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CN107607914B - Modeling method for ultra-low-altitude target and multipath echo of missile-borne PD system radar - Google Patents

Modeling method for ultra-low-altitude target and multipath echo of missile-borne PD system radar Download PDF

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CN107607914B
CN107607914B CN201710749990.2A CN201710749990A CN107607914B CN 107607914 B CN107607914 B CN 107607914B CN 201710749990 A CN201710749990 A CN 201710749990A CN 107607914 B CN107607914 B CN 107607914B
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许京伟
梁士福
廖桂生
朱圣棋
李婕
冯阳
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Xidian University
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Abstract

The invention discloses a modeling method for an ultra-low-altitude target and multipath echoes of a missile-borne PD system radar, which mainly comprises the following steps of: determining a radar, wherein an ultra-low-altitude target exists in a detection range of the radar, establishing a multi-path propagation space geometric configuration of the ultra-low-altitude target, and determining a scattering area; determining an equivalent single-base radar, calculating a ground wiping angle of the equivalent single-base radar, and further calculating a scattering coefficient of the equivalent single-base radar; calculating dielectric constants of the ground and the sea surface, further calculating to obtain a reflection coefficient corresponding to the Brewster effect, and then calculating to obtain a scattering coefficient of a scattering area according to the scattering coefficient of the equivalent single-base radar; according to the scattering coefficient of the scattering area, four-path baseband echo signals received by the radar at the time t are calculated, and the four-path baseband echo signals received by the radar at the time t are modeling results of the ultra-low-altitude target and the multi-path echoes of the missile-borne PD system radar; t represents a time variable.

Description

一种弹载PD体制雷达超低空目标与多径回波建模方法A method for modeling ultra-low-altitude targets and multipath echoes of missile-borne PD system radar

技术领域technical field

本发明属于雷达技术领域，特别涉及一种弹载PD体制雷达超低空目标与多径回波建模方法，适用于对超低空目标与多径回波进行建模，实现对动目标的检测。The invention belongs to the technical field of radar, and particularly relates to a method for modeling ultra-low altitude targets and multipath echoes of missile-borne PD system radars, which is suitable for modeling ultra-low altitude targets and multipath echoes to realize detection of moving targets.

背景技术Background technique

当雷达在探测与跟踪超低空目标时，目标的多路径传播现象明显；由于目标在相对平坦的海面或地面飞行时，雷达接收到的回波信号不仅包含目标的直接路径信号，还包含目标经地海面反射形成的多径信号；而当目标低空飞行时，各路径回波之间的路程差很小，回波信号叠加在同一距离单元内，多路径传播会造成回波信号幅度的规律性变化(目标闪烁)，或相干叠加，或相干相消，造成无法得到真实目标回波信息；因此，深入研究多路径效应，为克服多路径影响而采取相应的技术措施,是提高防空导弹低空探测性能的必由之路。When the radar detects and tracks ultra-low-altitude targets, the multi-path propagation phenomenon of the target is obvious; when the target is flying on a relatively flat sea or ground, the echo signal received by the radar not only includes the direct path signal of the target, but also includes the target's path signal. The multipath signal formed by the reflection of the ground and sea surface; when the target flies at a low altitude, the path difference between the echoes of each path is very small, the echo signals are superimposed in the same distance unit, and the multipath propagation will cause the regularity of the echo signal amplitude Change (target flickering), or coherent superposition, or coherent cancellation, resulting in the inability to obtain real target echo information; therefore, in-depth research on multi-path effects and taking corresponding technical measures to overcome multi-path effects is to improve the low-altitude detection of air defense missiles. Performance is the way to go.

杨勇等在论文“多径环境下海面低空目标检测技术研究”(电波科学学报,2011(3)：443-449.)中提出了一种低空环境下的目标多径散射建模方法，但该种低空环境下的目标多径散射建模方法研究的是反射波与直达波的路程差小于雷达距离分辨单元的情况，不适用于弹载雷达对于区分目标与多径信号的情况，因此，该技术的适用性受到很大限制。In the paper "Research on Low-altitude Target Detection Technology on Sea Surface in Multipath Environment" (Journal of Radio Wave Science, 2011(3): 443-449.), Yang Yong et al. proposed a target multipath scattering modeling method in low-altitude environment, but This kind of target multipath scattering modeling method in low-altitude environment studies the case where the path difference between the reflected wave and the direct wave is smaller than the radar range resolution unit, which is not suitable for the missile-borne radar to distinguish the target from the multipath signal. Therefore, The applicability of this technique is greatly limited.

DING J C等在论文“Non-fluctuating target detection in low-grazingangle with MIMO radar”(Journal of Central South University，2013，20(10)：2728－2734.)中直接采用Swerling模型描述低空多径环境下的目标回波，而实质上多径与目标RCS起伏间是相互独立的关系，应对Swerling模型加以改进以适用于低空多径环境。DING J C et al. in the paper "Non-fluctuating target detection in low-grazingangle with MIMO radar" (Journal of Central South University, 2013, 20(10): 2728-2734.) directly used the Swerling model to describe the low-altitude multipath environment. In fact, the multipath and target RCS fluctuations are independent of each other, and the Swerling model should be improved to be suitable for low-altitude multipath environments.

周豪等在论文“低空多径环境下雷达目标检测性能研究”(现代雷达，2017，39(2)：33-38.)中引入了多径功率传播因子，将经典的Swerling目标起伏模型推广应用于低空多径环境。但该方法未考虑地海面散射区域的非均匀反射，难以在实际情况中运用。Zhou Hao et al. introduced the multipath power propagation factor in the paper "Research on radar target detection performance in low-altitude multipath environment" (Modern Radar, 2017, 39(2): 33-38.), and generalized the classic Swerling target fluctuation model Applied to low altitude multipath environment. However, this method does not take into account the non-uniform reflection in the scattering area of the ground-sea surface, so it is difficult to apply in practical situations.

发明内容SUMMARY OF THE INVENTION

针对上述现有技术存在的问题，本发明的目的在于提出一种弹载PD体制雷达超低空目标与多径回波建模方法，该种弹载PD体制雷达超低空目标与多径回波建模方法首先确定多径传播的几何构型，并在此基础上进行多径回波建模，确定接收信号模型，通过对每一路径信号的雷达方程进行计算后得到回波信号功率；多径传播路线回波的功率中，关键在于如何计算地海面反射等效的后向散射截面积，将散射区域进行划分后，通过基于等效双基构型的散射系数模型和布儒斯特反射特性进行分析，散射系数考虑采用双基等效成单基的几何构型进行计算，即将超低空目标T→第p个散射地块的散射点Sp→雷达R的几何构型视为双基构型，计算擦地角，进而通过Barton/Morchin模型进行散射系数计算。In view of the problems existing in the above-mentioned prior art, the purpose of the present invention is to propose a method for modeling ultra-low-altitude targets and multipath echoes of missile-borne PD-based radars. The modulo method first determines the geometric configuration of multipath propagation, and on this basis, carries out multipath echo modeling, determines the received signal model, and obtains the echo signal power by calculating the radar equation of each path signal; In the power of the echoes from the propagation route, the key lies in how to calculate the equivalent backscattering cross-sectional area of the ground-sea surface reflection. After dividing the scattering area, the scattering coefficient model based on the equivalent double-base configuration and the Brewster reflection characteristics are used to carry out the calculation. In the analysis, the scattering coefficient is considered to be calculated using the geometric configuration of the double base equivalent to a single base, that is, the geometric configuration of the ultra-low-altitude target T → the scattering point Sp of the p -th scattering block → the radar R is regarded as a double base configuration , calculate the rubbing angle, and then calculate the scattering coefficient through the Barton/Morchin model.

一种弹载PD体制雷达超低空目标与多径回波建模方法，包括以下步骤：A method for modeling ultra-low-altitude targets and multipath echoes of missile-borne PD system radar, comprising the following steps:

步骤1，确定雷达，该雷达的检测范围内存在超低空目标，建立超低空目标多路径传播空间几何构型，并确定散射区域；Step 1, determine the radar, there is an ultra-low altitude target in the detection range of the radar, establish the multi-path propagation space geometry of the ultra-low altitude target, and determine the scattering area;

步骤2，确定等效单基雷达，并计算等效单基雷达的擦地角，进而计算等效单基雷达的散射系数；Step 2: Determine the equivalent single-base radar, calculate the rubbing angle of the equivalent single-base radar, and then calculate the scattering coefficient of the equivalent single-base radar;

步骤3，计算地、海面的介电常数，进而计算得到布儒斯特效应对应的反射系数，然后根据等效单基雷达的散射系数，计算得到散射区域的散射系数；Step 3: Calculate the dielectric constants of the ground and sea surface, and then calculate the reflection coefficient corresponding to the Brewster effect, and then calculate the scattering coefficient of the scattering area according to the scattering coefficient of the equivalent monostatic radar;

步骤4，根据散射区域的散射系数，计算t时刻雷达接收到的四路径基带回波信号，所述t时刻雷达接收到的四路径基带回波信号为弹载PD体制雷达超低空目标与多径回波建模结果；t表示时间变量。Step 4: Calculate the four-path baseband echo signal received by the radar at time t according to the scattering coefficient of the scattering area, where the four-path baseband echo signal received by the radar at time t is the ultra-low-altitude target and multipath of the missile-borne PD system radar. Echo modeling results; t represents the time variable.

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:

第一，本发明方法是基于雷达方程的散射系数计算方法，相比基于统计的计算方法的准确度更高；First, the method of the present invention is a method for calculating the scattering coefficient based on the radar equation, which is more accurate than the calculation method based on statistics;

第二，本发明方法是基于双基等效单基的散射系数计算方法，是经过实测验证的高吻合度计算方法；Second, the method of the present invention is based on the calculation method of the scattering coefficient of the double base equivalent to the single base, and is a high coincidence calculation method verified by actual measurement;

第三，本发明方法考虑了布儒斯特效应，符合地海杂波的物理特性。Thirdly, the method of the present invention takes into account the Brewster effect, which conforms to the physical characteristics of the ground sea clutter.

附图说明Description of drawings

下面结合附图和具体实施方式对本发明作进一步详细说明。The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

图1是本发明的一种弹载PD体制雷达超低空目标与多径回波建模方法流程图；1 is a flowchart of a method for modeling ultra-low-altitude targets and multipath echoes of a missile-borne PD system radar of the present invention;

图2是超低空目标多径传播示意图；Figure 2 is a schematic diagram of multipath propagation of ultra-low altitude targets;

图3是超低空目标多径传播几何构型；Figure 3 shows the multipath propagation geometry of ultra-low altitude targets;

图4是Q个散射块的散射系数仿真示意图；FIG. 4 is a schematic diagram of the simulation of scattering coefficients of Q scattering blocks;

图5(a)是雷达接收到的直接-直接路径的基带回波信号仿真示意图；Figure 5(a) is a schematic diagram of the baseband echo signal simulation of the direct-direct path received by the radar;

图5(b)是雷达接收到直接-反射路径的基带回波信号、雷达接收到反射-直接路径路径的基带回波信号仿真示意图；Figure 5(b) is a simulation schematic diagram of the baseband echo signal of the direct-reflection path received by the radar and the baseband echo signal received by the radar of the reflection-direct path path;

图5(c)是雷达接收到反射-反射路径的基带回波信号仿真示意图；Figure 5(c) is a schematic diagram of the baseband echo signal simulation of the radar receiving the reflection-reflection path;

图5(d)是超低空目标和多径回波信号仿真示意图；Figure 5(d) is a schematic diagram of the simulation of ultra-low altitude targets and multipath echo signals;

图6是超低空目标和多径回波信号相干积累后的距离-多普勒信号仿真示意图。FIG. 6 is a schematic diagram of range-Doppler signal simulation after coherent accumulation of ultra-low-altitude targets and multipath echo signals.

具体实施方式：Detailed ways:

参照图1，为本发明的一种弹载PD体制雷达超低空目标与多径回波建模方法流程图；其中所述弹载PD体制雷达超低空目标与多径回波建模方法，包括以下步骤：1 is a flowchart of a method for modeling ultra-low-altitude targets and multipath echoes of a missile-borne PD system radar according to the present invention; wherein the method for modeling ultra-low-altitude targets and multipath echoes of missile-borne PD system radars includes the following steps: The following steps:

步骤1，建立雷达多径信号传播空间几何构型。Step 1, establish the spatial geometry of radar multipath signal propagation.

确定雷达，本实施例中雷达为弹载PD体制雷达，所述弹载PD体制雷达为弹载脉冲多普勒体制雷达；雷达的检测范围内存在超低空目标，其中超低空为飞行高度距离海平面或地面100m以下；雷达在探测与跟踪超低空目标时，超低空目标的多路径传播现象明显。由于超低空目标在相对平坦的地海面飞行时，雷达接收到的回波信号不仅包含超低空目标的直接路径信号，还包含超低空目标经地海面反射形成的多径信号；超低空目标多路径传播示意图如图2所示。Determine the radar. In this embodiment, the radar is a missile-borne PD system radar, and the missile-borne PD system radar is a missile-borne pulse Doppler system radar; there are ultra-low-altitude targets within the detection range of the radar, where the ultra-low altitude is the flight height and distance to the sea. 100m below the plane or the ground; when the radar detects and tracks ultra-low-altitude targets, the multi-path propagation phenomenon of ultra-low-altitude targets is obvious. Since the ultra-low-altitude target is flying on a relatively flat ground and sea surface, the echo signal received by the radar not only includes the direct path signal of the ultra-low-altitude target, but also includes the multi-path signal formed by the ultra-low-altitude target reflected by the ground and sea surface; the multi-path signal of the ultra-low-altitude target A schematic diagram of the propagation is shown in Figure 2.

在图2中，雷达向其检测范围内的超低空目标发射信号并接收回波信号，雷达发射的信号到达超低空目标，超低空目标反射其中一部分信号回到雷达的路径记为直达路径；另一部分信号经超低空目标反射到地、海面，再经地、海面反射回到雷达的路径记为镜面反射路径，该另一部分信号经超低空目标散射到地、海面，再经地、海面漫反射回到雷达的路径记为漫反射路径，所述另一部分信号经超低空目标散射到地、海面，再经地、海面散射后得到的回波信号回到雷达，其中雷达接收回波信号对应的地、海面区域记为反射面。In Figure 2, the radar transmits signals to the ultra-low-altitude target within its detection range and receives the echo signal. The signal transmitted by the radar reaches the ultra-low-altitude target, and the path that the ultra-low-altitude target reflects part of the signal back to the radar is recorded as the direct path; A part of the signal is reflected by the ultra-low-altitude target to the ground and sea surface, and then reflected back to the radar by the ground and sea surface. The path is recorded as the specular reflection path. The other part of the signal is scattered by the ultra-low-altitude target to the ground and sea surface, and then diffusely reflected by the ground and sea surface. The path back to the radar is recorded as the diffuse reflection path. The other part of the signal is scattered to the ground and the sea surface by the ultra-low-altitude target, and the echo signal obtained after being scattered by the ground and the sea surface returns to the radar, where the radar receives the corresponding echo signal. The ground and sea areas are recorded as reflective surfaces.

在讨论超低空目标多路径问题时，做出如下假设：第一，地球表面是平坦光滑反射面(满足Rayleigh判据的相对平坦反射区)；第二，雷达天线主波束始终对准目标方向；忽略地球曲率的影响，本实施例用平面地球模型代替球面的地球表面模型，图3给出了超低空目标的多路径传播空间几何构型。When discussing the multi-path problem of ultra-low-altitude targets, the following assumptions are made: first, the earth's surface is a flat and smooth reflecting surface (a relatively flat reflecting area that satisfies the Rayleigh criterion); second, the main beam of the radar antenna is always aimed at the target direction; Ignoring the influence of the curvature of the earth, in this embodiment, a plane earth model is used to replace the spherical earth surface model, and FIG. 3 shows the multipath propagation space geometry of the ultra-low altitude target.

图3中考虑从雷达正下方的地球表面的点建立地面XOYZ坐标系，并分别定义俯仰角向上为正，定义方位角相对X轴逆时针旋转为正；建立XOYZ坐标系，雷达R初始位置在Z轴正半轴上，并以速度矢量VR平行于X轴正半轴运动，雷达R向其检测范围内的超低空目标T发射信号，且雷达发射的信号经超低空目标T方位向切面反射回到雷达，并记为雷达-超低空目标方位向切面反射路径，将雷达-超低空目标方位向切面反射路径与地、海面的交点，记为反射点S；以反射点S为中心、以

Figure GDA0002485478600000041
为边长的正方形区域，记为散射区域，
Figure GDA0002485478600000042
c表示光速，B表示雷达向超低空目标发射的信号带宽，Q表示散射区域经过划分后包括的散射块总个数，Q为大于0的正整数，△r表示每个散射块的边长，散射区域的面积为Q·△r·△r；假设每个散射块的等效散射系数由该个散射块的散射中心的散射系数代替，选取Q个散射块中任意一个散射块，记为第p个散射块，将第p个散射块的散射中心记为第p个散射块的散射点Sp，p∈{1,2,…,Q}；超低空目标T的速度矢量为VT，超低空目标T对应的俯仰角为φT，第p个散射块的散射点Sp对应的方位角为θSp。In Figure 3, the ground XOYZ coordinate system is considered to be established from the point on the surface of the earth directly below the radar, and the elevation angle is defined as positive upward, and the azimuth angle is defined as positive counterclockwise relative to the X axis; the XOYZ coordinate system is established, and the initial position of the radar R is at On the positive half-axis of the Z-axis, and moving parallel to the positive half-axis of the X-axis with the velocity vector VR R , the radar R transmits signals to the ultra-low altitude target T within its detection range, and the signal transmitted by the radar passes through the ultra-low altitude target T azimuth section. It is reflected back to the radar and recorded as the radar-ultra-low-altitude target azimuth tangential reflection path, and the intersection of the radar-ultra-low-altitude target azimuth tangential reflection path with the ground and sea surface is recorded as the reflection point S; with the reflection point S as the center, by
Figure GDA0002485478600000041
is a square area with side length, denoted as the scattering area,
Figure GDA0002485478600000042
c is the speed of light, B is the signal bandwidth emitted by the radar to the ultra-low-altitude target, Q is the total number of scattering blocks included in the divided scattering area, Q is a positive integer greater than 0, Δr is the side length of each scattering block, The area of the scattering region is Q·△r·△r; assuming that the equivalent scattering coefficient of each scattering block is replaced by the scattering coefficient of the scattering center of the scattering block, select any scattering block among the Q scattering blocks, and denote it as the first scattering block. There are p scattering blocks, and the scattering center of the p-th scattering block is recorded as the scattering point Sp of the p -th scattering block, p∈{1,2,…,Q}; the velocity vector of the ultra-low-altitude target T is V T , The elevation angle corresponding to the ultra-low-altitude target T is φ T , and the azimuth angle corresponding to the scattering point Sp of the p -th scattering block is θ Sp .

步骤2，地海面散射区域划分。Step 2, division of the ground-sea surface scattering area.

由于地海面的反射形成电磁波的多径传播，而对于多径信号，首先需要确定散射区域的大小及划分方法；分析可知，要确定镜面反射发生的区域范围，即散射区域需要确定符合Rayleigh判据的地海面区域，需要根据实际地形确定；此处的散射区域是以反射点S为中心的正方形区域，将该散射区域划分为Q个散射块，每个散射块都满足均匀分布，从而整个散射区域的回波信号等效为每个散射块回波信号的叠加。Since the reflection of the ground and sea surface forms the multipath propagation of electromagnetic waves, for multipath signals, the size and division method of the scattering area need to be determined first; the analysis shows that to determine the area where the specular reflection occurs, that is, the scattering area needs to be determined to meet the Rayleigh criterion. The area of the ground sea surface needs to be determined according to the actual terrain; the scattering area here is a square area with the reflection point S as the center, and the scattering area is divided into Q scattering blocks, each of which satisfies the uniform distribution, so that the entire scattering area The echo signal of the area is equivalent to the superposition of the echo signals of each scattering block.

其中，反射点S的位置矢量由雷达R、超低空目标T的位置矢量推导出，且反射点S的位置矢量Ps为：Among them, the position vector of the reflection point S is derived from the position vector of the radar R and the ultra-low altitude target T, and the position vector P s of the reflection point S is:

Figure GDA0002485478600000043
Figure GDA0002485478600000043

其中，H为雷达平台高度，h为超低空目标T的高度，X0为超低空目标T的在X轴的坐标。Among them, H is the height of the radar platform, h is the height of the ultra-low-altitude target T, and X 0 is the coordinate of the ultra-low-altitude target T on the X axis.

考虑每个散射块的大小都由雷达距离分辨率决定，每个散射块的面积为AS，AS＝△r2，

Figure GDA0002485478600000044
c表示光速，B表示雷达向超低空目标发射的信号带宽。Considering that the size of each scattering block is determined by the radar range resolution, the area of each scattering block is A S , A S =Δr 2 ,
Figure GDA0002485478600000044
c represents the speed of light, and B represents the bandwidth of the signal emitted by the radar to the ultra-low-altitude target.

第p个散射块的散射点Sp的位置矢量

Figure GDA0002485478600000045
为：The position vector of the scattering point Sp of the p -th scattering block
Figure GDA0002485478600000045
for:

Figure GDA0002485478600000046
Figure GDA0002485478600000046

其中，m表示第p个散射块的散射点Sp在X轴方向距离反射点S的散射块数，n表示第p个散射块的散射点Sp在Y轴方向距离反射点S的散射块数，沿X轴和Y轴正半轴方向分别为正，沿X轴和Y轴负半轴方向分别为负。Among them, m represents the number of scattering blocks from the scattering point Sp of the p -th scattering block to the reflection point S in the X-axis direction, and n represents the scattering point Sp of the p -th scattering block from the reflection point S in the Y-axis direction. The numbers are positive along the positive semi-axis directions of the X-axis and Y-axis, respectively, and negative along the negative semi-axis directions of the X-axis and Y-axis, respectively.

步骤3，建立双基等效单基的散射系数计算模型。In step 3, a calculation model of the scattering coefficient of the double-base equivalent single-base is established.

散射点的散射系数考虑采用双基等效成单基的几何构型进行计算，具体为：将图3的超低空目标多径传播几何构型作为双基构型，然后将双基构型等效为单基构型；超低空目标散射雷达发射过来的信号到第p个散射块的散射点Sp，再由第p个散射块的散射点Sp散射至雷达R所产生的路径，记为反射路径；将反射路径的反射夹角∠RSpT记为双基角，双基角的角平分线与超低空目标T、雷达R连线的交点，记为等效单基点，将等效单基点上的雷达记为等效单基雷达，所述等效单基雷达自发自收，计算单基构型对应的擦地角，进而通过Barton/Morchin模型等进行散射区域的散射系数计算。The scattering coefficient of the scattering point is calculated by considering the geometric configuration of the double-base equivalent to a single-base. Specifically, the multi-path propagation geometry of the ultra-low-altitude target in Figure 3 is taken as the double-base configuration, and then the double-base configuration, etc. The effect is a single-base configuration; the ultra-low-altitude target scatters the signal from the radar to the scattering point Sp of the p -th scattering block, and then scatters from the scattering point Sp of the p -th scattering block to the path generated by the radar R, denoted by is the reflection path; the reflection angle ∠RS p T of the reflection path is recorded as the double base angle, and the intersection of the angle bisector of the double base angle and the line connecting the ultra-low-altitude target T and the radar R is recorded as the equivalent single base point. The radar on the effective single-base point is recorded as the equivalent single-base radar. The equivalent single-base radar spontaneously emits and self-receives, and the ground-wiping angle corresponding to the single-base configuration is calculated, and then the scattering coefficient of the scattering area is calculated by the Barton/Morchin model, etc. .

所述单基构型为：超低空目标散射雷达发射过来的信号到第p个散射块的散射点Sp，再由第p个散射块的散射点Sp散射至雷达R。The single-base configuration is as follows: the signal transmitted by the ultra-low-altitude target scattering radar reaches the scattering point Sp of the p -th scattering block, and is then scattered to the radar R by the scattering point Sp of the p -th scattering block.

下面介绍等效单基擦地角的确定方法：The following describes the method for determining the equivalent single-base rubbing angle:

3.1确定散射点指向等效单基雷达的方向矢量：3.1 Determine the direction vector of the scatter point to the equivalent monostatic radar:

分别将第p个散射块的散射点指向雷达R的单位方向矢量记为aSR，将第p个散射块的散射点指向超低空目标T的单位方向矢量记为aST，进而得到第p个散射块的散射点指向等效单基雷达的方向矢量为a0：The unit direction vector of the scattering point of the p-th scattering block pointing to the radar R is denoted as a SR , and the unit direction vector of the scattering point of the p-th scattering block pointing to the ultra-low-altitude target T is denoted as a ST , and then the p-th scattering point is obtained. The direction vector of the scattering point of the scattering block pointing to the equivalent monostatic radar is a 0 :

Figure GDA0002485478600000051
Figure GDA0002485478600000051

其中，

Figure GDA0002485478600000052
PR表示雷达R的位置矢量，PSp表示第p个散射块的散射点的位置矢量，PTa表示超低空目标T的位置矢量，|| ||2表示2范数操作。in,
Figure GDA0002485478600000052
P R represents the position vector of the radar R, P Sp represents the position vector of the scattering point of the p-th scattering block, P Ta represents the position vector of the ultra-low altitude target T, and || || 2 represents the 2-norm operation.

3.2根据第p个散射块的散射点指向等效单基雷达的方向矢量a0，计算得到第p个散射块的散射点指向等效单基雷达的方向矢量a0与XOYZ坐标系中Z轴的夹角θ：3.2 According to the direction vector a 0 of the scattering point of the p-th scattering block pointing to the equivalent single-base radar, the direction vector a 0 of the scattering point of the p-th scattering block pointing to the equivalent single-base radar and the Z axis in the XOYZ coordinate system are calculated. The included angle θ:

θ＝<a0,ez>，θ=<a 0 , e z >,

其中，ez表示指向XOYZ中Z轴正方向的单位矢量，ez＝[0,0,1]；进而计算得到等效单基雷达的擦地角θg，

Figure GDA0002485478600000061
Among them, ez represents the unit vector pointing to the positive direction of the Z axis in XOYZ , ez =[0,0,1]; and then calculate the ground rubbing angle θ g of the equivalent single-base radar,
Figure GDA0002485478600000061

3.3根据等效单基雷达的擦地角θg，通过Barton/Morchin模型计算得到等效单基雷达的散射系数

Figure GDA0002485478600000062
其表达式为：3.3 According to the rubbing angle θ g of the equivalent single-base radar, the scattering coefficient of the equivalent single-base radar is calculated by the Barton/Morchin model
Figure GDA0002485478600000062
Its expression is:

Figure GDA0002485478600000063
Figure GDA0002485478600000063

其中，

Figure GDA0002485478600000064
表示每个散射块的方向性系数，
Figure GDA0002485478600000065
k表示设定参数，k∈[1,4]，通常取值为1.9；θc表示临界擦地角，与海况有关，
Figure GDA0002485478600000066
he表示海面粗糙度，he＝0.025+0.046N1.72(m)；β0表示设定常数，
Figure GDA0002485478600000067
N表示海况等级，λ表示雷达向超低空目标发射的信号波长，θg表示等效单基雷达的擦地角。in,
Figure GDA0002485478600000064
represents the directivity coefficient of each scattering block,
Figure GDA0002485478600000065
k represents the setting parameter, k∈[1,4], usually 1.9; θc represents the critical rubbing angle, which is related to the sea state,
Figure GDA0002485478600000066
h e represents the sea surface roughness , he = 0.025+0.046N 1.72 (m); β 0 represents the setting constant,
Figure GDA0002485478600000067
N represents the sea state level, λ represents the wavelength of the signal emitted by the radar to the ultra-low-altitude target, and θ g represents the ground-grazing angle of the equivalent single-base radar.

步骤4，计算地海面环境下的电磁波布儒斯特反射系数。Step 4: Calculate the Brewster reflection coefficient of electromagnetic waves in the ground-sea environment.

地海面的布儒斯特角主要由介质表面的粗糙度和入射波波长决定，电磁波入射到海面，在分界面处发生类似于光波的反射和折射现象；当电磁波为垂直极化时，其量反射系数在特定角度上发生极大的衰减，此时发生全透射，即布儒斯特效应，发生全透射时的入射角即为布儒斯特角，海面的布儒斯特角主要由介质表面的粗糙度和入射波波长决定。The Brewster angle of the ground sea surface is mainly determined by the roughness of the medium surface and the wavelength of the incident wave. When the electromagnetic wave is incident on the sea surface, the reflection and refraction phenomena similar to the light wave occur at the interface; when the electromagnetic wave is vertically polarized, its amount The reflection coefficient is greatly attenuated at a specific angle, and the total transmission occurs at this time, that is, the Brewster effect. The incident angle when the total transmission occurs is the Brewster angle. The Brewster angle on the sea surface is mainly determined by the medium. The roughness of the surface and the wavelength of the incident wave are determined.

首先计算地、海面的介电常数ε(Ts,Ss)，公式如下：First calculate the dielectric constant ε(T s ,S s ) of the ground and sea surface, the formula is as follows:

Figure GDA0002485478600000068
Figure GDA0002485478600000068

其中，ε1(Ts,Ss)为媒介频率介电常数，εS(Ts,Ss)为零频(固态)介电常数，ε∞(Ts,Ss)为无限频率介电常数，ε0为真空介电常数，ε0＝8.8854×10-12F/m；f1(Ts,Ss)为一阶德拜松弛频率(GHz)，f2(Ts,Ss)为二阶德拜松弛频率(GHz)，Ts表示海水温度(℃)，Ss表示海水盐度(‰)，f表示雷达向超低空目标发射的信号频率，j表示虚数单位，σ(Ts,Ss)表示海水电导率。Among them, ε 1 (T s , S s ) is the dielectric constant of the medium frequency, ε S (T s , S s ) is the zero-frequency (solid-state) dielectric constant, and ε ∞ (T s , S s ) is the infinite frequency dielectric constant Electric constant, ε 0 is the vacuum dielectric constant, ε 0 =8.8854×10 -12 F/m; f 1 (T s ,S s ) is the first-order Debye relaxation frequency (GHz), f 2 (T s ,S ) s ) is the second-order Debye relaxation frequency (GHz), T s is the seawater temperature (°C), S s is the seawater salinity (‰), f is the signal frequency emitted by the radar to the ultra-low altitude target, j is the imaginary unit, σ (T s , S s ) represents seawater conductivity.

可见，地、海面的介电常数主要由海水温度Ts和海水盐度Ss影响，在温度和盐度固定时，海面的复介电常数主要受入射波频率影响。It can be seen that the dielectric constants of the ground and sea surface are mainly affected by the seawater temperature T s and the seawater salinity S s . When the temperature and salinity are fixed, the complex dielectric constant of the sea surface is mainly affected by the frequency of the incident wave.

由Fresnel公式和Shell法则，并根据地、海面的介电常数ε(Ts,Ss)，计算得到布儒斯特效应对应的反射系数Γ，其表达式为：According to the Fresnel formula and Shell's law, and according to the dielectric constants ε(T s ,S s ) of the ground and sea surface, the reflection coefficient Γ corresponding to the Brewster effect is calculated, and its expression is:

Figure GDA0002485478600000071
Figure GDA0002485478600000071

其中，sin表示正弦函数，cos表示余弦函数，θ表示反射点S指向等效单基雷达的方向矢量a0与Z轴的夹角。Among them, sin represents the sine function, cos represents the cosine function, and θ represents the angle between the direction vector a 0 of the reflection point S pointing to the equivalent single-base radar and the Z axis.

通过布儒斯特效应对应的反射系数Γ的表达式可知，垂直极化分量的反射系数随角度变化，在特定角度可达到0，此时发生全透射，称之为布儒斯特效应；进而计算得到散射区域的散射系数σ0，

Figure GDA0002485478600000072
Figure GDA0002485478600000073
表示等效单基雷达的散射系数。From the expression of the reflection coefficient Γ corresponding to the Brewster effect, it can be known that the reflection coefficient of the vertically polarized component varies with the angle, and can reach 0 at a specific angle, at which time total transmission occurs, which is called the Brewster effect; Calculate the scattering coefficient σ 0 of the scattering area,
Figure GDA0002485478600000072
Figure GDA0002485478600000073
Represents the scattering coefficient of an equivalent monostatic radar.

步骤5，建立多径信号回波模型。Step 5, establishing a multipath signal echo model.

(1)直接-直接路径回波信号建模：(1) Direct-direct path echo signal modeling:

将雷达发射信号从雷达R到达超低空目标T，经过超低空目标T反射回到雷达R，记为直接-直接路径，传播路径为R→T→R；进而计算得到t时刻雷达接收到的直接-直接路径的基带回波信号x0(t)：The radar transmit signal reaches the ultra-low-altitude target T from the radar R, and is reflected back to the radar R by the ultra-low-altitude target T, which is recorded as the direct-direct path, and the propagation path is R→T→R; then the direct signal received by the radar at time t is calculated. - baseband echo signal x 0 (t) of the direct path:

Figure GDA0002485478600000074
Figure GDA0002485478600000074

其中，

Figure GDA0002485478600000075
表示t时刻雷达发射的信号波形，
Figure GDA0002485478600000076
上标*表示求共轭；定义t时刻雷达发射的信号波形区间为[-T'/2,T'/2]，T'表示脉冲重复周期，f0表示雷达发射的信号载频，τ表示雷达发射的信号脉冲宽度，ξ0表示直接-直接路径的回波信号幅度，rRT表示雷达到超低空目标的距离，c表示光速，t表示时间变量，λ表示雷达发射的信号波长，
Figure GDA0002485478600000077
表示超低空目标T到第p个散射块的散射点的距离，
Figure GDA0002485478600000078
表示第p个散射块的散射点到雷达R的距离，rect表示矩形窗函数，exp表示指数函数。in,
Figure GDA0002485478600000075
represents the signal waveform emitted by the radar at time t,
Figure GDA0002485478600000076
The superscript * means to find the conjugate; the waveform interval of the signal transmitted by the radar at time t is defined as [-T'/2, T'/2], T' means the pulse repetition period, f 0 means the carrier frequency of the signal transmitted by the radar, and τ means The pulse width of the signal emitted by the radar, ξ 0 is the amplitude of the echo signal of the direct-direct path, r RT is the distance from the radar to the ultra-low-altitude target, c is the speed of light, t is the time variable, λ is the wavelength of the signal emitted by the radar,
Figure GDA0002485478600000077
represents the distance from the ultra-low-altitude target T to the scattering point of the p-th scattering block,
Figure GDA0002485478600000078
Represents the distance from the scattering point of the p-th scattering block to the radar R, rect represents the rectangular window function, and exp represents the exponential function.

直接-直接路径的回波信号为真实超低空目标回波信号，假设超低空目标为远场点目标，根据雷达方程，得到直接-直接路径的回波信号幅度为ξ0：The echo signal of the direct-direct path is the real echo signal of the ultra-low-altitude target. Assuming that the ultra-low-altitude target is a far-field point target, according to the radar equation, the amplitude of the echo signal of the direct-direct path is ξ 0 :

Figure GDA0002485478600000081
Figure GDA0002485478600000081

其中，PT为雷达发射的信号峰值功率，

Figure GDA0002485478600000082
Pav为雷达发射的信号平均功率，GTmax表示雷达发射天线最大增益，GRmax表示雷达接收天线最大增益，FT(θT,φT)表示雷达指向超低空目标方向的发射方向图，FR(θT,φT)表示雷达指向超低空目标方向的接收方向图，LS为雷达功率损耗，所述雷达功率损耗包括雷达发射机与天线之间的功率损耗，以及天线与雷达接收机之间的功率损耗；σT表示超低空目标的散射截面积，表征超低空目标的散射特性；λ表示雷达发射的信号波长，rRT表示雷达到超低空目标的距离，θT表示超低空目标对应的方位角，φT表示超低空目标对应的俯仰角。Among them, P T is the peak power of the signal transmitted by the radar,
Figure GDA0002485478600000082
P av is the average power of the signal transmitted by the radar, G Tmax is the maximum gain of the radar transmitting antenna, G Rmax is the maximum gain of the radar receiving antenna, F T (θ T , φ T ) is the emission pattern of the radar pointing to the ultra-low altitude target, F R (θ T , φ T ) represents the receiving pattern of the radar pointing to the ultra-low-altitude target, L S is the radar power loss, the radar power loss includes the power loss between the radar transmitter and the antenna, and the antenna and the radar receiver. σ T represents the scattering cross-sectional area of the ultra-low-altitude target, which characterizes the scattering characteristics of the ultra-low-altitude target; λ represents the signal wavelength emitted by the radar, r RT represents the distance from the radar to the ultra-low-altitude target, and θ T represents the ultra-low-altitude target The corresponding azimuth angle, φ T represents the pitch angle corresponding to the ultra-low altitude target.

(2)直接-反射路径、反射-直接路径回波信号建模：(2) Direct-reflection path, reflection-direct path echo signal modeling:

将雷达发射的信号从雷达R到达超低空目标T，然后由超低空目标T反射到第p个散射块的散射点Sp，再经第p个散射块的散射点Sp反射回到雷达R，记为直接-反射路径，传播路径为R→T→Sp→R；将雷达发射的信号从雷达R到达第p个散射块的散射点Sp，经第p个散射块的散射点Sp反射到达超低空目标T，再由超低空目标T反射回到雷达R，记为反射-直接路径，传播路径为R→Sp→T→R；进而分别计算得到t时刻雷达接收到直接-反射路径的基带回波信号x1(t)和t时刻雷达接收到反射-直接路径的基带回波信号x2(t)，其表达式分别为：The signal transmitted by the radar reaches the ultra-low-altitude target T from the radar R, and is then reflected by the ultra-low-altitude target T to the scattering point Sp of the p -th scattering block, and then reflected back to the radar R by the scattering point Sp of the p -th scattering block. , denoted as the direct-reflection path, and the propagation path is R→T→S p →R; the signal transmitted by the radar reaches the scattering point Sp of the pth scattering block from the radar R to the scattering point S p of the pth scattering block. The p reflection reaches the ultra-low-altitude target T, and is reflected back to the radar R by the ultra-low-altitude target T, which is recorded as the reflection-direct path, and the propagation path is R→S p →T→R. The baseband echo signal x 1 (t) of the reflection path and the baseband echo signal x 2 (t) of the reflection-direct path received by the radar at time t are expressed as:

Figure GDA0002485478600000083
Figure GDA0002485478600000083

Figure GDA0002485478600000084
Figure GDA0002485478600000084

其中，ξp表示第p个散射块的散射点Sp对应的回波信号幅度，取决于雷达方程、多径散射系数、布儒斯特效应；

Figure GDA0002485478600000085
表示超低空目标T到第p个散射块的散射点Sp的距离，
Figure GDA0002485478600000086
表示第p个散射块的散射点Sp到雷达R的距离，rect表示矩形窗函数，exp表示指数函数。Among them, ξ p represents the echo signal amplitude corresponding to the scattering point Sp of the p -th scattering block, which depends on the radar equation, the multipath scattering coefficient, and the Brewster effect;
Figure GDA0002485478600000085
represents the distance from the ultra-low-altitude target T to the scattering point Sp of the p -th scattering block,
Figure GDA0002485478600000086
Represents the distance from the scattering point Sp of the p -th scattering block to the radar R, rect represents the rectangular window function, and exp represents the exponential function.

多径传播信号与超低空目标回波模型不同，由于发生了地、海面的反射过程，其回波信号功率主要受雷达发射功率、雷达方向图调制、超低空目标后向散射特性，和地、海面反射系数，以及多径传播距离等因素影响；直接-反射路径和反射-直接路径具有相同的回波信号功率，任意给定散射区域内Q个散射块中任意一个散射块，则第p个散射块的散射点Sp对应的回波信号幅度ξp为：The multipath propagation signal is different from the echo model of the ultra-low-altitude target. Due to the reflection process on the ground and the sea surface, the echo signal power is mainly affected by the radar transmit power, radar pattern modulation, the backscattering characteristics of the ultra-low-altitude target, and the ground, Sea surface reflection coefficient, multipath propagation distance and other factors; the direct-reflection path and the reflection-direct path have the same echo signal power, any one of the Q scattering blocks in any given scattering area, then the pth The echo signal amplitude ξ p corresponding to the scattering point Sp of the scattering block is:

Figure GDA0002485478600000091
Figure GDA0002485478600000091

式中，第一项

Figure GDA0002485478600000092
表示雷达发射到超低空目标所在位置处的功率谱密度，第二项
Figure GDA0002485478600000093
表示超低空目标截获雷达发射信号进行二次散射到第p个散射块的散射点Sp处的功率，并由第p个散射块的散射点Sp接收；第三项
Figure GDA0002485478600000094
表示经第p个散射块的散射点Sp反射到达雷达处的功率，并由雷达接收天线接收；其中，σ0表示散射区域的散射系数，
Figure GDA0002485478600000095
表示第p个散射块的的面积，GT(θT,φT)表示雷达指向超低空目标方向的发射增益，
Figure GDA0002485478600000096
表示雷达指向第p个散射块的散射点Sp方向的接收增益，FT(θT,φT)表示雷达指向超低空目标方向的发射方向图，
Figure GDA0002485478600000097
表示雷达指向第p个散射块的散射点Sp方向的接收方向图，Ae表示第p个散射块的散射点Sp的等效前向散射截面积，
Figure GDA0002485478600000098
表示超低空目标T到第p个散射块的散射点Sp的距离，rRT表示雷达R到超低空目标T的距离，σT表示超低空目标的散射截面积，θT表示超低空目标对应的方位角，φT表示超低空目标对应的俯仰角，
Figure GDA0002485478600000099
表示第p个散射块的散射点Sp对应的方位角，
Figure GDA00024854786000000910
表示第p个散射块的散射点Sp对应的俯仰角，GTmax表示雷达发射天线最大增益，GRmax表示雷达接收天线最大增益，λ表示雷达发射的信号波长，PT表示雷达发射的信号峰值功率。In the formula, the first term
Figure GDA0002485478600000092
Represents the power spectral density at the location where the radar transmits to the ultra-low-altitude target, the second term
Figure GDA0002485478600000093
Represents the power of the ultra-low-altitude target intercepted radar transmission signal for secondary scattering to the scattering point Sp of the p -th scattering block, and received by the scattering point Sp of the p -th scattering block; the third term
Figure GDA0002485478600000094
represents the power reflected by the scattering point Sp of the p -th scattering block to reach the radar and received by the radar receiving antenna; where σ 0 represents the scattering coefficient of the scattering area,
Figure GDA0002485478600000095
represents the area of the p-th scattering block, G T (θ T , φ T ) represents the emission gain of the radar pointing to the ultra-low-altitude target,
Figure GDA0002485478600000096
Represents the receiving gain of the radar pointing to the scattering point Sp of the p -th scattering block, F T (θ T , φ T ) represents the emission pattern of the radar pointing to the ultra-low-altitude target,
Figure GDA0002485478600000097
Represents the receiving pattern of the radar in the direction of the scattering point Sp of the p -th scattering block, A e represents the equivalent forward scattering cross-sectional area of the scattering point Sp of the p -th scattering block,
Figure GDA0002485478600000098
Represents the distance from the ultra-low-altitude target T to the scattering point Sp of the p -th scattering block, r RT represents the distance from the radar R to the ultra-low-altitude target T, σ T represents the scattering cross-sectional area of the ultra-low-altitude target, θ T represents the corresponding ultra-low-altitude target azimuth angle, φ T represents the elevation angle corresponding to the ultra-low-altitude target,
Figure GDA0002485478600000099
represents the azimuth angle corresponding to the scattering point Sp of the p -th scattering block,
Figure GDA00024854786000000910
Represents the pitch angle corresponding to the scattering point Sp of the p -th scattering block, G Tmax represents the maximum gain of the radar transmitting antenna, G Rmax represents the maximum gain of the radar receiving antenna, λ represents the wavelength of the signal transmitted by the radar, and P T represents the peak value of the signal transmitted by the radar power.

(3)反射-反射路径回波信号建模：(3) Modeling of the echo signal of the reflection-reflection path:

将雷达发射的信号从雷达R到达第p个散射块的散射点Sp，由第p个散射块的散射点Sp发射到超低空目标T，再由超低空目标T反射至第p个散射块的散射点Sp，最后回到雷达R，记为反射-反射路径，传播路径为R→Sp→T→Sp→R；进而计算得到t时刻雷达接收到反射-反射路径的基带回波信号为x3(t)：The signal transmitted by the radar reaches the scattering point Sp of the p -th scattering block from the radar R, and is transmitted from the scattering point Sp of the p -th scattering block to the ultra-low-altitude target T, and then reflected by the ultra-low-altitude target T to the p-th scattering point The scattering point Sp of the block, and finally returns to the radar R, which is denoted as the reflection-reflection path, and the propagation path is R→S p →T→S p →R; and then calculate the baseband return of the reflection-reflection path received by the radar at time t . The wave signal is x 3 (t):

Figure GDA0002485478600000101
Figure GDA0002485478600000101

其中，ξ'p表示反射-反射路径中第p个散射块的散射点Sp对应的回波信号幅度，其表达式为：Among them, ξ' p represents the echo signal amplitude corresponding to the scattering point Sp of the p -th scattering block in the reflection-reflection path, and its expression is:

Figure GDA0002485478600000102
Figure GDA0002485478600000102

其中，第一项

Figure GDA0002485478600000103
表示雷达发射信号到达第p个散射块的散射点Sp处的功率，并由第p个散射块的散射点Sp接收；第二项
Figure GDA0002485478600000104
表示第p个散射块的散射点Sp二次辐射的信号到达超低空目标所在位置处的功率，并由超低空目标接收；第三项
Figure GDA0002485478600000105
表示超低空目标进行二次辐射的信号到达第p个散射块的散射点Sp，并由第p个散射块的散射点Sp接收；第四项
Figure GDA0002485478600000106
表示第p个散射块的散射点Sp二次辐射的信号回到雷达，并由雷达接收；其中
Figure GDA0002485478600000107
表示雷达到第p个散射块的散射点Sp的距离，
Figure GDA0002485478600000108
表示超低空目标到第p个散射块的散射点Sp的距离，
Figure GDA0002485478600000111
表示雷达指向第p个散射块的散射点Sp方向的发射方向图，
Figure GDA0002485478600000112
表示雷达指向第p个散射块的散射点Sp方向的接收方向图。Among them, the first
Figure GDA0002485478600000103
represents the power of the radar transmit signal reaching the scattering point Sp of the p -th scattering block and received by the scattering point Sp of the p -th scattering block; the second term
Figure GDA0002485478600000104
Represents the power of the secondary radiation signal from the scattering point Sp of the p -th scattering block reaching the position of the ultra-low-altitude target and received by the ultra-low-altitude target; the third term
Figure GDA0002485478600000105
The signal representing the secondary radiation of the ultra-low-altitude target reaches the scattering point Sp of the p -th scattering block, and is received by the scattering point Sp of the p -th scattering block; the fourth term
Figure GDA0002485478600000106
The signal representing the secondary radiation of the scattering point Sp of the p -th scattering block returns to the radar and is received by the radar; where
Figure GDA0002485478600000107
represents the distance from the radar to the scattering point Sp of the pth scattering block,
Figure GDA0002485478600000108
represents the distance from the ultra-low-altitude target to the scattering point Sp of the p -th scattering block,
Figure GDA0002485478600000111
represents the emission pattern of the radar pointing in the direction of the scattering point Sp of the p -th scattering block,
Figure GDA0002485478600000112
Represents the receiving pattern of the radar pointing in the direction of the scattering point Sp of the p -th scattering block.

(4)将t时刻雷达接收到的直接-直接路径的基带回波信号、t时刻雷达接收到直接-反射路径的基带回波信号、t时刻雷达接收到反射-直接路径的基带回波信号、t时刻雷达接收到反射-反射路径的基带回波信号进行脉压和相干积累，获得超低空目标的多径回波；进而计算得到t时刻雷达接收到的四路径基带回波信号x(t)为：(4) The baseband echo signal of the direct-direct path received by the radar at time t, the baseband echo signal of the direct-reflection path received by the radar at time t, the baseband echo signal of the reflected-direct path received by the radar at time t, At time t, the radar receives the baseband echo signal of the reflection-reflection path and performs pulse pressure and coherent accumulation to obtain the multipath echo of the ultra-low altitude target; and then calculates the four-path baseband echo signal x(t) received by the radar at time t for:

x(t)＝x0(t)+x1(t)+x2(t)+x3(t)x(t)=x 0 (t)+x 1 (t)+x 2 (t)+x 3 (t)

通过以下仿真实验对本发明效果进行验证说明。The effects of the present invention are verified and explained by the following simulation experiments.

(一)仿真参数：(1) Simulation parameters:

本发明的实例所用的弹载PD体制雷达参数如表1所示。The parameters of the missile-borne PD system radar used in the example of the present invention are shown in Table 1.

表1Table 1

Figure GDA0002485478600000113
Figure GDA0002485478600000113

Figure GDA0002485478600000121
Figure GDA0002485478600000121

(二)仿真内容与结果(2) Simulation content and results

在所述仿真条件下，进行如下实验。Under the simulation conditions, the following experiments were carried out.

实验一：对Q个散射块的散射系数进行仿真，结果如图4所示，图4为Q个散射块的散射系数仿真示意图；Q个散射地块的散射系数以X轴具有对称分布的特点，在镜面反射点S处反射系数最大，以反射点S为中心向外逐渐减小；由图4可见，多径信号的主要分量来自有效散射区域，有效散射区域外的多径信号贡献较小；通过实测分析，基于雷达方程和等效双基的散射系数计算，相比基于统计的计算方法的准确度更高。Experiment 1: Simulation of the scattering coefficients of Q scattering blocks, the results are shown in Figure 4, which is a schematic diagram of the scattering coefficient simulation of Q scattering blocks; the scattering coefficients of Q scattering blocks have the characteristic of symmetrical distribution along the X axis , the reflection coefficient is the largest at the specular reflection point S, and gradually decreases outward with the reflection point S as the center; it can be seen from Figure 4 that the main component of the multipath signal comes from the effective scattering area, and the contribution of the multipath signal outside the effective scattering area is small. ; Through the analysis of the actual measurement, the calculation of the scattering coefficient based on the radar equation and the equivalent double base is more accurate than the calculation method based on statistics.

实验二：对目标和多径回波信号仿真，结果如图5(a)、图5(b)、图5(c)和图5(d)所示，图5(a)为雷达接收到的直接-直接路径的基带回波信号仿真示意图，图5(b)为雷达接收到直接-反射路径的基带回波信号、雷达接收到反射-直接路径路径的基带回波信号仿真示意图，图5(c)为雷达接收到反射-反射路径的基带回波信号仿真示意图，图5(d)为超低空目标和多径回波信号仿真示意图；由5(b)和5(c)可见，由于多径信号是有大量的散射块的多径叠加而形成的，其回波在脉冲内和脉冲间都表现出较大的幅度起伏。Experiment 2: Simulation of the target and multipath echo signals, the results are shown in Figure 5(a), Figure 5(b), Figure 5(c) and Figure 5(d), Figure 5(a) is the radar received Figure 5(b) is the simulation schematic diagram of the baseband echo signal of the direct-reflected path received by the radar, and the baseband echo signal of the radar received the reflected-direct path, Figure 5 (c) is a schematic diagram of the simulation of the baseband echo signal of the reflection-reflection path received by the radar, and Figure 5(d) is a schematic diagram of the simulation of the ultra-low altitude target and the multipath echo signal; it can be seen from 5(b) and 5(c), because The multipath signal is formed by the multipath superposition of a large number of scattering blocks, and its echoes show large amplitude fluctuations both within the pulse and between the pulses.

实验三：对目标和多径的回波信号相干积累后的距离-多普勒信号进行仿真，结果如图6，图6为超低空目标和多径回波信号相干积累后的距离-多普勒信号仿真示意图；由图6的结果可以看出，通过合理的设计雷达系统参数，在脉冲压缩与多普勒处理之后，目标和多径信号在距离维实现了分辨。而目标和多径在多普勒维的区分度很小。Experiment 3: Simulate the range-Doppler signal after coherent accumulation of the echo signals of the target and multipath. The results are shown in Figure 6. Figure 6 shows the range-Doppler signal after coherent accumulation of the ultra-low-altitude target and the multipath echo signals It can be seen from the results in Figure 6 that through reasonable design of radar system parameters, after pulse compression and Doppler processing, the target and multipath signals can be distinguished in the range dimension. However, the discrimination between target and multipath in Doppler dimension is very small.

综上所述，仿真实验验证了本发明的正确性，有效性和可靠性。In conclusion, the simulation experiment verifies the correctness, effectiveness and reliability of the present invention.

显然，本领域的技术人员可以对本发明进行各种改动和变型而不脱离本发明的精神和范围；这样，倘若本发明的这些修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention; in this way, if these modifications and variations of the present invention belong to the scope of the claims of the present invention and its equivalent technology, It is then intended that the present invention also includes such modifications and variations.

Claims (6)

1. A modeling method for ultra-low-altitude targets and multipath echoes of a missile-borne PD system radar is characterized by comprising the following steps:
step 1, determining a radar, establishing a multi-path propagation space geometric configuration of the ultra-low-altitude target and determining a scattering area, wherein the ultra-low-altitude target exists in a detection range of the radar;
step 2, determining the equivalent single-base radar, calculating the ground wiping angle of the equivalent single-base radar, and further calculating the scattering coefficient of the equivalent single-base radar;
step 3, calculating dielectric constants of the ground and the sea surface, further calculating to obtain a reflection coefficient corresponding to the Brewster effect, and then calculating to obtain a scattering coefficient of a scattering area according to the scattering coefficient of the equivalent single-base radar;
step 4, four-path baseband echo signals received by the radar at the time t are calculated according to the scattering coefficient of the scattering area, and the four-path baseband echo signals received by the radar at the time t are modeling results of the ultra-low-altitude target and the multi-path echoes of the missile-borne PD system radar; t represents a time variable.
2. The modeling method for the ultra-low-altitude target and the multipath echoes of the missile-borne PD system radar as set forth in claim 1, wherein in the step 1, the multi-path propagation space geometry of the ultra-low-altitude target is established by the following steps:
establishing an XOYZ coordinate system, wherein the radar initial position is on a positive half shaft of a Z axis and takes a velocity vector VRMoving parallel to the positive X half axis; the radar transmits signals to the ultra-low-altitude target in the detection range, the signals transmitted by the radar are reflected back to the radar through the ultra-low-altitude target azimuth tangent plane and are marked as radar-ultra-low-altitude target azimuth tangent plane reflection paths, and the intersection points of the radar-ultra-low-altitude target azimuth tangent plane reflection paths, the ground and the sea surface are marked as reflection points S; centering on the reflection point S
Figure FDA0002485478590000011
Is a square area with side length and is marked as a scattering area, Q represents the total number of scattering blocks included after the scattering area is divided, △ r represents the side length of each scattering block, and the area of the scattering area is
Figure FDA0002485478590000012
Selecting any one of the Q scattering blocks as the p-th scattering block, and recording the scattering center of the p-th scattering block as the scattering point S of the p-th scattering blockp(ii) a The velocity vector of the ultra-low altitude target is VTThe pitch angle corresponding to the ultra-low altitude target is phiTScattering point S of the p-th scattererpCorresponding azimuth angle is
Figure FDA0002485478590000013
3. The modeling method for the ultra-low-altitude target and the multipath echo of the missile-borne PD system radar as claimed in claim 2, wherein in the step 2, the equivalent single-base radar is determined by the following process: a path generated by scattering points of the p-th scattering block to the radar is recorded as a reflection path; recording a reflection included angle of a reflection path as a double base angle, recording an intersection point of an angular bisector of the double base angle, an ultra-low altitude target and a radar connecting line as an equivalent single base point, and recording a radar on the equivalent single base point as an equivalent single base radar;
the ground wiping angle of the equivalent single-base radar and the scattering coefficient of the equivalent single-base radar are obtained by the following steps:
unit direction vectors respectively pointing the scattering point of the p-th scattering block to the radar are marked as aSRThe unit direction vector of the scattering point of the p-th scattering block pointing to the ultra-low altitude target is marked as aSTAnd further obtaining a direction vector a of a scattering point of the p-th scattering block pointing to the equivalent single-base radar0：
Figure FDA0002485478590000021
Wherein,
Figure FDA0002485478590000022
PRrepresenting a position vector, P, of the radarSpRepresenting the position vector of the scattering point of the P-th scatterer, PTaPosition vector representing ultra-low altitude target, | | | | | non-conducting phosphor2Represents a 2-norm operation;
the direction vector pointing to the equivalent single-base radar according to the scattering point of the p-th scattering block is recorded as a0Calculating to obtain a direction vector a of a scattering point of the p-th scattering block pointing to the equivalent single-base radar0Angle θ to the Z axis in XOYZ coordinate system:
θ＝<a0,ez>，
wherein e iszRepresents a unit vector pointing to the positive direction of the Z axis in the XOYZ coordinate system; and then calculating to obtain the ground wiping angle theta of the equivalent single-base radarg，
Figure FDA0002485478590000023
Finally according to the ground wiping angle theta of the equivalent single-base radargAnd calculating to obtain the scattering coefficient of the equivalent single-base radar
Figure FDA0002485478590000024
Figure FDA0002485478590000025
Wherein,
Figure FDA0002485478590000026
the directivity coefficient of each scattering block is represented,
Figure FDA0002485478590000027
k represents a setting parameter, thetacThe critical angle of the floor surface is shown,
Figure FDA0002485478590000028
heindicating sea roughness, β0Representing a set constant, N representing the sea state level, lambda representing the wavelength of a signal emitted by the radar to the ultra-low altitude target, thetagRepresenting the ground angle of an equivalent monostatic radar.
4. The modeling method for the ultra-low-altitude target and the multipath echoes of the missile-borne PD regime radar as claimed in claim 3, wherein in the step 3, the dielectric constant of the ground and the sea surface is marked as epsilon (T)s,Ss) The expression is as follows:
Figure FDA0002485478590000029
wherein epsilon1(Ts,Ss) Is dielectric constant of medium frequency,. epsilonS(Ts,Ss) Is a zero-frequency dielectric constant,. epsilon∞(Ts,Ss) Is dielectric constant of infinite frequency,. epsilon0Is a vacuum dielectric constant, f1(Ts,Ss) Is the first order Debye relaxation frequency, f2(Ts,Ss) Is the second order Debye relaxation frequency, TsIndicates the temperature of seawater, SsRepresenting the salinity of seawater, f representing the frequency of a signal transmitted by a radar to an ultra-low altitude target, j representing an imaginary unit, and sigma (T)s,Ss) Representing the conductivity of the seawater;
the scattering coefficient of the scattering region is sigma0，
Figure FDA0002485478590000031
Figure FDA0002485478590000032
The scattering coefficient of the equivalent single-base radar is expressed, and the gamma value represents the reflection coefficient corresponding to the Brewster effect, and the expression is as follows:
Figure FDA0002485478590000033
wherein theta represents a direction vector a of a scattering point of the p-th scattering block pointing to the equivalent single-base radar0And the included angle between the sine function and the Z axis in the XOYZ coordinate system, sin represents a sine function, and cos represents a cosine function.
5. The modeling method for the ultra-low-altitude target and the multi-path echo of the missile-borne PD system radar as claimed in claim 4, wherein in the step 4, the four-path baseband echo signals received by the radar at the time t are obtained by the following processes:
(1) the radar transmitting signal reaches the ultra-low altitude target from the radar, is reflected back to the radar through the ultra-low altitude target and is marked as a direct-direct path, and then a baseband echo signal x of the direct-direct path received by the radar at the moment t is calculated and obtained0(t)：
Figure FDA0002485478590000034
Wherein,
Figure FDA0002485478590000035
represents the waveform of the signal emitted by the radar at the time t,
Figure FDA0002485478590000036
the superscript denotes the conjugation, τ denotes the pulse width of the signal emitted by the radar, ξ0Representing the amplitude of the echo signal of the direct-direct path, rRTIndicating the distance of the radar to the ultra-low altitude target, c indicating the speed of light, t indicating a time variable, lambda indicating the wavelength of the signal emitted by the radar,
Figure FDA0002485478590000037
represents the distance from the ultra-low altitude target to the scattering point of the p-th scatterer,
Figure FDA0002485478590000038
representing the distance from a scattering point of the p-th scattering block to the radar, rect representing a rectangular window function, and exp representing an exponential function;
(2) the signals transmitted by the radar reach the ultra-low-altitude target from the radar, and then are reflected to the scattering point S of the p-th scattering block by the ultra-low-altitude targetpThen passes through the scattering point S of the p-th scattererpReflected back to the radar, denoted as a direct-reflected path; the signal emitted by the radar reaches a scattering point S of the p-th scattering block from the radarpScattering point S of the p-th scattererpThe reflection reaches the ultra-low altitude target, the ultra-low altitude target is reflected back to the radar and is marked as a reflection-direct path, and then the baseband echo signals x of the direct-reflection path received by the radar at the moment t are respectively calculated and obtained1(t) and time t the radar receives the baseband echo signal x of the reflection-direct path2(t) which are respectively expressed as:
Figure FDA0002485478590000041
Figure FDA0002485478590000042
wherein, ξpScattering point S representing the p-th scattererpThe amplitude of the corresponding echo signal is,
Figure FDA0002485478590000043
represents the scattering point S from the ultra-low altitude target to the p-th scattererpThe distance of (a) to (b),
Figure FDA0002485478590000044
scattering point S representing the p-th scattererpDistance to radar;
(3) the signal emitted by the radar reaches a scattering point S of the p-th scattering block from the radarpFrom scattering point S of the p-th scattererpIs emitted to the ultra-low altitude target and then is reflected to the scattering point S of the p-th scattering block by the ultra-low altitude targetpAnd finally returning to the radar, recording as a reflection-reflection path, and further calculating to obtain a baseband echo signal x of the reflection-reflection path received by the radar at the moment t3(t)：
Figure FDA0002485478590000045
Wherein, ξ'pRepresenting scattering point S of the p-th scatterer in the reflected-reflected pathpThe amplitude of the corresponding echo signal is,
Figure FDA0002485478590000046
indicating the scattering point S of the p-th scatterer reached by the radarpThe distance of (d);
(4) according to the baseband echo signal of the direct-direct path received by the radar at the time t, the baseband echo signal of the direct-reflection path received by the radar at the time t, the baseband echo signal of the reflection-direct path received by the radar at the time t and the baseband echo signal of the reflection-reflection path received by the radar at the time t, calculating to obtain a four-path baseband echo signal x (t) received by the radar at the time t, wherein x (t) is as follows: x (t) ═ x0(t)+x1(t)+x2(t)+x3(t)。
6. The modeling method for ultra-low-altitude targets and multi-path echoes of the missile-borne PD system radar as claimed in claim 5, wherein the echo signal amplitude ξ of the direct-direct path0Scattering point S of the p-th scattererpCorresponding echo signal amplitude ξpScattering point S of the p-th scatterer in the reflection-reflection pathpCorresponding echo signal amplitude, the expressions of which are respectively:
Figure FDA0002485478590000047
Figure FDA0002485478590000051
Figure FDA0002485478590000052
wherein, PTFor the peak power of radar-transmitted signals, GTmaxRepresenting the maximum gain, G, of the radar transmitting antennaRmaxRepresenting the maximum gain, F, of the radar receiving antennaT(θT,φT) Emission pattern representing direction of radar pointing to ultra-low altitude target, FR(θT,φT) A receiving direction diagram L representing the direction of the radar pointing to the ultra-low altitude targetSFor radar power loss, σTRepresents the scattering cross section of the ultra-low altitude target, lambda represents the signal wavelength emitted by the radar, rRTIndicating the distance, theta, of the lightning to an ultra-low altitude targetTIndicating the azimuth angle, phi, corresponding to the ultra-low altitude targetTRepresents the pitch angle, sigma, corresponding to the ultra-low altitude target0The scattering coefficient of the scattering area is represented,
Figure FDA0002485478590000053
denotes the area of the p-th scatterer, GT(θT,φT) Emission indicating radar pointing direction to ultra-low altitude targetThe gain of the power amplifier is increased,
Figure FDA0002485478590000054
indicating scattering point S of radar pointing to p-th scattererpThe gain of the reception in the direction of the antenna,
Figure FDA0002485478590000055
indicating scattering point S of radar pointing to p-th scattererpDirection of reception of direction, AeScattering point S representing the p-th scattererpThe equivalent forward scattering cross-sectional area of (a),
Figure FDA0002485478590000056
represents the scattering point S from the ultra-low altitude target to the p-th scattererpA distance of rRTIndicating the distance of the mine to the ultra-low altitude target,
Figure FDA0002485478590000057
scattering point S representing the p-th scattererpThe corresponding azimuth angle is the angle of the azimuth,
Figure FDA0002485478590000058
scattering point S representing the p-th scattererpCorresponding pitch angle, PTRepresents the peak power of the signal transmitted by the radar,
Figure FDA0002485478590000059
indicating the scattering point S of the p-th scatterer reached by the radarpThe distance of (a) to (b),
Figure FDA00024854785900000510
indicating scattering point S of radar pointing to p-th scattererpDirectional emission pattern.
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