CN110426670B - Super-resolution DOA estimation method for external radiation source radar based on TLS-CS - Google Patents

Super-resolution DOA estimation method for external radiation source radar based on TLS-CS Download PDF

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CN110426670B
CN110426670B CN201910632496.7A CN201910632496A CN110426670B CN 110426670 B CN110426670 B CN 110426670B CN 201910632496 A CN201910632496 A CN 201910632496A CN 110426670 B CN110426670 B CN 110426670B
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王俊
左罗
陈刚
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S3/00Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/04Details
    • G01S3/06Means for increasing effective directivity, e.g. by combining signals having differently oriented directivity characteristics or by sharpening the envelope waveform of the signal derived from a rotating or oscillating beam antenna
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S3/00Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/04Details
    • G01S3/12Means for determining sense of direction, e.g. by combining signals from directional antenna or goniometer search coil with those from non-directional antenna
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses a TLS-CS-based super-resolution DOA estimation method for an external radiation source radar. The method mainly solves the problem that compressed sensing super-resolution DOA estimation angle measurement precision and target resolution are reduced due to array amplitude-phase errors in the prior art. It includes: obtaining echo received by an array antenna and direct wave received by a reference antenna; utilizing the direct wave and the multipath interference signal in the delay suppression echo of the direct wave to perform distance-Doppler two-dimensional correlation processing on the echo signal after clutter suppression to obtain a complex vector signal S; then adding amplitude-phase disturbance to S to obtain complex vector signal with amplitude-phase error
Figure DDA0002129161940000011
Constructing a guide vector D of the whole observation space, and solving the guide vector D to obtain a guide vector after correcting the amplitude-phase error
Figure DDA0002129161940000012
By using
Figure DDA0002129161940000013
And
Figure DDA0002129161940000014
and carrying out sparse reconstruction on the azimuth information of the plurality of targets to obtain the azimuth of the targets. The invention reduces the influence of array amplitude-phase errors on the steering vectors, improves the angle measurement precision and the resolution performance of the target, and can be used for positioning the target.

Description

基于TLS-CS的外辐射源雷达超分辨DOA估计方法Super-resolution DOA estimation method for external radiator radar based on TLS-CS

技术领域technical field

本发明属于雷达信号处理技术领域,尤其涉及外辐射源雷达超分辨DOA估计方法,可用于目标定位。The invention belongs to the technical field of radar signal processing, and in particular relates to an external radiation source radar super-resolution DOA estimation method, which can be used for target positioning.

背景技术Background technique

外辐射源雷达,指不主动发射电磁波,依靠目标反射环境中已有的第三方非合作照射源信号实施,如调频广播FM、电视信号、手机信号对目标进行探测、定位及跟踪的雷达系统。该体制雷达利用的辐射源信号频段低、面向地面照射,具有隐身和探测低空目标的能力,因此受到了广泛的关注。External radiation source radar refers to a radar system that does not actively emit electromagnetic waves and relies on the existing third-party non-cooperative radiation source signals in the target reflection environment, such as FM radio, TV signals, and mobile phone signals to detect, locate and track the radar system. The radiation source signal used by this system of radar has a low frequency band, faces the ground, and has the ability to stealth and detect low-altitude targets, so it has received extensive attention.

在外辐射源雷达系统中,阵列信号的波达方向DOA估计是目标定位过程中一个非常重要的环节。通常,阵列天线接收到来自目标反射的回波信号能量远低于来自辐射源的强直达波和经地面及建筑反射的多路径杂波以及噪声信号,很难实现对目标的直接测向。为了在外辐射源雷达中对目标的DOA进行估计,首先利用杂波相消算法抑制阵列天线接收的回波信号中的强直达波和多径杂波信号;然后利用距离-多普勒二维相关处理提高接收目标回波信号的信噪比;最后在目标所处的距离-多普勒单元上对多个目标的方位信息进行压缩感知稀疏重构,实现超分辨DOA估计。然而,利用压缩感知只有在阵列不存在误差条件下才能取得良好的性能。在实际外辐射源雷达系统中,阵列各通道间的幅度和相位增益通常不一致,即阵列存在幅相误差,会引起导向矢量失配,而基于压缩感知的超分辨DOA估计方法中,感知矩阵由导向矢量构成,导向矢量的失配会导致超分辨性能迅速下降。In an external radiator radar system, DOA estimation of the direction of arrival of the array signal is a very important link in the target positioning process. Usually, the energy of the echo signal reflected from the target received by the array antenna is much lower than the strong direct wave from the radiation source and the multi-path clutter and noise signal reflected by the ground and buildings, so it is difficult to achieve direct direction finding of the target. In order to estimate the DOA of the target in the external radiator radar, the clutter cancellation algorithm is used to suppress the strong direct wave and multipath clutter in the echo signal received by the array antenna; The processing improves the signal-to-noise ratio of the received target echo signal; finally, the azimuth information of multiple targets is sparsely reconstructed by compressed sensing on the range-Doppler unit where the target is located to achieve super-resolution DOA estimation. However, using compressed sensing can achieve good performance only if the array is free of errors. In the actual external radiation source radar system, the amplitude and phase gains of each channel of the array are usually inconsistent, that is, the array has amplitude and phase errors, which will cause steering vector mismatch. In the super-resolution DOA estimation method based on compressive sensing, the sensing matrix is composed of Steering vector composition, the mismatch of the steering vector will cause the super-resolution performance to drop rapidly.

综上所述,当阵列中存在幅相误差时,上述现有方法的测角精度和目标分辨性能急剧下降,不能有效实现目标的超分辨DOA估计。To sum up, when there are amplitude and phase errors in the array, the angle measurement accuracy and target resolution performance of the above existing methods drop sharply, and the super-resolution DOA estimation of the target cannot be effectively achieved.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于针对上述现有技术的不足,提出一种提出了一种基于总体最小二乘-压缩感知TLS-CS的外辐射源雷达超分辨DOA估计方法,以提高目标超分辨DOA估计的测角精度和目标分辨性能,有效实现目标的超分辨DOA估计。The purpose of the present invention is to propose a method for super-resolution DOA estimation of external radiation source radar based on total least squares-compressed sensing TLS-CS in view of the above-mentioned deficiencies of the prior art, so as to improve the target super-resolution DOA estimation accuracy. The angle measurement accuracy and target resolution performance can effectively realize the super-resolution DOA estimation of the target.

实现本发明目的的思路是,通过奇异值分解方法求解存在幅相误差的总体最小二乘TLS信号模型,得到修正幅相误差后的导向矢量,将修正后的导向矢量作为感知矩阵,利用贪恋迭代追踪匹配算法对目标的方位信息进行压缩感知稀疏重构,实现超分辨DOA估计。The idea of realizing the purpose of the present invention is to solve the overall least squares TLS signal model with amplitude and phase errors by a singular value decomposition method, obtain a steering vector after correcting the amplitude and phase errors, use the corrected steering vector as a perception matrix, and use greedy iteration. The tracking and matching algorithm sparsely reconstructs the orientation information of the target by compressed sensing, and realizes super-resolution DOA estimation.

根据上述思路,本发明的实现方案包括如下:According to the above-mentioned ideas, the implementation scheme of the present invention includes the following:

(1)分别获取阵列天线接收的回波信号Sech和参考天线接收辐射源方向的直达波信号Sref(1) respectively obtain the echo signal S ech received by the array antenna and the direct wave signal S ref in the direction of the radiation source received by the reference antenna;

(2)利用参考天线接收辐射源方向的直达波信号,采用扩展相消算法对回波信号中的直达波和多路径干扰进行抑制,得到杂波抑制后的回波信号Ssur(2) Utilize the reference antenna to receive the direct wave signal in the direction of the radiation source, adopt the extended cancellation algorithm to suppress the direct wave and multipath interference in the echo signal, and obtain the echo signal S sur after clutter suppression;

(3)对杂波抑制后的回波信号Ssur进行距离-多普勒二维相关处理,得到复矢量信号S;(3) Perform range-Doppler two-dimensional correlation processing on the clutter-suppressed echo signal S sur to obtain a complex vector signal S;

S=A*Star+Z <1>S=A*S tar +Z <1>

Star表示目标回波信号,A表示目标对应的导向矢量,Z表示噪声信号; Star represents the target echo signal, A represents the steering vector corresponding to the target, and Z represents the noise signal;

(4)对复矢量信号S加入幅相扰动参数ΔA,得到存在幅相误差的TLS信号模型,

Figure BDA0002129161920000021
为存在幅相误差的复矢量信号:(4) Add the amplitude and phase disturbance parameter ΔA to the complex vector signal S to obtain the TLS signal model with amplitude and phase errors,
Figure BDA0002129161920000021
is a complex vector signal with amplitude and phase errors:

Figure BDA0002129161920000022
Figure BDA0002129161920000022

(5)设整个观测空间导向矢量的行数为阵元个数M,列数为观测空间的划分个数N,构建一个M×N维矩阵,作为观测区间的导向矢量D;(5) Set the number of rows of the steering vector of the entire observation space as the number of array elements M, and the number of columns as the number of divisions of the observation space N, and construct an M×N-dimensional matrix as the steering vector D of the observation interval;

(6)将整个观测区间的导向矢量D作为存在幅相扰动的导向矢量,代入复矢量信号

Figure BDA0002129161920000023
中,并利用奇异值分解方法对其进行求解,得到修正幅相误差后的导向矢量
Figure BDA0002129161920000024
(6) Take the steering vector D of the entire observation interval as the steering vector with amplitude and phase disturbance, and substitute it into the complex vector signal
Figure BDA0002129161920000023
, and use the singular value decomposition method to solve it, and get the steering vector after correcting the amplitude and phase errors
Figure BDA0002129161920000024

(7)将复矢量信号

Figure BDA0002129161920000025
作为测量矢量,修正幅相误差后的导向矢量
Figure BDA0002129161920000026
作为感知矩阵,利用贪恋迭代追踪算法对处于同一距离-多普勒单元的多个目标的方位信息进行压缩感知稀疏重构,得到多个目标的方位信息。(7) Convert the complex vector signal
Figure BDA0002129161920000025
As the measurement vector, the steering vector after correcting the amplitude and phase errors
Figure BDA0002129161920000026
As a perception matrix, the orientation information of multiple targets in the same range-Doppler unit is sparsely reconstructed by compressive sensing using the greedy iterative tracking algorithm, and the orientation information of multiple targets is obtained.

本发明与现有技术相比具有以下优点:Compared with the prior art, the present invention has the following advantages:

1.本发明由于考虑了幅相误差对回波信号的影响,在回波信号模型中加入幅相误差,利用奇异值分解方法求解修正幅相误差,再利用贪恋迭代匹配追踪算法对多个目标的方位信息进行稀疏重构,得到目标的方位,提高了目标的测角精度和分辨性能。1. In the present invention, since the influence of the amplitude and phase error on the echo signal is considered, the amplitude and phase error is added to the echo signal model, and the singular value decomposition method is used to solve and correct the amplitude and phase error, and then the greedy iterative matching and tracking algorithm is used to detect multiple targets. The azimuth information of the target is sparsely reconstructed to obtain the azimuth of the target, which improves the angular measurement accuracy and resolution performance of the target.

2.本发明仅需要接收回波信号的阵列天线和接收直达波信号的参考天线,不需要额外的校准天线,实现简单。2. The present invention only needs an array antenna for receiving echo signals and a reference antenna for receiving direct wave signals, no additional calibration antenna is required, and the implementation is simple.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案,下面将对实施例或现有技术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一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他的附图。In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

图1为外辐射源雷达的应用场景示意图;Figure 1 is a schematic diagram of the application scenario of the external radiation source radar;

图2为本发明的实现流程图;Fig. 2 is the realization flow chart of the present invention;

图3为不存在幅相误差时传统方法和本发明方法的仿真实验结果图;Fig. 3 is the simulation experiment result diagram of traditional method and the inventive method when there is no amplitude-phase error;

图4为存在幅相误差时传统方法和本发明方法的仿真实验结果图。FIG. 4 is a graph showing the simulation results of the traditional method and the method of the present invention when there is an amplitude-phase error.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

首先,为便于理解,以下都将基于图1所示的外辐射源雷达的应用场景,外辐射源雷达应用场景介绍如下:First of all, for ease of understanding, the following will be based on the application scenario of the external radiation source radar shown in Figure 1. The application scenarios of the external radiation source radar are introduced as follows:

如图1所示,第三方非合作外辐射源置于位于外辐射源雷达接收站的远场作为发射站,以此来发射电磁波信号,电磁波信号照射在阵列天线覆盖空域中的目标所反射回来的信号称为目标回波信号,不经过反射直接照射到参考天线上的电磁波称为直达波信号,又称参考信号。外辐射源雷达通过阵列天线接收目标回波信号,通过参考天线接收直达波信号,然后使用雷达信号处理算法对目标回波信号和直达波信号进行处理,进而获得目标的距离、速度及方位信息。由图1可知,外辐射源雷达阵列天线除接收目标回波信号外,还会不可避免的接收到来自发射站方向的强直达波信号和经过不同障碍物反射的多路径干扰信号,通常情况下目标回波信号能量远低于直达波和多径干扰信号,因此需要利用参考天线接收的直达波来消除阵列天线接收的直达波和多路径干扰信号并通过距离—多普勒处理提高目标回波的能量。As shown in Figure 1, the third-party non-cooperative external radiation source is placed in the far field of the radar receiving station of the external radiation source as a transmitting station to transmit electromagnetic wave signals, and the electromagnetic wave signals are reflected by the targets in the airspace covered by the array antenna. The signal is called the target echo signal, and the electromagnetic wave that directly irradiates the reference antenna without reflection is called the direct wave signal, also known as the reference signal. The external radiation source radar receives the target echo signal through the array antenna, receives the direct wave signal through the reference antenna, and then uses the radar signal processing algorithm to process the target echo signal and the direct wave signal, and then obtains the target distance, speed and azimuth information. It can be seen from Figure 1 that in addition to receiving the target echo signal, the radar array antenna of the external radiation source will inevitably receive the strong direct wave signal from the direction of the transmitting station and the multi-path interference signal reflected by different obstacles. The energy of the target echo signal is much lower than the direct wave and multipath interference signal, so it is necessary to use the direct wave received by the reference antenna to eliminate the direct wave and multipath interference signal received by the array antenna and improve the target echo through range-Doppler processing. energy of.

参照图2,本发明的实施例提供的基于总体最小二乘-压缩感知的外辐射源雷达超分辨DOA估计方法,其实现步骤包括如下:Referring to Fig. 2, an embodiment of the present invention provides an external radiation source radar super-resolution DOA estimation method based on overall least squares-compressed sensing, and its implementation steps include the following:

步骤1:分别获取阵列天线接收的回波信号Sech和参考天线接收辐射源方向的直达波信号SrefStep 1: respectively obtain the echo signal S ech received by the array antenna and the direct wave signal S ref in the direction of the radiation source received by the reference antenna;

设阵列天线由阵元间距为半波长的均匀线阵组成,阵元数为M,M≥11,接收M路回波信号Sech,其中每路回波信号Sech包含来自发射台方向的强直达波、经多路径反射的多径干扰信号及噪声信号;Suppose that the array antenna is composed of a uniform linear array with an array element spacing of half wavelength, the number of array elements is M, M≥11, and receives M echo signals S ech , wherein each echo signal S ech contains a strong straight line from the direction of the transmitting station. Arrival waves, multipath interference signals and noise signals reflected by multipath;

设参考天线由一根单独指向发射台方向的窄波束天线构成,接收来自辐射源方向的直达波信号SrefIt is assumed that the reference antenna consists of a narrow-beam antenna that points to the direction of the transmitting station alone, and receives the direct wave signal S ref from the direction of the radiation source.

步骤2:利用参考天线接收辐射源方向的直达波信号Sref,采用扩展相消算法对回波信号Sech中的直达波和多路径干扰信号进行抑制,得到杂波抑制后的回波信号SsurStep 2: Use the reference antenna to receive the direct wave signal S ref in the direction of the radiation source, and use the extended cancellation algorithm to suppress the direct wave and multipath interference signals in the echo signal S ech to obtain the echo signal S after clutter suppression sur .

由于阵列天线接收的回波信号Sref中不仅包含目标反射的回波信号,还包括来自辐射源的直达波信号和经过建筑、道路反射的多径杂波信号,其能量均远远大于目标回波信号,使得目标回波淹没在杂波信号中,不能检测到目标,因此必须对杂波信号进行抑制。通过将回波信号投影到由直达波信号Sref及其时延构成的正交子空间V上,杂波信号在该正交子空间V会存在一组不全为零的投影系数,它代表了各种杂波信号的强度,求解这组不全为零的投影系数就可以将回波信号中存在的杂波对消掉,得到杂波抑制后的回波信号SsurSince the echo signal S ref received by the array antenna includes not only the echo signal reflected by the target, but also the direct wave signal from the radiation source and the multipath clutter signal reflected by buildings and roads, the energy of which is far greater than that of the target echo signal. The target echo is submerged in the clutter signal, and the target cannot be detected, so the clutter signal must be suppressed. By projecting the echo signal onto the orthogonal subspace V composed of the direct wave signal S ref and its time delay, the clutter signal will have a set of projection coefficients that are not all zero in the orthogonal subspace V, which represent According to the intensity of various clutter signals, the clutter existing in the echo signal can be eliminated by solving this group of projection coefficients that are not all zero, and the echo signal S sur after clutter suppression can be obtained.

本步骤的具体实现如下:The specific implementation of this step is as follows:

(2a)利用直达波Sref及其时延构建杂波正交子空间V:(2a) Use the direct wave S ref and its time delay to construct the clutter orthogonal subspace V:

Figure BDA0002129161920000041
Figure BDA0002129161920000041

其中,G为直达波信号的数据长度,C为杂波对消阶数,矩阵的第一列表示直达波信号,第二列表示时延单元为一的多径信号,第N列表示时延单元为C的多径信号;Among them, G is the data length of the direct wave signal, C is the clutter cancellation order, the first column of the matrix represents the direct wave signal, the second column represents the multipath signal with one delay unit, and the Nth column represents the delay The multipath signal whose unit is C;

(2b)将回波信号Sech投影到杂波正交子空间V中,求解这组在该子空间上不全为零的投影系数W:(2b) Project the echo signal S ech into the clutter orthogonal subspace V, and solve the set of projection coefficients W that are not all zero on this subspace:

W=(VH*V)-1VHSech, <3>其中VH表示对矩阵V的共轭转置,(VH*V)-1表示对矩阵乘积结果求逆;W=(V H *V) -1 V H S ech , <3> where V H represents the conjugate transpose of the matrix V, and (V H *V) -1 represents the inversion of the matrix product result;

(2c)根据将回波信号Sech、杂波正交子空间V和不全为零投影系数W,得到杂波抑制后的剩余回波信号Ssur(2c) According to the echo signal S ech , the clutter orthogonal subspace V and the non-zero projection coefficient W, the residual echo signal S sur after clutter suppression is obtained:

Ssur=Sech-V*W。 <4>S sur =S ech -V*W. <4>

步骤3:对剩余回波信号Ssur进行距离-多普勒二维相关处理,得到复矢量信号S。Step 3: Perform range-Doppler two-dimensional correlation processing on the residual echo signal S sur to obtain a complex vector signal S.

经过杂波抑制后,回波信号Sech中包含的杂波信号已经消除,然而剩余回波信号Ssur中的目标回波信号的能量仍低于噪声信号,因此进行距离-多普勒二维相关处理提高目标回波信号的能量,得到理想情况下的信号模型,S为距离-多普勒二维相关处理后得到复矢量信号。After clutter suppression, the clutter signal contained in the echo signal S ech has been eliminated, but the energy of the target echo signal in the remaining echo signal S sur is still lower than the noise signal, so the distance-Doppler two-dimensional The correlation processing increases the energy of the target echo signal, and obtains the signal model under ideal conditions. S is the complex vector signal obtained after range-Doppler two-dimensional correlation processing.

本步骤的具体实现如下:The specific implementation of this step is as follows:

(3a)将杂波抑制后的剩余回波信号Ssur与时延后的共轭参考信号Sref *[g-τ]点乘,得到距离维相关处理后的复矢量信号Sm(3a) Dot-multiply the residual echo signal S sur after clutter suppression and the time-delayed conjugate reference signal S ref * [g-τ] to obtain the complex vector signal S m after range dimension correlation processing:

Figure BDA0002129161920000051
Figure BDA0002129161920000051

式中τ表示运动目标的距离,G为剩余回波信号Ssur的长度;where τ represents the distance of the moving target, and G is the length of the residual echo signal S sur ;

(3b)对距离维相关处理后的复矢量信号Sm进行多普勒维相关积累后,得到多普勒维相关积累后的目标信号Star(3b) After performing Doppler-dimensional correlation accumulation on the complex vector signal S m after range-dimensional correlation processing, the target signal S tar after Doppler-dimensional correlation accumulation is obtained:

Figure BDA0002129161920000052
Figure BDA0002129161920000052

(3c)对目标信号Star加入导向矢量A、噪声Z,得到距离-多普勒二维相关处理复矢量信号S:(3c) Add the steering vector A and the noise Z to the target signal S tar to obtain the range-Doppler two-dimensional correlation processing complex vector signal S:

S=A*Star+Z。 <7>S=A* Star +Z. <7>

步骤4:对复矢量信号S加入幅相扰动参数ΔA,得到存在幅相误差的TLS信号模型,

Figure BDA0002129161920000053
为存在幅相误差的复矢量信号:。Step 4: Add the amplitude and phase disturbance parameter ΔA to the complex vector signal S to obtain the TLS signal model with amplitude and phase errors,
Figure BDA0002129161920000053
is a complex vector signal with amplitude and phase errors: .

步骤3中的复矢量信号S是理想情况下推导得到的,但是在外辐射源雷达实际工作中,复矢量信号S不可避免的受到幅相误差的影响,因此在<7>式加入幅相误差ΔA,得到TLS模型,

Figure BDA0002129161920000054
为存在幅相误差的复矢量信号:The complex vector signal S in step 3 is derived under ideal conditions, but in the actual operation of the external radiation source radar, the complex vector signal S is inevitably affected by the amplitude and phase error, so the amplitude and phase error ΔA is added to the formula <7>. , get the TLS model,
Figure BDA0002129161920000054
is a complex vector signal with amplitude and phase errors:

Figure BDA0002129161920000055
Figure BDA0002129161920000055

步骤5:构建整个观测空间的导向矢量D。Step 5: Construct the steering vector D for the entire observation space.

设整个观测空间导向矢量的行数为阵元个数M,列数为观测空间的划分个数N,构建一个M×N维矩阵,作为观测区间的导向矢量D:Let the number of rows of the steering vector of the entire observation space be the number of array elements M, and the number of columns to be the number of divisions of the observation space N, and construct an M×N-dimensional matrix as the steering vector D of the observation interval:

Figure BDA0002129161920000056
Figure BDA0002129161920000056

其中,θ1为观测区间的起始方位,θN为观测区间的截止方位,d为天线阵元间距,λ为发射电磁波波长。Among them, θ 1 is the starting azimuth of the observation interval, θ N is the end azimuth of the observation interval, d is the distance between the antenna elements, and λ is the wavelength of the emitted electromagnetic wave.

步骤6:将整个观测区间的导向矢量D作为存在幅相扰动的导向矢量,替代<6>式的A+ΔA,并利用奇异值分解方法对其进行求解,得到修正幅相误差后的导向矢量

Figure BDA0002129161920000061
Step 6: Take the steering vector D of the entire observation interval as the steering vector with amplitude and phase disturbance, replace A+ΔA in the formula <6>, and solve it by the singular value decomposition method, and obtain the steering vector after correcting the amplitude and phase error.
Figure BDA0002129161920000061

本步骤的具体实现如下:The specific implementation of this step is as follows:

(6a)构建M×(N+1)维扩展矩阵

Figure BDA0002129161920000062
其中
Figure BDA0002129161920000063
为M×1维存在幅相误差的复矢量信号,D为M×N维修正幅相误差后的导向矢量;(6a) Construct M×(N+1) dimensional extended matrix
Figure BDA0002129161920000062
in
Figure BDA0002129161920000063
is the complex vector signal with amplitude and phase error in M×1 dimension, D is the steering vector after M×N repairing the positive amplitude and phase error;

(6b)计算扩展矩阵B的奇异值分解:(6b) Calculate the singular value decomposition of the extended matrix B:

B=UΣVH,B=UΣV H ,

其中Σ为M×MM×M维的对角阵Σ=(diag(σ12,…,σM),0),0为M×(N-M+1)维矩阵,其元素均为0;diag(σ12,…,σM)是主对角元素为σ12,…,σM的M×M维矩阵,VH表示矩阵V的共轭转置;where Σ is an M×MM×M dimensional diagonal matrix Σ=(diag(σ 12 ,…,σ M ),0), 0 is an M×(N-M+1) dimensional matrix, and its elements are is 0; diag(σ 12 ,…,σ M ) is an M×M-dimensional matrix whose main diagonal elements are σ 12 ,…,σ M , and V H represents the conjugate transpose of matrix V;

(6c)从主对角元素σ12,…,σM寻找一个突变元素σp,当σp满足σp>σM+ξ≥σp+1≥…≥σM时,ξ=max[(σ12),(σ23),…,(σM-1M)],将下标P作为有效秩阶次,构造(N+1)×(N+1)维校正矩阵:E=[Ip,0]T,Ip为p×p维单位矩阵,0是零矩阵;(6c) Find a mutation element σ p from the main diagonal elements σ 1 , σ 2 ,…,σ M , when σ p satisfies σ pM +ξ≥σ p+1 ≥…≥σ M , ξ= max[(σ 12 ),(σ 23 ),…,(σ M-1M )], using the subscript P as the effective rank order, construct (N+1)×(N +1) dimensional correction matrix: E=[I p ,0] T , I p is a p×p dimensional unit matrix, and 0 is a zero matrix;

(6d)将校正矩阵E加入式<7>,左乘对角阵Σ,得到增广矩阵B的最佳逼近矩阵

Figure BDA0002129161920000064
(6d) Add the correction matrix E to formula <7>, and multiply the diagonal matrix Σ to the left to obtain the best approximation matrix of the augmented matrix B
Figure BDA0002129161920000064

Figure BDA0002129161920000065
Figure BDA0002129161920000065

(6e)对最佳逼近矩阵

Figure BDA0002129161920000066
进行拆分,将
Figure BDA0002129161920000067
的第2列至第N+1列作为修正幅相误差后的导向矢量
Figure BDA0002129161920000068
Figure BDA0002129161920000069
为M×N维矩阵。(6e) For the best approximation matrix
Figure BDA0002129161920000066
split,
Figure BDA0002129161920000067
Columns 2 to N+1 of , are used as the steering vector after correcting the amplitude and phase errors
Figure BDA0002129161920000068
Figure BDA0002129161920000069
is an M×N dimensional matrix.

步骤7:将复矢量信号

Figure BDA00021291619200000610
作为测量矢量,修正幅相误差后的导向矢量
Figure BDA00021291619200000611
作为感知矩阵,利用贪恋迭代追踪算法对处于同一距离-多普勒单元的多个目标的方位信息进行压缩感知稀疏重构,得到多个目标的方位信息。Step 7: Convert the complex vector signal
Figure BDA00021291619200000610
As the measurement vector, the steering vector after correcting the amplitude and phase errors
Figure BDA00021291619200000611
As a perception matrix, the orientation information of multiple targets in the same range-Doppler unit is sparsely reconstructed by compressive sensing using the greedy iterative tracking algorithm, and the orientation information of multiple targets is obtained.

本步骤的具体实现如下:The specific implementation of this step is as follows:

(7a)将测量矢量

Figure BDA00021291619200000612
作为初始输入,记作e0;(7a) will measure the vector
Figure BDA00021291619200000612
As the initial input, denoted as e 0 ;

(7b)从感知矩阵

Figure BDA00021291619200000613
中筛选与e0内积绝对值最大的一列,并表示为
Figure BDA00021291619200000614
(7b) From the perception matrix
Figure BDA00021291619200000613
Filter the column with the largest absolute value of the inner product with e 0 and express it as
Figure BDA00021291619200000614

(7c)根据(7a)和(7b)的结果,计算得到残值e1(7c) According to the results of (7a) and (7b), calculate the residual value e 1 :

Figure BDA00021291619200000615
Figure BDA00021291619200000615

其中

Figure BDA00021291619200000616
表示e0
Figure BDA00021291619200000617
的内积;in
Figure BDA00021291619200000616
means e 0 with
Figure BDA00021291619200000617
The inner product of ;

(7d)将(7c)计算得到的残值作为(7a)新的输入,重复执行(7b)和(7c)共K次,得到感知矩阵

Figure BDA0002129161920000071
中与测量矢量
Figure BDA0002129161920000072
最相关的K个矢量
Figure BDA0002129161920000073
K的范围小于等于7,本实例取值为7;(7d) Use the residual value calculated in (7c) as the new input of (7a), and repeat (7b) and (7c) K times to obtain the perception matrix
Figure BDA0002129161920000071
Neutral and measure vector
Figure BDA0002129161920000072
Most relevant K vectors
Figure BDA0002129161920000073
The range of K is less than or equal to 7, and the value in this example is 7;

(7e)当相关矢量

Figure BDA0002129161920000074
位于感知矩阵
Figure BDA0002129161920000075
中的第n列,则目标的方位θ为:(7e) When the correlation vector
Figure BDA0002129161920000074
in the perception matrix
Figure BDA0002129161920000075
In the nth column, the orientation θ of the target is:

θ=(n-N/2)*(θN1)/N,n∈1,2,…,Nθ=(nN/2)*(θ N1 )/N, n∈1,2,...,N

其中,N为整个空间的总列数,θ1为观测区间的起始方位,θN为观测区间的截止方位。Among them, N is the total number of columns in the entire space, θ 1 is the starting orientation of the observation interval, and θ N is the ending orientation of the observation interval.

本发明的效果可通过以下仿真实验进一步说明:The effect of the present invention can be further illustrated by the following simulation experiments:

1.实验条件:1. Experimental conditions:

本发明试验中将调频广播信号FM作为辐射源,频率为93.1MHz,带宽200kHz,采样率为200kHz,积累时间为1s;阵列天线由间隔为半波长的均匀线阵组成,阵元个数为15,同时阵列天线接收到2个位于同一个距离-多普勒单元的目标回波信号。以下通过两组仿真实验来说明本发明方法的性能,目标的仿真参数如表一所示。In the experiment of the invention, the FM broadcast signal FM is used as the radiation source, the frequency is 93.1MHz, the bandwidth is 200kHz, the sampling rate is 200kHz, and the accumulation time is 1s; , and the array antenna receives two target echo signals located in the same range-Doppler unit. The performance of the method of the present invention is described below through two sets of simulation experiments, and the simulation parameters of the target are shown in Table 1.

表一目标的仿真参数Table 1. Simulation parameters of the target

Figure BDA0002129161920000076
Figure BDA0002129161920000076

2.仿真内容与结果2. Simulation content and results

仿真一,在阵列不存在幅相误差条件下,利用传统方法和本发明的方法对两个目标的方位信息进行压缩感知稀疏重构仿真,得到的两个目标的方位,结果如图3所示,其中:Simulation 1: Under the condition that there is no amplitude and phase error in the array, the traditional method and the method of the present invention are used to perform compressive sensing sparse reconstruction simulation on the orientation information of the two targets, and the orientations of the two targets are obtained. The results are shown in Figure 3 ,in:

图3(a)为利用传统压缩感知超分辨DOA估计方法得到的方位信息;Figure 3(a) is the orientation information obtained by using the traditional compressed sensing super-resolution DOA estimation method;

图3(b)为本发明方法得到的方位信息;Figure 3 (b) is the orientation information obtained by the method of the present invention;

从图3可以看出,传统方法和本发明方法均可以有效分辨出两个目标,并且检测出目标的方位为[5°,14°],与假设目标方位一致。It can be seen from Figure 3 that both the traditional method and the method of the present invention can effectively distinguish two targets, and the detected target orientation is [5°, 14°], which is consistent with the assumed target orientation.

仿真二,在阵列存在幅相误差为-30dB条件下,利用传统方法和本发明方法对两个目标的方位信息进行压缩感知稀疏重构仿真,得到的两个目标的方位,结果如图4所示,其中:Simulation 2, under the condition that the amplitude and phase error of the array is -30dB, the traditional method and the method of the present invention are used to carry out compressive sensing sparse reconstruction simulation on the orientation information of the two targets, and the orientations of the two targets are obtained. The results are shown in Figure 4. shown, including:

图4(a)为阵列幅相误差为-30dB时利用传统压缩感知超分辨DOA估计方法得到的方位信息;Figure 4(a) shows the azimuth information obtained by using the traditional compressed sensing super-resolution DOA estimation method when the amplitude and phase error of the array is -30dB;

图4(b)为阵列幅相误差为-30dB时利用本发明方法得到的方位信息;Figure 4(b) is the azimuth information obtained by the method of the present invention when the amplitude and phase error of the array is -30dB;

从图4可以看出,当阵列的幅相误差为-30dB时,利用本发明方法检测到两个目标的方位分别为5°和14°,说明该方法能够在阵列存在幅相误差的时,抑制幅相误差对导向矢量影响,并且对两个目标进行有效分辨,且与假设的目标来向一致,而利用传统方法进行检测会多个虚假方位信息,且均与假设的目标方位信息不一致,不能对两个目标进行有效分辨。It can be seen from Fig. 4 that when the amplitude and phase error of the array is -30dB, the azimuths of the two targets detected by the method of the present invention are respectively 5° and 14°, indicating that the method can be used when the array has amplitude and phase errors. Suppressing the influence of amplitude and phase errors on the steering vector, and effectively distinguishing the two targets, which are consistent with the assumed target direction, while using the traditional method to detect multiple false azimuth information, which are inconsistent with the assumed target azimuth information, The two targets cannot be effectively distinguished.

以上所述,仅为本发明的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,可轻易想到变化或替换,都应涵盖在本发明的保护范围之内。因此,本发明的保护范围应以所述权利要求的保护范围为准。The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention. should be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (5)

1. A TLS-CS-based super-resolution DOA estimation method for an external radiation source radar is characterized by comprising the following steps:
(1) respectively acquiring echo signals S received by array antennas ech And a reference antenna for receiving the direct wave signal S in the radiation source direction ref
(2) Utilizing a reference antenna to receive a direct wave signal in the radiation source direction, and adopting an extended cancellation algorithm to suppress the direct wave and multipath interference in an echo signal to obtain an echo signal S after clutter suppression sur
(3) Echo signal S after clutter suppression sur Performing distance-Doppler two-dimensional correlation processing to obtain a complex vector signal S;
S=A*S tar +Z <1>
S tar representing a target echo signal, A representing a steering vector corresponding to a target, and Z representing a noise signal;
(4) adding the complex vector signal S into the amplitude-phase disturbance parameter delta A to obtain a TLS signal model with amplitude-phase errors,
Figure FDA0003779243450000012
for complex vector signals with amplitude and phase errors:
Figure FDA0003779243450000011
(5) setting the number of rows of a guide vector of the whole observation space as the number M of array elements and the number of columns as the number N of division of the observation space, and constructing an MxN dimensional matrix as a guide vector D of an observation interval;
(6) taking the guide vector D of the whole observation interval as a guide vector with amplitude-phase disturbance instead of the guide vector D<2>A + delta A of the formula, and solving by using a singular value decomposition method<2>After obtaining the corrected amplitude-phase errorGuide vector of
Figure FDA0003779243450000014
(7) Will complex vector signal
Figure FDA0003779243450000015
As a measurement vector, a guide vector after correcting an amplitude-phase error
Figure FDA0003779243450000019
As a sensing matrix, compressed sensing sparse reconstruction is performed on the orientation information of a plurality of targets in the same range-Doppler unit by using a greedy iterative tracking algorithm to obtain the orientation information of the plurality of targets, and the implementation is as follows:
(7a) will measure the vector
Figure FDA0003779243450000016
As an initial input, note e 0
(7b) From the perception matrix
Figure FDA0003779243450000017
Middle screening with e 0 One column with the largest absolute value of inner product is shown as
Figure FDA0003779243450000018
(7c) Calculating residual value e according to the results of (7a) and (7b) 1
Figure FDA0003779243450000021
Wherein
Figure FDA0003779243450000022
Denotes e 0 And
Figure FDA0003779243450000023
inner product of (d);
(7d) taking the residual value obtained by the calculation of (7c) as a new input of (7a), and repeatedly executing (7b) and (7c) for K times to obtain a perception matrix
Figure FDA0003779243450000024
Neutralization measurement vector
Figure FDA0003779243450000025
Most relevant K vectors
Figure FDA0003779243450000026
(7e) When the vector is correlated
Figure FDA0003779243450000027
Is located in the sensing matrix
Figure FDA0003779243450000028
Column n in (d), the azimuth θ of the target is:
θ=(n-N/2)*(θ N1 )/N,n∈1,2,…,N
where N is the total number of columns in the entire space, θ 1 To the starting position of the observation interval, θ N Is the cut-off orientation of the observation interval.
2. The method of claim 1, wherein the step (2) is implemented as follows:
(2a) using direct waves S ref And constructing a clutter orthogonal subspace V by time delay:
Figure FDA0003779243450000029
wherein G is the data length of the direct wave signal, C is the clutter cancellation order, the first column of the matrix represents the direct wave signal, the second column represents the multipath signal with the time delay unit of one, and the Nth column represents the multipath signal with the time delay unit of C;
(2b) echo signal S ech Projecting into a clutter orthogonal subspace V, solving the set of projection coefficients W which are not all zero on the subspace:
W=(V H *V) -1 V H S ech , <3>
wherein V H Represents a conjugate transpose of the matrix V; (V) H *V) -1 Expressing the inversion of the matrix product result;
(2c) according to the echo signal S ech Obtaining a clutter suppressed residual echo signal S by using a clutter orthogonal subspace V and a projection coefficient W which is not completely zero sur
S sur =S ech -V*W <4>。
3. The method of claim 1 wherein step (3) is practiced with respect to clutter suppressed echo signal S sur And (3) performing distance-Doppler two-dimensional correlation processing, which is realized as follows:
(3a) the residual echo signal S after clutter suppression sur With time-delayed conjugate reference signal S ref * [g-τ]Point multiplication to obtain complex vector signal S after distance dimension correlation processing m
Figure FDA0003779243450000031
Wherein τ represents the distance of the moving object, f d Representing the Doppler induced by relative motion between the moving object and the array antenna, G being the residual echo signal S sur Length of (d);
(3b) the complex vector signal S after the distance dimension correlation processing m After Doppler dimension correlation accumulation is carried out, a target signal S after Doppler dimension correlation accumulation is obtained tar
Figure FDA0003779243450000032
(3c) For the target signal S tar Adding a guide vector A and a noise Z to obtain a distance-Doppler two-dimensional correlation processing complex vector signal S:
S=A*S tar +Z <7>。
4. the method of claim 1, wherein the observation space steering vector D in step (5),
is represented as follows:
Figure FDA0003779243450000033
wherein M is the number of array elements, N is the total column number of the whole space, and theta 1 To the starting position of the observation interval, θ N D is the distance between the antenna elements, and lambda is the wavelength of the emitted electromagnetic wave.
5. The method according to claim 1, characterized in that said step (6) is implemented as follows:
(6a) construction of M × (N +1) -dimensional extended matrix
Figure FDA0003779243450000034
Figure FDA0003779243450000035
Complex vector signals with amplitude-phase errors exist in MxN 1 dimensions, and D is a guide vector after the M xN maintenance of positive amplitude-phase errors;
(6b) calculating the singular value decomposition of the expansion matrix B:
B=UΣV H , <8>
wherein Σ is M × MM × M dimensional diagonal matrix ═ i (diag (σ) 12 ,…,σ M ) 0), 0 is an M × (N-M +1) -dimensional matrix, the elements of which are all 0; diag (sigma) 12 ,…,σ M ) Is that the main diagonal element is sigma 12 ,…,σ M M × M dimensional matrix of (a); v H Conjugate transitions of the representation matrix VPlacing;
(6c) from the principal diagonal element σ 12 ,…,σ M Search for a mutant element sigma p When σ is p Satisfy sigma p >σ M +ξ≥σ p+1 ≥…≥σ M When xi is max [ (sigma) 12 ),(σ 23 ),…,(σ M-1M )]Taking P as an effective rank order, constructing a (N +1) × (N +1) -dimensional correction matrix: e ═ I p ,0] T ,I p The matrix is a p multiplied by p dimension unit matrix, 0 is a zero matrix, and the elements of the zero matrix are 0;
(6d) adding the correction matrix E to the equation<8>Left-hand multiplication of the diagonal matrix sigma to obtain the optimal approximation matrix of the augmented matrix B
Figure FDA0003779243450000041
Figure FDA0003779243450000042
(6e) For the best approximation matrix
Figure FDA0003779243450000043
Carrying out the resolution of
Figure FDA0003779243450000044
As a guide vector after correcting the amplitude-phase error
Figure FDA0003779243450000045
Figure FDA0003779243450000046
Is an M × N dimensional matrix.
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