WO2022127076A1 - 基于张量高阶奇异值分解的雷达角度和距离估计方法 - Google Patents
基于张量高阶奇异值分解的雷达角度和距离估计方法 Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/418—Theoretical aspects
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S2013/0236—Special technical features
- G01S2013/0245—Radar with phased array antenna
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- the invention relates to the technical field of bistatic MIMO radar systems, in particular to a radar angle and distance estimation method based on tensor high-order singular value decomposition.
- Frequency-controlled array MIMO radar is a new system radar that has been continuously developed in recent years. On the premise of retaining the advantages of phased array, it has been better improved. It has high resolution and excellent parameter estimation performance. Research hotspots.
- the frequency-controlled array MIMO radar can be divided into two categories according to the relative positions of the receiving array and the transmitting array, namely the stand-alone ground-frequency-controlled-array MIMO radar and the bistatic frequency-controlled-array MIMO radar.
- the research on frequency-controlled array MIMO radar has mostly focused on the monostatic field, and some algorithms have appeared, such as ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm and MUSIC (multiple signal classification) algorithm.
- ESPRIT estimation of signal parameters via rotational invariance techniques
- MUSIC multiple signal classification
- a sub-array partition mode is proposed to design the radar transmitting array.
- the accuracy of this algorithm is based on a large amount of computational complexity and requires high speed. Number of shots to guarantee.
- Another algorithm proposes a new idea of sub-array division, which consists of multiple sub-arrays to form a transmitting array, and realizes joint estimation of target DOA, DOD and distance through rotation invariance.
- the methods mentioned above are all subspace algorithms based on matrix decomposition, which simply store the received echo data as a matrix, but this method will lose the inherent multi-dimensional structure of the received data.
- this kind of algorithm has poor performance in the case of low snapshot and low signal-to-noise ratio.
- parameter matching errors are prone to occur in the case of multiple targets.
- the case of multiple targets is more common, and in the harsh electromagnetic environment, the application performance of the above method will be seriously affected.
- the purpose of the present invention is to provide a radar angle and distance estimation method based on tensor high-order singular value decomposition, so as to solve the problems raised in the above background art.
- a radar angle and distance estimation method based on tensor high-order singular value decomposition comprising the following steps:
- constructing a MIMO radar receiving array including k sub-arrays obtaining the received data of the target echo through the MIMO radar receiving array, and constructing a third-order tensor signal model
- the third-order tensor signal model is decomposed by high-order singular value to obtain a tensor-based signal subspace
- Extract the signal subspace and emission matrix corresponding to each subarray eliminate the phase ambiguity caused by target DOD parameters and distance coupling, and realize the automatic pairing of target DOD and distance with DOA parameters, and finally realize the target DOD parameters and distance of MIMO radar. parameter estimation.
- the received data of the target echo is obtained through the MIMO radar receiving array, and a third-order tensor signal model is constructed, including:
- the received data of the target echo is expressed as:
- Ar is the receiving steering matrix
- Ats is the transmitting steering matrix
- N is the noise matrix
- S T is the space signal vector matrix
- Stacking received data along different directions in 3D to form a tensor signal model Its dimension is M ⁇ N ⁇ L, N is the number of radar receiving array antennas, M is the number of receiving array antennas, and the tensor By modulo-3 expansion, the third-order tensor signal model can be obtained:
- a high-order singular value decomposition third-order tensor signal model is used to obtain a tensor-based signal subspace, including:
- extracting the receiving matrix of the signal subspace includes:
- the receiving matrix of the signal subspace is obtained using the least squares criterion:
- 0 (N-1) ⁇ 1 represents a (N-1) ⁇ 1-dimensional zero matrix
- I M and I (N-1) both represent unit matrices.
- eigenvalue decomposition is performed on the receiving matrix to realize DOA parameter estimation of the MIMO radar target, including:
- the receiving matrix is subjected to eigenvalue decomposition to obtain:
- E r Represents a matrix composed of eigenvectors, and ⁇ r represents a diagonal matrix composed of eigenvalues;
- a matrix containing the DOA information of the target is obtained:
- T represents the matrix composed of eigenvectors
- T -1 represents the inverse matrix of T
- ⁇ r represents the diagonal matrix composed of eigenvalues
- the DOA parameter estimation of the MIMO radar target is achieved by the following formula:
- extract the signal subspace and subarray emission matrix corresponding to each subarray including:
- the signal subspace corresponding to each sub-matrix is extracted and expressed as:
- the least squares criterion is used to obtain the emission matrix of the signal subspace corresponding to each subarray:
- phase ambiguity problem caused by the coupling of target DOD parameters and distance is eliminated, and at the same time, automatic pairing of target DOD and distance and DOA parameters is realized, including:
- ⁇ t k T -1 ⁇ t k T.
- the estimation of DOD and distance parameters of the MIMO radar target is realized, including:
- phase ambiguity parameters are:
- the present invention provides a radar angle and distance estimation method based on tensor high-order singular value decomposition.
- the tensor signal model is processed by using the high-order singular value decomposition method of tensor. Compared with the traditional SVD/EVD method, this method can more effectively suppress noise interference and improve the performance of target parameter estimation.
- ESPRIT algorithm based on matrix factorization has better angle estimation performance;
- FIG. 1 is a structural diagram of a radar angle and distance estimation method based on tensor high-order singular value decomposition provided by the present invention
- Figure 2 is a schematic structural diagram of a bistatic frequency-controlled array MIMO radar system
- FIG. 3 is a schematic diagram of the division structure of a transmitting array in a sub-array mode
- Figure 4 is a three-dimensional point cloud image of the target DOA, DOD and distance parameter estimation results
- Figure 5 is a schematic diagram of the comparison of the subspace accuracy of the tensor signal with the number of snapshots
- FIG. 6 is a schematic diagram of the comparison of tensor signal subspace accuracy with a fixed signal-to-noise ratio
- Figure 7 is a comparison diagram of the variation of the root mean square error of different algorithm pairs with the target DOA, DOD and distance parameters with the signal-to-noise ratio;
- Figure 8 is another comparison graph of the variation of the RMS error of different algorithm pairs with the target DOA, DOD and distance parameters as a function of signal-to-noise ratio
- Fig. 9 is a comparison diagram of different algorithm pairs and the target DOA, DOD and the root mean square error of the distance parameters as a function of the number of snapshots;
- Figure 10 is another comparison graph of different algorithm pairs versus target DOA, DOD, and the RMSE of the distance parameters as a function of the number of snapshots.
- the radar angle and distance estimation method based on tensor high-order singular value decomposition includes the following steps:
- Step 101 constructing a MIMO radar receiving array including k sub-arrays, obtaining received data of target echoes through the MIMO radar receiving array, and constructing a third-order tensor signal model;
- the preset bistatic frequency controlled array MIMO radar receiving array antennas are N, receiving array antennas are M, and the receiving array is divided into K sub-arrays, and the transmission waveforms between the transmitting antennas are the same as each other.
- Orthogonal, in the subarray mode, the transmit frequency of the mth antenna of the kth subarray can be expressed as
- the receive steering vector can be expressed as:
- a non-overlapping sub-array is designed, and the number of antennas of each sub-array should be the same, so
- the carrier frequency of the last antenna of the sub-array is equal to the carrier frequency of the first antenna of the next sub-array, i.e. and and ⁇ f 1 ⁇ f 2 ... ⁇ f K .
- the signal model array prevalence matrix of the bistatic frequency-controlled array MIMO radar can be expressed as:
- the received data X is stacked in different directions in three dimensions to form a tensor signal model Its dimension is M ⁇ N ⁇ L, the tensor By modulo-3 expansion, the third-order tensor signal model can be obtained:
- Step 102 use high-order singular value decomposition of a third-order tensor signal model to obtain a tensor-based signal subspace;
- high-order singular value decomposition is used to process tensors It can be expressed as
- U 1 ⁇ ⁇ M ⁇ M , U 2 ⁇ ⁇ N ⁇ N and U 3 ⁇ ⁇ L ⁇ L respectively represent the tensors composed of is composed of left singular vectors modulo n decomposition, namely
- the tensor-based signal subspace can be obtained as
- Step 103 extract the receiving matrix of the signal subspace to realize the DOA parameter estimation of the MIMO radar target;
- the first selection matrix is defined as follows:
- 0 (N-1) ⁇ 1 represents a (N-1) ⁇ 1-dimensional zero matrix
- I M and I (N-1) both represent unit matrices.
- U s is decomposed into two parts as the receiving matrix of the signal subspace, which is specifically expressed as:
- the method for realizing the DOA parameter estimation of the MIMO radar target is:
- the eigenvalue decomposition of the receiving matrix can be obtained:
- E r Represents a matrix composed of eigenvectors, and ⁇ r represents a diagonal matrix composed of eigenvalues;
- T represents the matrix composed of eigenvectors
- T -1 represents the inverse matrix of T
- ⁇ r represents the diagonal matrix composed of eigenvalues
- ⁇ r is as follows:
- the target DOA parameters are obtained by the following formulas
- Step 104 Extract the signal subspace and emission matrix corresponding to each sub-array, and eliminate the phase ambiguity caused by target DOD parameters and distance coupling, and realize automatic pairing of target DOD, distance and DOA parameters, and finally achieve target DOD for MIMO radar. Estimation of parameters and distance parameters.
- each transmitting sub-array and receiving array can be regarded as a whole, which contains the corresponding signal sub-space. Therefore, a second selection matrix is constructed to select the signal subspace of each subarray, and the constructed second selection matrix is as follows:
- the specific construction of the third selection matrix is as follows:
- ⁇ r and ⁇ t k span into the same subspace, which can be used to diagonalize ⁇ t k using a matrix T consisting of a matrix ⁇ that contains the DOA information of the target r is composed of eigenvectors, so that the target DOD and distance are automatically paired with the DOA parameters, as follows:
- phase ambiguity caused by target DOD parameters and distance coupling and realize the estimation of MIMO radar target DOD and distance parameters, including:
- phase ambiguity parameters are:
- the preset DOD, DOA and distance to three incoherent targets are (-15°, -50°, 30km), (20°, 35°, 9km) and (40°, 10°, 58km), respectively.
- the X-axis, Y-axis and Z-axis represent DOA, DOD and distance respectively. It can be seen from Figure 4 that the estimated target landing points are highly concentrated, and the same location as the actual target. This can prove that the stability and accuracy of the present invention are very excellent.
- Figures 5-6 show the accuracy of the signal subspace as a function of signal-to-noise ratio and number of snapshots.
- the present invention outperforms the ESPRIT method.
- the performance of the present invention is continuously improved, but the performance improvement of the ESPRIT method is very small. This is because the present invention uses a tensor signal model to preserve the structural characteristics of the radar array antenna, so as the number of antennas increases, the performance of the tensor-based method will be better than that of the matrix decomposition-based method.
- the performance of the present invention is better than that of the ESPRIT method.
- the present invention uses tensors to construct a signal model, it can make good use of the inherent multi-dimensional structure information of the received data, so it has higher performance under the same signal-to-noise ratio and number of snapshots, and a lower signal-to-noise ratio.
- the performance is better in the case of the number of snapshots.
- the RMSE of the present invention decreases with the increase of the number of snapshots, which indicates that the performance of the present invention is continuously improving and is gradually approaching the CRB.
- the trend of the curve of the present invention is close to the trend of CRB, which indicates that the performance of the present invention gradually tends to be stable.
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Abstract
本发明提供一种基于张量高阶奇异值分解的雷达角度和距离估计方法,包括下列步骤:构建包含k个子阵的MIMO雷达接收阵列,通过所述MIMO雷达接收阵列获取目标回波的接收数据,并构造三阶张量信号模型;采用高阶奇异值分解三阶张量信号模型,获得基于张量的信号子空间;提取所述信号子空间的接收矩阵,实现MIMO雷达目标DOA参数估计;提取每个子阵对应的信号子空间和发射矩阵,并消除因目标DOD参数和距离耦合造成的相位模糊问题,同时实现目标DOD和距离与DOA参数自动配对,最终实现对MIMO雷达目标DOD参数和距离参数的估计。
Description
本发明涉及双基地MIMO雷达系统技术领域,尤其涉及基于张量高阶奇异值分解的雷达角度和距离估计方法。
频控阵MIMO雷达是近年来不断发展的新体制雷达,在保留了相控阵优点的前提下,有了更好的提升,具有高分辨率和优秀的参数估计性能,是目前信号处理领域的研究热点。频控阵MIMO雷达主要可以根据接收阵列和发射阵列的相对位置来划分成两类,分别是单机地频控阵MIMO雷达和双基地频控阵MIMO雷达。近年来,针对频控阵MIMO雷达的研究多集中于单基地领域,已经有出现了一些算法,比如ESPRIT(estimation of signal parameters via rotational invariance techniques)算法和MUSIC(multiple signal classification)算法,但是因为单基地频控阵MIMO雷达的抗干扰能力弱,难以应对在日益复杂的电磁环境下对雷达目标探测的挑战,因此为了开发抗干扰能力更强的频控阵MIMO雷达,双基地频控阵MIMO雷达研究至关重要。
为了实现双基地频控阵MIMO雷达的DOD和距离解耦合,一种子阵划分模式被提出来用于设计雷达发射阵列,然而该算法的精度是建立在大量计算复杂度上的,并且需要高快拍数来保证。另一种算法提出了子阵划分的新思路,通过多个子阵组成发射阵列,通过旋转不变性实现对目标DOA、DOD和距离的联合估计。然而,上述所提到的方法都是基于矩阵分解的子空间算法,只是简单将接收的回波数据存储为一个矩阵,但是这种方式会丢失接收数据固有的多维结构。其次这类算法在低快拍和低信噪比的情况下性能较差。此外对于多目标的情况下容易出现参数匹配错误,在实际应用中,多目标的情况更为常见,且在恶劣的电磁环境下,上述方法的应用性能会受到严重影响。
发明内容
本发明的目的在于提供基于张量高阶奇异值分解的雷达角度和距离估计方法,以解决上述背景技术中提出的问题。
本发明是通过以下技术方案实现的:基于张量高阶奇异值分解的雷达角度和距离估计方法,包括下列步骤:
构建包含k个子阵的MIMO雷达接收阵列,通过所述MIMO雷达接收阵列获取目标回波的接收数据,并构造三阶张量信号模型;
采用高阶奇异值分解三阶张量信号模型,获得基于张量的信号子空间;
提取所述信号子空间的接收矩阵,实现MIMO雷达目标DOA参数估计;
提取每个子阵对应的信号子空间和发射矩阵,并消除因目标DOD参数和距离耦合造成的相位模糊问题,同时实现目标DOD和距离与DOA参数自动配对,最终实现对MIMO雷达目标DOD参数和距离参数的估计。
优选的,通过所述MIMO雷达接收阵列获取目标回波的接收数据,并构造三阶张量信号模型,包括:
在接收L个快拍数后,将目标回波的接收数据表示为:
X=AS
T+N=[A
r□A
ts]S
T+N
其中,A
r为接收导向矩阵,A
ts为发射导向矩阵,N为噪声矩阵,S
T为空间信号矢量矩阵;
优选的,采用高阶奇异值分解三阶张量信号模型,获得基于张量的信号子 空间,包括:
其截断式的核心张量表示为:
将核心张量代入高阶奇异值分解的表达式,可获得:
优选的,提取所述信号子空间的接收矩阵,包括:
构建第一选择矩阵:
采用最小二乘准则获得所述信号子空间的接收矩阵:
式中,0
(N-1)×1表示一个(N-1)×1维的零矩阵,I
M、I
(N-1)均表示单位矩阵。
优选的,对所述接收矩阵进行特征值分解,实现MIMO雷达目标DOA参数估计,包括:
所述接收矩阵进行特征值分解,获得:
将E
r分成四个子矩阵,具体为:
对Ψ
r进行特征值分解:
式中,T表示特征向量组成的矩阵,T
-1表示T的逆矩阵,Φ
r表示由特征值组成的对角矩阵;
通过如下公式实现MIMO雷达目标DOA参数估计:
优选的,提取每个子阵对应的信号子空间和子阵发射矩阵,包括:
构建第二选择矩阵:
基于第二选择矩阵,提取每个子阵对应的信号子空间表示为:
构建第三选择矩阵:
优选的,消除因目标DOD参数和距离耦合造成的相位模糊问题,,同时实 现目标DOD和距离与DOA参数自动配对,包括:
利用旋转不变形和最小二乘准则,得到包含目标DOD和距离信息的矩阵Ψ
t
k;
使用矩阵T对矩阵Ψ
t
k进行对角化,从而实现目标DOD和距离与DOA参数自动配对:Φ
t
k=T
-1Ψ
t
kT。
优选的,实现对MIMO雷达目标DOD和距离参数的估计,包括:
确定雷达的最大目标探测距离:
提取每个子阵的发射矩阵相位,获得DOD和距离信息:
通过推导得出相位模糊参数为:
从而可以得出目标的距离:
采用向下取整方法确定k
i:
与现有技术相比,本发明达到的有益效果如下:
本发明提供的一种基于张量高阶奇异值分解的雷达角度和距离估计方法,(1)通过利用张量构建信号模型,重新堆叠保存目标回波的接收数据,保存了接收数据固有的多维结构信息,相较于传统子空间算法具有很大的优越性;
(2)通过采用张量的高阶奇异值分解方法处理张量信号模型,该方法与传统的SVD/EVD方法相比,可以更有效的抑制噪声干扰,提升目标参数估计性能,本发明比传统基于矩阵分解的ESPRIT算法有更好的角度估计性能;
(3)通过在张量域实现了对每个子阵信号子空间的独立提取,从而获得目标DOD和距离耦合信息,利用子阵之间不同的频率增益以及对目标范围的限定,解决了耦合信息的相位模糊问题;
(4)通过利用张量信号模型固有的多维结构信息,提高了信号子空间的估计精确度,减小了与真实信号子空间的夹角,并且利用旋转不变性实现了对目标DOA和DOD与距离参数的配自动匹配。
为了更清楚地说明本发明实施例中的技术方案,下面将对实施例描述中所需要使用的附图作简单地介绍,显而易见地,下面描述中的附图仅仅是本发明的优选实施例,对于本领域普通技术人员来讲,在不付出创造性劳动性的前提下,还可以根据这些附图获得其他的附图。
图1为本发明提供的基于张量高阶奇异值分解的雷达角度和距离估计方法的结构图;
图2是双基地频控阵MIMO雷达系统的结构示意图;
图3是子阵模式下发射阵列的划分结构示意图;
图4是目标DOA、DOD和距离参数估计结果的三维点云图;
图5是张量信号子空间精确度随快拍数的对比示意图;
图6是张量信号子空间精确度随固定信噪比的对比示意图;
图7是不同算法对与目标DOA、DOD和距离参数均方根误差随信噪比变化的一个对比图;
图8是不同算法对与目标DOA、DOD和距离参数均方根误差随信噪比变化的另一个对比图
图9是不同算法对与目标DOA、DOD和距离参数均方根误差随快拍数变化的一个对比图;
图10是不同算法对与目标DOA、DOD和距离参数均方根误差随快拍数变化的另一个对比图。
为了更好理解本发明技术内容,下面提供具体实施例,并结合附图对本发明做进一步的说明。
参见图1,基于张量高阶奇异值分解的雷达角度和距离估计方法,包括下列步骤:
步骤101:构建包含k个子阵的MIMO雷达接收阵列,通过所述MIMO雷达接收阵列获取目标回波的接收数据,并构造三阶张量信号模型;
参见图2-图3,其中预设双基地频控阵MIMO雷达接收阵列天线为N个,接收阵列天线为M个,并将接收阵列划分为K个子阵,发射天线之间的发射波形是彼此正交的,在子阵模式下第k个子阵的第m个天线的发射频率可以表示为
接收导向矢量可以表示为:
在子阵模式下,双基地频控阵MIMO雷达的信号模型阵列流行矩阵可以表示为:
在接收了L个快拍数之后,将接收到的数据排列为X=[x(1),x(2),…,x(L)],则X可以表示为:
X=AS
T+N=[A
r□A
ts]S
T+N
其中,接收矩阵为A
r=[a
r(θ
1),a
r(θ
2),…,a
r(θ
P)]∈□
N×P;a
r(θ
P)代表接收导向矢量,子阵模式下发射矩阵为
代表发射导向矢量,且有X=[x(1),x(2),…,x(L)]∈□
MN×L,S=[s(1),s(2),…,s(L)]
T∈□
L×P,N是均匀高斯白噪声矩阵,并且N∈□
MN×L,S
T为空间信号矢量矩阵。
步骤102:采用高阶奇异值分解三阶张量信号模型,获得基于张量的信号子 空间;
将核心张量代入高阶奇异值分解的表达式,可获得:
至此,获得了基于张量的信号子空间U
s。
步骤103:提取所述信号子空间的接收矩阵,实现MIMO雷达目标DOA参数估计;
在本实施例中,为了提取接收矩阵,定义第一选择矩阵如下:
式中,0
(N-1)×1表示一个(N-1)×1维的零矩阵,I
M、I
(N-1)均表示单位矩阵。
根据旋转不变性和最小二乘准则,将U
s分解为两部分作为所述信号子空间的接收矩阵,具体表示为:
可选的,通过所述信号子空间的接收矩阵,实现MIMO雷达目标DOA参数估计的方式为:
对接收矩阵进行特征值分解,可以得到:
将E
r∈□
K×K分为四个子矩阵,具体为
其中E
r11、E
r12、E
r21和E
r22的维度均为K×K,至此得到包含目标的DOA信息的矩阵Ψ
r;
对Ψ
r进行特征值分解
T表示特征向量组成的矩阵,T
-1表示T的逆矩阵,Φ
r表示由特征值组成的对角矩阵;
其中Φ
r具体如下:
通过如下公式得到目标DOA参数
步骤104:提取每个子阵对应的信号子空间和发射矩阵,并消除因目标DOD参数和距离耦合造成的相位模糊问题,同时实现目标DOD和距离与DOA参数自动配对,最终实现对MIMO雷达目标DOD参数和距离参数的估计。
在子阵FDA-MIMO雷达模式下,每个发射子阵和接收阵列都可以视为一个整体,其中包含对应的信号子空间。因此,构建第二选择矩阵以选择每个子阵的信号子空间,所构建的第二选择矩阵具体如下:
通过构建第三选择矩阵,用于从每个子阵信号子空间获得目标的DOD和距离信息,所构建第三选择矩阵的具体如下:
同样利用旋转不变形和最小二乘准则,得到包含目标DOD和距离信息的矩阵Ψ
t
k;
由于旋转不变性的存在,Ψ
r和Ψ
t
k张成相同的子空间,可以采用这一特性,使用矩阵T对Ψ
t
k进行对角化,该矩阵T由包含目标的DOA信息的矩阵Ψ
r的特征向量组成,从而实现目标DOD和距离与DOA参数自动配对,具体如下:
Φ
t
k=T
-1Ψ
t
kT
矩阵Φ
t
k的具体形式如下:
可选的,消除因目标DOD参数和距离耦合造成的相位模糊问题,并实现对MIMO雷达目标DOD和距离参数的估计,包括:
确定雷达的最大目标探测距离:
提取每个子阵的发射矩阵相位,获得DOD和距离信息:
将上述中的每个方程减去前一个方程,可以得到新方程组为:
通过推导得出相位模糊参数为:
在阵列设计时,发射阵列天线之间的间距保证了2d
tf
1/c≤1,经过推导可以得出k
i(i=1,2,…,K)如下:
至此,通过本发明已经成功估计出目标的DOA、DOD和距离参数,并且实现了目标参数自动配对。
下面结合MALTAB模拟仿真实验结果对本发明作进一步说明:
在仿真实验中将第一个发射天线的发射频率设置为f
1=10GHz,天线的间距为
其中f
max为最大发射频率。预设发射天线和接收天线数量为M=N=18,并将发射阵列划分为K=3个子阵,每个子阵具有M
ts=6个发射天线。每个子阵的发射频率增量分别为Δf
1=5000Hz、Δf
2=10000Hz和Δf
3=15000Hz,并且信噪比为SNR=20dB,快拍数为L=300。预设三个非相干目标到的DOD、DOA和距离分别为(-15°,-50°,30km)、(20°,35°,9km)和(40°,10°,58km)。
对每次仿真均进行T=500次蒙特卡洛实验后获得仿真结果,其具体结果如 图,4-图6所示。
图4展示了在SNR=20dB和L=300情况下估计目标的位置,X轴、Y轴和Z轴分别表示DOA,DOD和距离,从图4可以看出,估计的目标落点高度集中,并且与实际目标的位置相同。这可以证明本发明的稳定性和准确性是非常优秀的。
图5-图6展示了信号子空间的精度随信噪比和快拍数变化的关系。图图5中固定快拍数为L=300,图图6中固定信噪比为SNR=20dB。雷达结构和目标参数与上个仿真保持一致,且设置天线数量为M=N=9,12,15,18。
从图中可以看出,当信噪比和快拍数增加时,本发明的性能会逐渐提升。在相同的条件下,本发明的性能优于ESPRIT方法。同时可以看出,随着天线数量的增加,本发明的性能在不断提升,但是对ESPRIT方法的性能提升很小。这是因为本发明使用了张量信号模型来保存雷达阵列天线的结构特性,因此随着天线数量的增加,基于张量的方法性能会更加优于基于矩阵分解的方法。
图7-图8展示了在快拍数为L=50的情况下,估计方法的角度和距离RMSE随信噪比的关系。
可以看出,本发明的性能优于ESPRIT方法。同时,由于本发明采用张量构建信号模型,可以很好的利用接收数据固有的多维结构信息,因此在相同的信噪比和快拍数下具有较高的性能,且在较低信噪比和快拍数的情况下性能更优秀。
图9-图10展示了在信噪比为SNR=5dB的情况下,估计方法的角度和距离RMSE随快拍数的关系。
可以发现,本发明的RMSE随着快拍数的增加而降低,这表明本发明的性能在不断提高,并逐渐接近于CRB。此外,当快拍数较大时,本发明的曲线走向接近于CRB的趋势,这表明本发明的性能逐渐趋于稳定。
以上所述仅为本发明的较佳实施例而已,并不用以限制本发明,凡在本发明的精神和原则之内,所做的任何修改、等同替换、改进等,均应包含在本发明保护的范围之内。
Claims (8)
- 基于张量高阶奇异值分解的雷达角度和距离估计方法,其特征在于,包括下列步骤:构建包含k个子阵的MIMO雷达接收阵列,通过所述MIMO雷达接收阵列获取目标回波的接收数据,并构造三阶张量信号模型;采用高阶奇异值分解三阶张量信号模型,获得基于张量的信号子空间;提取所述信号子空间的接收矩阵,实现MIMO雷达目标DOA参数估计;提取每个子阵对应的信号子空间和发射矩阵,并消除因目标DOD参数和距离耦合造成的相位模糊问题,同时实现目标DOD和距离与DOA参数自动配对,最终实现对MIMO雷达目标DOD参数和距离参数的估计。
- 根据权利要求4所述的基于张量高阶奇异值分解的雷达角度和距离估计方法,其特征在于,对所述接收矩阵进行特征值分解,实现MIMO雷达目标DOA参数估计,包括:所述接收矩阵进行特征值分解,获得:将E r分成四个子矩阵,具体为:对Ψ r进行特征值分解:式中,T表示特征向量组成的矩阵,T -1表示T的逆矩阵,Φ r表示由特征值组成的对角矩阵;通过如下公式实现MIMO雷达目标DOA参数估计:
- 根据权利要求6所述的基于张量高阶奇异值分解的雷达角度和距离估计方法,其特征在于,消除因目标DOD参数和距离耦合造成的相位模糊问题,,同时实现目标DOD和距离与DOA参数自动配对,包括:利用旋转不变形和最小二乘准则,得到包含目标DOD和距离信息的矩阵Ψ t k;使用矩阵T对矩阵Ψ t k进行对角化,从而实现目标DOD和距离与DOA参数自动配对:Φ t k=T -1Ψ t kT。
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