

Figure BDA0003567530350000065
特征值分解后得到的特征值，按大小降序排列，em是相应特征值对应的特征向量；将特征向量构成矩阵E＝[e1,e2,…,eM]表示为E＝[E1,E2]，其中E1包含最大的2～3个特征值对应的特征向量，E2包含其余特征值对应的特征向量；则导航信号子空间表示为
Figure BDA0003567530350000066
导航信号导向矢量as属于该子空间，且as正交于导航信号补子空间
Figure BDA0003567530350000067
其中I为单位矩阵。当E1中包含的特征向量越少，导航信号导向矢量as和
Figure BDA0003567530350000068
的正交性越强，通过实验可得，一般取2～3个最大特征值对应的特征向量，构成期望信号子空间
Figure BDA0003567530350000069
即可保证导航信号导向矢量as和
Figure BDA00035675303500000610
的正交性。where ηm is
Figure BDA0003567530350000065
The eigenvalues obtained after the eigenvalues are decomposed are arranged in descending order of size, and em is the eigenvector corresponding to the corresponding eigenvalue; the eigenvectors constitute a matrix E=[e 1 ,e 2 ,...,e M ] is expressed as E=[E 1 , E 2 ], where E 1 contains the eigenvectors corresponding to the largest 2 to 3 eigenvalues, and E2 contains the eigenvectors corresponding to the remaining eigenvalues; then the navigation signal subspace is expressed as
Figure BDA0003567530350000066
The navigation signal steering vector a s belongs to this subspace, and a s is orthogonal to the complementary subspace of the navigation signal
Figure BDA0003567530350000067
where I is the identity matrix. When there are fewer eigenvectors contained in E1, the navigation signal steering vector a s and
Figure BDA0003567530350000068
The stronger the orthogonality is, it can be obtained through experiments. Generally, the eigenvectors corresponding to 2 to 3 maximum eigenvalues are taken to form the desired signal subspace.
Figure BDA0003567530350000069
It can be guaranteed that the navigation signal steering vector a s and
Figure BDA00035675303500000610
orthogonality.

步骤3、将接收信号投影到构造的子空间，得到干扰加噪声协方差矩阵；具体实现方法为：将

Figure BDA00035675303500000611
表示为
Figure BDA00035675303500000612
导航信号导向矢量as和子空间B也正交；当阵列接收信号投影到子空间B时，得到的投影信号为：Step 3. Project the received signal to the constructed subspace to obtain the interference plus noise covariance matrix; the specific implementation method is:
Figure BDA00035675303500000611
Expressed as
Figure BDA00035675303500000612
The navigation signal steering vector a s is also orthogonal to the subspace B; when the array received signal is projected to the subspace B, the resulting projected signal is:

Figure BDA00035675303500000613
Figure BDA00035675303500000613

因为导航信号导向矢量和投影子空间正交，所以投影后去除了导航信号；Because the navigation signal steering vector is orthogonal to the projection subspace, the navigation signal is removed after projection;

投影后的信号对应的样本协方差矩阵为：The sample covariance matrix corresponding to the projected signal is:

Figure BDA0003567530350000071
Figure BDA0003567530350000071

将信号x(t)展开，投影后的信号对应的样本协方差矩阵还表示为：Expanding the signal x(t), the sample covariance matrix corresponding to the projected signal is also expressed as:

Figure BDA0003567530350000072
Figure BDA0003567530350000072

其中，

Figure BDA0003567530350000073
为噪声功率的估计值，取样本协方差矩阵
Figure BDA0003567530350000074
的最小特征值；并且通过实验可知，子空间B不会对非导航信号空间角区域的导向矢量产生影响，因此
Figure BDA0003567530350000075
从而得到：in,
Figure BDA0003567530350000073
is the estimated value of noise power, take the sample covariance matrix
Figure BDA0003567530350000074
The smallest eigenvalues of
Figure BDA0003567530350000075
which results in:

Figure BDA0003567530350000076
Figure BDA0003567530350000076

进而得到干扰加噪声协方差矩阵，具体表示为：Then the interference plus noise covariance matrix is obtained, which is specifically expressed as:

Figure BDA0003567530350000077
Figure BDA0003567530350000077

步骤4、对得到的干扰加噪声协方差矩阵进行收缩估计；Step 4. Perform shrinkage estimation on the obtained interference plus noise covariance matrix;

在得到干扰加噪声协方差矩阵，完成预处理后，本发明采用收缩估计方法最得到的干扰加噪声协方差矩阵进行进一步精确估计。由于信号协方差矩阵的理论值是Toeplitz矩阵，因此收缩估计的目标矩阵是一个Toeplitz矩阵，具体表示为：After obtaining the interference-plus-noise covariance matrix and completing the preprocessing, the present invention uses the most-obtained interference-plus-noise covariance matrix by the shrinkage estimation method for further accurate estimation. Since the theoretical value of the signal covariance matrix is the Toeplitz matrix, the target matrix of the shrinkage estimation is a Toeplitz matrix, which is specifically expressed as:

Figure BDA0003567530350000078
Figure BDA0003567530350000078

其中w为收缩因子，S为待估计的协方差矩阵，具体为步骤3得到的

Figure BDA0003567530350000079
T为具有Toeplitz结构的目标矩阵；收缩估计的关键是求得收缩因子w，而T具体表示为：where w is the shrinkage factor, and S is the covariance matrix to be estimated, specifically obtained in step 3
Figure BDA0003567530350000079
T is the target matrix with the Toeplitz structure; the key to shrinkage estimation is to obtain the shrinkage factor w, and T is specifically expressed as:

Figure BDA00035675303500000710
Figure BDA00035675303500000710

其中，tr(·)表示矩阵的迹；HM＝11T-IM，1为元素均为1的列向量，IM为单位矩阵，计算后HM是一个对角线元素都为0，其他元素都为1的矩阵；Among them, tr( ) represents the trace of the matrix; H M =11 T -I M , 1 is a column vector whose elements are all 1, and I M is a unit matrix. After calculation, H M is a diagonal element whose elements are all 0, A matrix whose other elements are all 1;

通过应用MSE准则和无偏估计获取收缩因子w，得到优化问题为：By applying the MSE criterion and unbiased estimation to obtain the shrinkage factor w, the optimization problem is obtained as:

Figure BDA0003567530350000081
Figure BDA0003567530350000081

其中，

Figure BDA0003567530350000082
Figure BDA0003567530350000083
Figure BDA0003567530350000084
cλ＝(1TS1)2-2(1TS21)+tr(S2)，
Figure BDA0003567530350000085
in,
Figure BDA0003567530350000082
Figure BDA0003567530350000083
Figure BDA0003567530350000084
c λ =(1 T S1) 2 -2(1 T S 2 1)+tr(S 2 ),
Figure BDA0003567530350000085

w的值通过求解如下优化问题获得：The value of w is obtained by solving the following optimization problem:

Figure BDA0003567530350000086
Figure BDA0003567530350000086

该优化问题的解为

Figure BDA0003567530350000087
其中m∨n表示取其中的较大值，m∧n表示取其中的较小值，即中间括号里面的计算结果先与0求较大的值，再与1求较小的值；则最终
Figure BDA0003567530350000088
的进一步估计值
Figure BDA0003567530350000089
The solution to this optimization problem is
Figure BDA0003567530350000087
Among them, m∨n means to take the larger value, m∧n means to take the smaller value, that is, the calculation result in the middle bracket is first calculated with 0 for the larger value, and then with 1 for the smaller value; then the final
Figure BDA0003567530350000088
a further estimate of
Figure BDA0003567530350000089

步骤5、估计导航信号导向矢量，获得最优权矢量；具体实现方法为：通过选取

Figure BDA00035675303500000810
中最大特征值对应的特征向量e1计算导航信号导向矢量的估计值
Figure BDA00035675303500000811
得到最终的最优权矢量
Figure BDA00035675303500000812
在最优权矢量下，干扰信号加噪声的总输出功率最小，从而在小样本数据情况下，无论是高信噪比环境还是低信噪比环境，都能取得较好的空域抗干扰性能。Step 5. Estimate the navigation signal steering vector to obtain the optimal weight vector; the specific implementation method is: by selecting
Figure BDA00035675303500000810
The eigenvector e 1 corresponding to the largest eigenvalue in the calculation of the estimated value of the navigation signal steering vector
Figure BDA00035675303500000811
get the final optimal weight vector
Figure BDA00035675303500000812
Under the optimal weight vector, the total output power of the interference signal plus noise is the smallest, so in the case of small sample data, whether it is a high SNR environment or a low SNR environment, better spatial anti-jamming performance can be achieved.

本领域的普通技术人员将会意识到，这里所述的实施例是为了帮助读者理解本发明的原理，应被理解为本发明的保护范围并不局限于这样的特别陈述和实施例。本领域的普通技术人员可以根据本发明公开的这些技术启示做出各种不脱离本发明实质的其它各种具体变形和组合，这些变形和组合仍然在本发明的保护范围内。Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to assist readers in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.

Claims (6)

1. The small sample data-based airspace anti-interference method of the satellite navigation receiver is characterized by comprising the following steps of:
step 1, acquiring a sample covariance matrix through snapshot data obtained by sampling of a receiver;
step 2, constructing a subspace orthogonal to the navigation signal guide vector;
step 3, projecting the received signal to a constructed subspace to obtain an interference and noise covariance matrix;
step 4, performing contraction estimation on the obtained interference and noise covariance matrix;
and 5, estimating a navigation signal guide vector to obtain an optimal weight vector.
2. The small sample data-based airspace anti-interference method for the satellite navigation receiver according to claim 1, wherein the specific implementation method in the step 1 is as follows: the core of the satellite navigation receiving device is an antenna array, and assuming that the antenna array is a uniform linear array and the number of array elements is M, at time t, signals received by the antenna array are represented as:
x(t)＝xs(t)+xi(t)+xn(t) (1)
wherein ,xs(t)、xi(t)、xn(t) respectively representing navigation signals, interference signals and noise received by the array; x is a radical of a fluorine atoms(t)＝ss(t)as, wherein ss(t) denotes a navigation signal waveform, asRepresenting a navigation signal steering vector; x is the number ofi(t)＝si(t)ai，si(t) represents an interference signal waveform, aiRepresenting an interference signal steering vector;
the covariance matrix of the samples sampled by the receiver is:
Figure FDA0003567530340000011
where T is the number of fast beats of samples.
3. The small sample data-based airspace anti-interference method for the satellite navigation receiver according to claim 2, wherein the step 2 is realized by the following steps: performing Capon power spectrum integration on the space angle region where the navigation signal is located to obtain a navigation signal covariance matrix:
Figure FDA0003567530340000012
wherein ,ΘsIs a navigation signal spatial angular region; for a signal incident from an arbitrary angle, its steering vector is determined from the signal space to the angle θ, expressed as:
Figure FDA0003567530340000013
wherein d represents the distance between adjacent array elements, lambda represents the signal wavelength, and M represents the number of the array elements;
to pair
Figure FDA0003567530340000014
Performing eigenvalue decomposition to obtain:
Figure FDA0003567530340000021
wherein ,ηmIs that
Figure FDA0003567530340000022
The eigenvalues obtained after the eigenvalue decomposition are arranged in descending order of magnitude, emIs the eigenvector corresponding to the corresponding eigenvalue; forming the feature vector into a matrix E ═ E1,e2,…,eM]Is represented by E ═ E1,E2], wherein E1Including the feature vector corresponding to the maximum 2-3 feature values, E2Including the eigenvectors corresponding to the other eigenvalues; the navigation signal subspace is represented as
Figure FDA0003567530340000023
Navigation signal steering vector asBelongs to the subspace, and asOrthogonal to the complement space of the navigation signal
Figure FDA0003567530340000024
Where I is the identity matrix.
4. The small sample data-based airspace anti-interference method for the satellite navigation receiver according to claim 3, wherein the specific implementation method in the step 3 is as follows: will be provided with
Figure FDA0003567530340000025
Is shown as
Figure FDA0003567530340000026
Navigation signal steering vector asAnd subspace B are also orthogonal; when the array received signal is projected into subspace B, the resulting projectionThe signals are:
Figure FDA0003567530340000027
the sample covariance matrix corresponding to the projected signal is:
Figure FDA0003567530340000028
also expressed as:
Figure FDA0003567530340000029
wherein ,
Figure FDA00035675303400000210
sampling the local covariance matrix for the estimate of noise power
Figure FDA00035675303400000211
The minimum eigenvalue of (d); the subspace B does not influence the steering vectors in the corner regions of the non-navigation signal space, and therefore
Figure FDA00035675303400000212
Thereby obtaining:
Figure FDA00035675303400000213
and further obtaining an interference plus noise covariance matrix, which is specifically expressed as:
Figure FDA00035675303400000214
5. the small sample data-based airspace anti-interference method for the satellite navigation receiver according to claim 4, wherein the specific implementation method in the step 4 is as follows: the theoretical value of the signal covariance matrix is a Toeplitz matrix, so the target matrix of the shrinkage estimation is a Toeplitz matrix, which is specifically expressed as:
Figure FDA0003567530340000031
wherein w is a shrinkage factor, S is a covariance matrix to be estimated, specifically obtained in step 3
Figure FDA0003567530340000032
T is a target matrix with a Toeplitz structure; the key to the shrinkage estimation is to find the shrinkage factor w, and T is specifically expressed as:
Figure FDA0003567530340000033
where tr (-) denotes the trace of the matrix, HM＝11T-IM1 is a column vector whose elements are all 1, IMIs an identity matrix;
acquiring a shrinkage factor w by applying an MSE (mean square error) criterion and unbiased estimation, and obtaining an optimization problem as follows:
Figure FDA0003567530340000034
wherein ,
Figure FDA0003567530340000035
Figure FDA0003567530340000036
Figure FDA0003567530340000037
cλ＝(1TS1)2-2(1TS21)+tr(S2)，
Figure FDA0003567530340000038
the value of w is obtained by solving the following optimization problem
Figure FDA0003567530340000039
The solution of the optimization problem is
Figure FDA00035675303400000310
Wherein m is V-n and m is N, m is V-n; then finally
Figure FDA00035675303400000311
Further estimate of (2)
Figure FDA00035675303400000312
6. The small sample data-based airspace anti-interference method for the satellite navigation receiver according to claim 5, wherein the step 5 is realized by the following steps: by selecting
Figure FDA0003567530340000041
Feature vector e corresponding to medium maximum feature value1Calculating an estimate of a navigation signal steering vector
Figure FDA0003567530340000042
Obtaining the final optimal weight vector
Figure FDA0003567530340000043
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CN116449398A (en) * 2023-04-10 2023-07-18 中国矿业大学 Self-adaptive anti-interference method for satellite navigation receiver in antenna array element mutual coupling environment
CN116449398B (en) * 2023-04-10 2023-11-03 中国矿业大学 Self-adaptive anti-interference method for satellite navigation receiver in antenna array element mutual coupling environment

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