﻿ 基于LMS滤波的复合跟瞄技术
 舰船科学技术  2023, Vol. 45 Issue (12): 168-172    DOI: 10.3404/j.issn.1672-7619.2023.12.034 PDF

Research on composite tracking-pointing techndogy based on LMS filtering
YAN Zhi-hui, LIU Wei-chao, ZHAO Yuan-zheng
The 713 Reseach Institute of CSSC, Zhengzhou 450015, China
Abstract: The general control structure of composite tracking-pointing system and typical controlled object model were established, and effect of image delay on tracking-pointing accuracy was analyzed. In order to compensate for the delay and improve accuracy, a method using coarse miss error as reference control quantity of fine tracking-pointing system was proposed according to the coupling characteristics of coarse and fine view field. Because of the sampling frequency difference between coarse and fine tracking system, and the characteristics of nonlinear and difficult to accurately model the coare miss error, a statistical learning and filtering prediction of coarse and fine miss error were carried out base on LMS adaptive filtering. Last, the system simulation model was established and verified based on the typical controlled object, results show that the tracking-pointing accuracy was improved obviously by using LMS adaptive filtering.
Key words: LMS filtering     composite tracking-pointing system     miss error     image delay
0 引　言

1 复合跟踪轴和典型被控对象 1.1 复合跟踪轴结构

 图 1 复合跟踪轴控制结构 Fig. 1 Control structure of combined tracking axis

1.2 典型被控对象模型

 图 2 随动系统速度环模型 Fig. 2 Velocity loop model of servo system

 $\begin{split} & {G_{vp}}(s) = \\ & {K_p} \cdot (\frac{{1 + {T_z}s}}{{{{(1 + 2 \times Zeta \cdot {T_w}s + {T_w}s)}^2}(1 + {T_p}s)}}) \cdot {e^{ - {T_d}s}}。\end{split}$ (1)

 图 3 FSM单轴控制模型 Fig. 3 Uniaxial control model of FSM

 $\begin{split} & {W_{FSM - x}}(s) = \\ &\frac{{2.4\times 10^{10}}}{{{s^3} + 6689{s^2} + 15720000s + 2.4\times 10^{10}}}。\end{split}$ (2)
2 延迟对精跟瞄精度的影响

 图 4 1 000 μrad，1 Hz信号控制精度 Fig. 4 Control accuracy under 1 000 μrad/1 Hz signal

 图 5 130 μrad、5 Hz信号控制精度 Fig. 5 Control accuracy under 130 μrad/5 Hz signal

3 基于脱靶量的LMS滤波 3.1 滤波算法的选择

 $\left\{ \begin{gathered} {{\hat x}_n} = {{\hat x}_{n - 1}} + \Delta t{{\hat {\dot x}}_n} + \frac{{2(2n - 1)}}{{n(n + 1)}}[{z_n} - ({{\hat x}_{n - 1}} + \Delta t{{\hat {\dot x}}_n})] ，\\ {{\hat {\dot x}}_n} = {{\hat {\dot x}}_{n - 1}} + \frac{6}{{n(n + 1)}}[{z_n} - ({{\hat x}_{n - 1}} + {{\hat {\dot x}}_{n - 1}}\Delta t)] 。\\ \end{gathered} \right.$ (3)

 $\left\{ \begin{gathered} {{\hat x}^ - }_n = A{{\hat x}_{n - 1}} + B{u_n} ，\\ \\ {{\hat x}^{}}_n = {{\hat x}^ - }_n + {K_k}({Z_n} - C{{\hat x}^ - }_n) 。\\ \end{gathered} \right.$ (4)

 图 6 典型粗跟踪脱靶量 Fig. 6 Typical coarse miss error

 图 7 典型粗跟踪脱靶量频谱 Fig. 7 Frequency spectrum of typical coarse miss error

3.2 最小均方LMS自适应滤波

LMS算法是在维纳滤波的基础上，借鉴最速下降法的思想发展而来的，其目的是使滤波器的均方误差达到最小。LMS算法具有以下特点：

1）算法简易，不需要对回归量的相关矩阵进行求逆；算法复杂度与FIR滤波器的维数呈线性关系，算法围绕此进行；

2）与维纳滤波器不同，不需要工作环境统计特性的相关知识；

3）具有一定鲁棒性。

LMS算法结构原理[8]图8所示。

 图 8 LMS算法结构 Fig. 8 Algorithm structure of LMS

LMS算法包括3部分：

1）FIR滤波器。工作在回归量（输入向量）u(n)上，生成期望响应的估计值d(n)；

2）比较器。期望响应d(n)减去估计值d(n)，结果为估计误差e(n)；

3）自适应权值控制机制，利用估计误差控制FIR滤波器上各抽头w(n)增量的调整。

LMS算法具体如下：

 $y(n) = {w^{\rm{H}}}(n)u(n) ，$ (5)
 $e(n) = d(n) - y(n) ，$ (6)
 $w(n + 1) = w{(n)_{}} + \mu u(n){e^*}(n)。$ (7)

 $\left|1-\mu {\Vert u(n)\Vert }^{2}\right|＜1 。$ (8)

3.3 基于脱靶量的LMS滤波结构

LMS算法采用最速下降法，本质上是一种局部方法，呈现局部最优，其收敛值是较之维纳解的次优解，和维纳解的差值为额外均方误差。因此，在滤波补偿的基础上仍需精跟瞄系统自身对额外的均方误差进行补偿。由此，在图1的基础上，建立如图9所示的基于粗、精脱靶量的LMS滤波控制结构。

 图 9 基于脱靶量的LMS滤波结构 Fig. 9 LMS filtering structure based on miss error

4 仿真及结果 4.1 系统仿真模型

 图 10 复合跟瞄系统仿真模型 Fig. 10 Simulation model of combined tracking system

LSM滤波器如模型图11所示。u取10组历史最近粗跟踪残差数据，ef取10组历史最近精跟瞄误差数据，Step为仿真步长，w(0)～w(9)等10组抽头权值，按式（7）计算，滤波器输出y按式（5）计算。

 图 11 LMS滤波器模型 Fig. 11 LMS filter model
4.2 仿真结果

1）粗精联合仿真

 图 12 粗精联合仿真结果 Fig. 12 Co-simulation of coarse and fine system

2）精跟瞄信号注入仿真

 图 13 最大频率分量信号注入仿真 Fig. 13 Injection simulation of maximun frequency signal

 图 14 典型粗跟踪残差注入 Fig. 14 Injection simulation of typical coarse miss error

5 结　语

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