CN105204017A - High-resolution radar angle tracking method based on regularization optimization - Google Patents

Abstract

Translated fromChinese

本发明提供一种基于正则优化的高分辨雷达角跟踪方法，可以利用正则优化方法对最优测角值进行搜索，减小测角误差，对高分辨雷达近程角跟踪具有重要意义。步骤一、对高分辨雷达和/差通道接收的回波进行脉冲压缩，并对和通道脉压后的信号进行目标检测，记录目标散射点所在距离单元；步骤二、对检测到的距离单元进行单脉冲测角；步骤三、对当前周期的测角值进行正则优化；将每一个可能的角度值代入代价函数，选择令C(θ)取得最小值的角度作为输出。

The invention provides a high-resolution radar angle tracking method based on canonical optimization, which can use the canonical optimization method to search for the optimal angle measurement value, reduce the angle measurement error, and is of great significance to high-resolution radar short-range angle tracking. Step 1. Perform pulse compression on the echo received by the high-resolution radar sum/difference channel, and perform target detection on the signal after the sum channel pulse pressure, and record the distance unit where the target scattering point is located; Step 2. Perform the detection on the detected distance unit Single-pulse angle measurement; Step 3: Regularly optimize the angle measurement value of the current cycle; substitute each possible angle value into the cost function, and select the angle that makes C(θ) obtain the minimum value as the output.

Description

Translated fromChinese

一种基于正则优化的高分辨雷达角跟踪方法A High Resolution Radar Angle Tracking Method Based on Regularized Optimization

技术领域technical field

本发明属于高分辨雷达技术领域，具体涉及一种基于正则优化的高分辨雷达角跟踪方法。The invention belongs to the technical field of high-resolution radar, in particular to a high-resolution radar angle tracking method based on canonical optimization.

背景技术Background technique

在雷达近程角跟踪中，角闪烁是跟踪误差的主要来源之一，在恶劣情况下，它甚至可能将波束指引向目标范围之外，从而导致目标丢失。根据当前的研究，角闪烁主要由同一分辨单元中多个散射点的相位相互叠加引起。这些散射点的相对运动加剧了回波的幅度起伏，从而增加了测角误差。同时，这些测角误差不满足高斯分布，导致大量基于高斯分布噪声设计的滤波器性能明显下降；另一方面，对于滤波器而言，较高的噪声抑制性能往往伴随较长的响应时间。因此，在实际应用中，仅仅依靠滤波器往往难以取得令人满意的效果。In radar short-range angular tracking, angular scintillation is one of the main sources of tracking error, and in severe cases, it may even direct the beam out of range of the target, resulting in loss of the target. According to the current research, the angular scintillation is mainly caused by the phase superposition of multiple scattering points in the same resolution unit. The relative movement of these scattering points aggravates the amplitude fluctuation of the echo, thus increasing the angle measurement error. At the same time, these angle measurement errors do not satisfy the Gaussian distribution, resulting in a significant decline in the performance of a large number of filters designed based on Gaussian distribution noise; on the other hand, for filters, higher noise suppression performance is often accompanied by longer response time. Therefore, in practical applications, it is often difficult to achieve satisfactory results only relying on filters.

降低角闪烁影响的另一个措施是使用高分辨雷达。高分辨雷达可以将目标分辨为多个散射点，因此避免了多个散射点相位叠加引起的回波波前衰减，也即减小了发生角闪烁的可能。但是高分辨雷达不能无限制地分辨目标，因此它只能减少而不能完全避免角闪烁。另一方面，高分辨雷达将一个目标分辨为多个散射点，这在一定程度上降低了每个散射点的信噪比，有可能引入新的测角误差。对于该问题，工程人员多采用取最大值、多点平均、加权平均等方法，这些方法可以在一定程度上降低测角误差，但是在信噪比较低的情况下仍然难以满足实际的应用需要。Another measure to reduce the effects of angular scintillation is the use of high-resolution radar. High-resolution radar can distinguish the target into multiple scattering points, thus avoiding the echo wavefront attenuation caused by the phase superposition of multiple scattering points, that is, reducing the possibility of angular scintillation. However, high-resolution radar cannot distinguish targets without limit, so it can only reduce but not completely avoid angular scintillation. On the other hand, high-resolution radar distinguishes a target into multiple scattering points, which reduces the signal-to-noise ratio of each scattering point to a certain extent, and may introduce new angle measurement errors. For this problem, engineers often use methods such as taking the maximum value, multi-point average, and weighted average. These methods can reduce the angle measurement error to a certain extent, but it is still difficult to meet the actual application needs when the signal-to-noise ratio is low. .

发明内容Contents of the invention

有鉴于此，本发明的目的是提供一种基于正则优化的高分辨雷达角跟踪方法，可以利用正则优化方法对最优测角值进行搜索，减小测角误差，对高分辨雷达近程角跟踪具有重要意义。In view of this, the purpose of the present invention is to provide a high-resolution radar angle tracking method based on regular optimization, which can use the regular optimization method to search for the optimal angle measurement value, reduce the angle measurement error, and improve the accuracy of the short-range angle of the high-resolution radar. Tracking is important.

该基于正则优化的高分辨雷达角跟踪方法，包括以下步骤：The high-resolution radar angle tracking method based on regular optimization includes the following steps:

步骤一、对高分辨雷达和/差通道接收的回波进行脉冲压缩，并对和通道脉压后的信号进行目标检测，记录目标散射点所在距离单元；Step 1. Perform pulse compression on the echo received by the sum/difference channel of the high-resolution radar, and perform target detection on the pulse-compressed signal of the sum channel, and record the distance unit where the target scattering point is located;

步骤二、对检测到的距离单元进行单脉冲测角；Step 2, performing single-pulse angle measurement on the detected distance unit;

根据检测结果，即目标所在距离单元序号i，取出和/差通道相应距离单元的幅度s_i和d_i，并计算每个散射点的角度值According to the detection result, that is, the number i of the distance unit where the target is located, take out the amplitude s_i and d_i of the corresponding distance unit of the sum/difference channel, and calculate the angle value of each scattering point

其中k为单脉冲差斜率；Where k is the slope of the single pulse difference;

步骤三、对当前周期的测角值进行正则优化；Step 3. Regularly optimize the angle measurement value of the current cycle;

根据公式(1)计算所有散射点的角度值，然后令σ_i为各散射点的幅度，θ₀为上一周期的输出角度，对下述代价函数(2)进行优化求解；设波束宽度为θ_w，则θ可能的取值范围为-θ_w/2～θ_w/2，对该取值范围进行离散化，λ为可调参数，用于在当前信息与过去信息之间的权衡，将每一个可能的角度值代入下列代价函数，选择令C(θ)取得最小值的角度作为输出：Calculate the angle values of all scattering points according to formula (1), then let_σi be the amplitude of each scattering point, and_θ0 be the output angle of the previous cycle, and optimize the following cost function (2); let the beam width be θ_w , then the possible value range of θ is -θ_w /2～θ_w /2, the value range is discretized, and λ is an adjustable parameter, which is used to balance between current information and past information. Substitute each possible angle value into the following cost function, and select the angle that minimizes C(θ) as the output:

本发明具有如下有益效果：The present invention has following beneficial effects:

本发明的一种基于正则优化的高分辨雷达角跟踪方法，利用正则优化实现了高分辨雷达近程角跟踪，该角跟踪方法较传统的最大值法、多点平均法、加权平均法等精度更高，较传统的滤波方法响应时间更短，因此，本发明的方法更具有应用优势。A high-resolution radar angle tracking method based on regular optimization of the present invention uses regular optimization to realize short-range angle tracking of high-resolution radar. Higher, shorter response time than the traditional filtering method, therefore, the method of the present invention has more application advantages.

附图说明Description of drawings

图1为目标散射点位置关系。Figure 1 shows the location relationship of target scattering points.

图2为和通道回波的脉冲压缩结果。Figure 2 shows the pulse compression results of the sum channel echo.

图3为本发明中角跟踪方法与幅度加权平均角跟踪方法仿真结果。Fig. 3 is the simulation result of the angle tracking method and the amplitude weighted average angle tracking method of the present invention.

图4为加权平均法的阶跃响应。Figure 4 shows the step response of the weighted average method.

图5为本发明方法的阶跃响应。Fig. 5 is the step response of the method of the present invention.

具体实施方式Detailed ways

下面结合附图并举实施例，对本发明进行详细描述。The present invention will be described in detail below with reference to the accompanying drawings and examples.

不失一般性，仅考虑方位向角跟踪。则和/差通道的接收信号可以表示为：Without loss of generality, only azimuth tracking is considered. Then the received signal of the sum/difference channel can be expressed as:

x_s＝s_t+s_c+n_sx_s = s_t + s_c + n_s

(1)(1)

x_d＝d_t+d_c+n_d其中：n_s和n_d分别为和/差通道中的噪声；s_t和d_t分别为和/差通道的目标回波，它们的比值与目标方位角θ_t之间近似为线性关系，即：x_d ＝d_t +d_c +n_d Among them: n_s and n_d are the noise in the sum/difference channel respectively; st_t and d_t are the target echoes of the sum/difference channel respectively, and their ratio and target azimuth The relationship between angle θ_t is approximately linear, that is:

其中：k定义为单脉冲差斜率。Among them: k is defined as the single pulse difference slope.

类似地，s_c和d_c分别是和/差通道中的杂波回波，它们的比值与杂波单元的方位角也具有相同的线性关系：Similarly,_sc and dc are the clutter_echoes in the sum/difference channel respectively, and their ratios also have the same linear relationship with the azimuth angle of the clutter unit:

根据公式，当只存在一个散射点且信杂比较高时，我们可以计算得到目标方位角的估计值为：According to the formula, when there is only one scattering point and the signal-to-noise ratio is high, we can calculate the estimated value of the target azimuth angle as:

而当信杂比较低，且在一个分辨单元中存在多个散射点时，利用上式计算得到的目标方位角将会很不稳定，以此作为跟踪系统的输入就有可能导致目标跟踪丢失。However, when the signal-to-noise ratio is low and there are multiple scattering points in one resolution unit, the target azimuth angle calculated by the above formula will be very unstable, and if it is used as the input of the tracking system, the target tracking may be lost.

而对于高分辨雷达，它将一个目标分辨为多个散射点，因此对于每一个散射点，我们都可以利用公式计算得到一个测角值同时，假设：For high-resolution radar, it resolves a target into multiple scattering points, so for each scattering point, we can use the formula to calculate an angle measurement value Also, assume that:

1.当前周期的测角结果服从以上一周期测角结果预测值为均值，为方差的高斯分布。1. The angle measurement results of the current cycle obey the average value of the angle measurement results of the previous cycle, Gaussian distribution with variance.

2.当前周期所有散射点的测角值，服从以真实角度为均值，为方差的高斯分布。2. The angle measurement values of all the scattering points in the current period are subject to the mean value of the real angle, Gaussian distribution with variance.

即：Right now:

则根据贝叶斯理论，我们可以得到真实方位角的后验概率密度函数(PDF)：Then according to Bayesian theory, we can get the posterior probability density function (PDF) of the true azimuth:

其中：为当前周期所有散射点测角结果组成的向量。in: It is a vector composed of angle measurement results of all scatter points in the current cycle.

式中，与待估计量没有关系，因此上式可以简化为：In the formula, has nothing to do with the quantity to be estimated, so the above formula can be simplified as:

对式两边同时取对数，可得：Taking the logarithm on both sides of the formula at the same time, we can get:

其中：in:

则根据极大似然理论，当式取得最大值时，相应的目标角度为一个最优估计。而式取得极大值等效于：According to the maximum likelihood theory, when the formula reaches the maximum value, the corresponding target angle is an optimal estimate. And the formula to obtain the maximum value is equivalent to:

取得极小值。为此，我们以定义代价函数：Get the minimum value. To do this, we define a cost function:

其中：λ是一个可调参数，用于在当前信息与过去信息之间的权衡。则当前周期的最优方位角估计由下式给出：Among them: λ is an adjustable parameter used for trade-off between current information and past information. The optimal azimuth estimate for the current period is then given by:

因此，本发明提供了一种基于正则优化的高分辨雷达近程角跟踪方法，包括如下步骤。Therefore, the present invention provides a high-resolution radar short-range angle tracking method based on regularization optimization, which includes the following steps.

步骤一，对高分辨雷达和/差通道接收的回波进行脉冲压缩，并对和通道脉压后的信号进行目标检测，记录目标散射点所在距离单元。以和通道脉压和检测为例，其具体步骤如下：Step 1: Perform pulse compression on the echoes received by the sum/difference channel of the high-resolution radar, and perform target detection on the pulse-compressed signal of the sum channel, and record the distance unit where the target scattering point is located. Taking the channel pulse pressure and detection as an example, the specific steps are as follows:

1)构造参考信号，对接收信号进行脉冲压缩：1) Construct a reference signal and perform pulse compression on the received signal:

S(t)＝ifft(fft(s(t))*conj(fft(s_ref)))(13)S(t)=ifft(fft(s(t))*conj(fft(s_ref )))(13)

其中：fft(·)和ifft(·)分别表示傅里叶变换和傅里叶逆变换，conj(·)表示取共轭操作。S(t)表示脉冲压缩后的信号，s(t)为和通道接收信号，S_ref为参考信号，在发射信号为线性调频信号的前提下，接收信号和参考信号可以分别表示为：Among them: fft(·) and ifft(·) represent Fourier transform and inverse Fourier transform respectively, conj(·) represents the conjugate operation. S(t) represents the pulse-compressed signal, s(t) is the received signal of the sum channel, and S_ref is the reference signal. On the premise that the transmitted signal is a chirp signal, the received signal and the reference signal can be expressed as:

其中：rect(·)表示矩形包络，T_p表示脉冲宽度，K_r表示线性调频率，R表示目标到雷达的距离，C表示光速，λ表示波长。Among them: rect(·) represents the rectangular envelope, T_p represents the pulse width, K_r represents the chirp frequency, R represents the distance from the target to the radar, C represents the speed of light, and λ represents the wavelength.

2)对脉压后的信号进行目标检测，脉压后的信号与一门限进行比较，若信号的幅度大于门限，则判断存在目标，并记录下该距离单元的序号i。不失一般性，这里使用最简单的固定门限检测，其门限值为：2) Carry out target detection on the signal after the pulse pressure, compare the signal after the pulse pressure with a threshold, if the amplitude of the signal is greater than the threshold, then judge that there is a target, and record the serial number i of the distance unit. Without loss of generality, the simplest fixed threshold detection is used here, and its threshold value is:

其中：P_fa表示虚警率。Among them: P_fa represents the false alarm rate.

步骤二，对检测到的距离单元进行单脉冲测角。Step 2, performing single-pulse angle measurement on the detected distance units.

根据检测结果，即目标所在距离单元序号i，取出和/差通道相应距离单元的幅度s_i和d_i，并根据公式计算每个散射点的角度值According to the detection result, that is, the number i of the distance unit where the target is located, take out the amplitude s_i and d_i of the corresponding distance unit of the sum/difference channel, and calculate the angle value of each scattering point according to the formula

步骤三，基于正则优化估计当前周期的测角值。Step 3: Estimate the angle measurement value of the current cycle based on the regularization optimization.

将所有散射点的角度值代入公式，并令σ_i为各散射点的幅度，θ₀为上一周期的输出角度，然后对代价函数进行优化求解。该求解过程可以使用最小二乘法、单纯形法等已有的约束优化方法，或者简单使用遍历搜索。及当前周期的角度输出范围一定限制在波束范围内，假设波束宽度为θ_w，则θ可能的取值范围为-θ_w/2～θ_w/2，对该取值范围进行离散化，将每一个可能的角度值代入公式，选择令C(θ)取得最小值的角度作为输出。Substitute the angle values of all scattering points into the formula, let σ_i be the amplitude of each scattering point, and θ₀ be the output angle of the previous cycle, and then optimize the cost function. The solution process can use existing constrained optimization methods such as least squares method and simplex method, or simply use traversal search. And the angle output range of the current cycle must be limited within the beam range, assuming that the beam width is θ_w , then the possible value range of θ is -θ_w /2～θ_w /2, the value range is discretized, and the Each possible angle value is substituted into the formula, and the angle that makes C(θ) obtain the minimum value is selected as the output.

实施例：Example:

在本实例中，相关参数如下：In this example, the relevant parameters are as follows:

表1仿真参数Table 1 Simulation parameters

目标的散射点模型如图1所示，利用式构造目标的雷达回波信号，其脉压结果如图2所示。The scattering point model of the target is shown in Figure 1, and the radar echo signal of the target is constructed using the formula, and the pulse pressure result is shown in Figure 2.

采用本发明所述的一种基于正则优化的高分辨雷达近程角跟踪方法，完成该参数下的跟踪仿真，具体流程如下：Using a high-resolution radar short-range angle tracking method based on regular optimization described in the present invention, the tracking simulation under this parameter is completed, and the specific process is as follows:

步骤一，对和/差通道的接收回波进行脉冲压缩。Step 1, performing pulse compression on the received echoes of the sum/difference channel.

步骤二，对脉冲压缩结果进行目标检测，并记录目标散射点所在距离单元，其中检测门限由公式给出。Step 2: Perform target detection on the pulse compression result, and record the distance unit where the target scattering point is located, where the detection threshold is given by a formula.

步骤三，对于检测到的目标散射点，提取相应和通道和差通道的信号幅度进行单脉冲测角，即公式。Step 3, for the detected target scattering points, extract the signal amplitudes of the corresponding sum channel and difference channel to perform single-pulse angle measurement, namely the formula.

步骤四，将所有测角值，代入公式，并结合上一周期的输出角度，在波束宽度范围内对当前周期的最优角度进行搜索，当C(θ)取得极小值时即得到最优输出角度。Step 4: Substituting all measured angle values into the formula, combined with the output angle of the previous cycle, searching for the optimal angle of the current cycle within the beam width range, when C(θ) achieves a minimum value, the optimal angle is obtained output angle.

利用该方法跟踪所得结果与幅度加权平均法所得结果的比较如图3所示。其中灰色曲线为本发明跟踪结果，其标准差约为0.013；而黑色曲线为加权平均法跟踪结果，其标准差约为0.027。可见本发明可以大大降低跟踪误差。Using this method to track the results and the comparison of the results obtained by the amplitude weighted average method is shown in Figure 3. Wherein the gray curve is the tracking result of the present invention, and its standard deviation is about 0.013; and the black curve is the tracking result of the weighted average method, and its standard deviation is about 0.027. It can be seen that the present invention can greatly reduce the tracking error.

同时，加权平均法和本发明方法的阶跃响应分别如图4和图5所示。从中可以看出，加权平均法的阶跃响应存在过冲振荡，在本仿真参数下，需要9.5s才能达到稳定状态；而本发明提出的方法比较稳定，其响应时间只有2.5s。Meanwhile, the step responses of the weighted average method and the method of the present invention are shown in Fig. 4 and Fig. 5 respectively. It can be seen that there is overshoot oscillation in the step response of the weighted average method, and it takes 9.5s to reach a steady state under the simulation parameters; while the method proposed by the present invention is relatively stable, and its response time is only 2.5s.

通过仿真结果可以看出利用这种基于正则优化的高分辨雷达角跟踪方法的有效性。利用本方法可以实现高分辨雷达的精确目标跟踪。Through the simulation results, it can be seen that the high-resolution radar angle tracking method based on regularization optimization is effective. The method can realize accurate target tracking of high-resolution radar.

综上所述，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (3)

1., based on the high resolution radar short range angle tracking method that canonical is optimized, it is characterized in that, comprise the steps:

Step one, to high resolution radar and/difference channel reception echo carry out pulse compression, and to passage pulse pressure after signal carry out target detection, record object scattering point place range unit;

Step 2, Monopulse estimation is carried out to the range unit detected;

According to testing result, i.e. target place range unit sequence number i, the amplitude s of taking-up and/difference passage respective distance unit_iand d_i, and calculate the angle value of each scattering point

${{\widehat{\mathrm{\θ}}}_t}^i=\frac{1}{k}\frac{d_i}{s_i}---\left(1\right)$

Wherein k is monopulse difference slope;

Step 3, canonical optimization is carried out to the angle measurement value of current period;

Calculate the angle value of all scattering points according to formula (1), then make σ_ifor the amplitude of each scattering point, θ₀for the output angle in a upper cycle, following cost function (2) was optimized and solves; Beam let width is θ_w, then the span that θ is possible is-θ_w/ 2 ~ θ_w/ 2, carry out discretize to this span, λ is adjustable parameter, in current information and the balance in the past between information, each possible angle value is substituted into following cost function, selects to make C (θ) obtain the angle of minimum value as output;

$C\left(\mathrm{\θ}\right)=\underset{i}{\Σ}\frac{1}{{\mathrm{\σ}}_i^2}{\left|{{\widehat{\mathrm{\θ}}}_t}^{\left(i\right)}-\mathrm{\θ}\right|}^2+\mathrm{\λ}{\left|{\mathrm{\θ}}_0-\mathrm{\θ}\right|}^2---\left(2\right).$

2. a kind of high resolution radar short range angle tracking method optimized based on canonical as claimed in claim 1, is characterized in that, in step 2 with passage pulse pressure and be detected as example, its concrete steps are as follows:

1) construct reference signal, carry out pulse compression to received signal:

S(t)＝ifft(fft(s(t))*conj(fft(s_ref)))

Wherein: fft () and ifft () represents Fourier transform and inverse Fourier transform respectively, conjugate operation is got in conj () expression; Signal after the compression of S (t) indicating impulse, s (t) is and channel receiving signal, S_reffor reference signal, transmitting as under the prerequisite of linear FM signal, Received signal strength and reference signal are expressed as:

$s\left(t\right)=rect(t,T_p)\exp \left({\mathrm{j\πK}}_r{\left(t-\frac{2R}{C}\right)}^2\right)\exp \left(j\frac{4\mathrm{\π}R}{\mathrm{\λ}}\right)$

s_ref＝rect(t,T_p)exp(jπK_rt²)

Wherein: rect () represents rectangular envelope, T_pindicating impulse width, K_rrepresent linear frequency modulation rate, R represents that target arrives the distance of radar, and C represents the light velocity, and λ represents wavelength;

2) carry out target detection to the signal after pulse pressure, the signal after pulse pressure and a thresholding compare, if the amplitude of signal is greater than thresholding, then judge to there is target, and record the sequence number i of this range unit, use the simplest fixed threshold to detect, its threshold value is:

$Thr=\sqrt{\frac{4}{\mathrm{\π}}ln\left(P_{fa}^{-1}\right)}$

Wherein: P_farepresent false alarm rate.

3. a kind of high resolution radar short range angle tracking method optimized based on canonical as claimed in claim 1 or 2, it is characterized in that, described solution procedure uses the constrained optimization method of least square method or simplicial method, or uses traversal search.