﻿ 一种基于目标跟踪的单线阵左右舷分辨方法
 舰船科学技术  2021, Vol. 43 Issue (7): 118-121    DOI: 10.3404/j.issn.1672-7649.2021.07.024 PDF

A port-starboard discrimination method of single towed array based on target tracking
FANG Yi-xi
The 715 Research Institute of CSSC, Hangzhou 310023, China
Abstract: The port-starboard fuzzy is a problem in the traditional single towed array, by which the effectiveness is affected. In this paper, a port-starboard discrimination method of single towed array based on target tracking is proposed, a mirror target is generated firstly, and a port-starboard target pair is formed, then the target tracking is combined by the platform maneuver, the port-starboard discrimination is realized by the difference of target velocity between the two targets. The simulation results show that, the port-starboard discrimination can be realized in two scanning periods after the platform turns a small angle, the effectiveness and practicability of the proposed method is verified, which has a certain engineering value.
Key words: single towed array     port-starboard discrimination     platform maneuver     target tracking
0 引　言

1 单线阵左右舷分辨基本原理

 图 1 单线阵左右舷分辨流程 Fig. 1 Flow chart of port-starboard discrimination of single towed array
2 目标跟踪算法

 ${{{x}}^j}\left( k \right) = \mathop {{\varPhi}} \nolimits^j {{{x}}^j}\left( {k - 1} \right) + \mathop {{G}}\nolimits^j \mathop {{W}}\nolimits^j \left( {k - 1} \right),$ (1)

 ${{Z}}\left( k \right) = {{{H}}^j}\left( k \right){{x}}\left( k \right) + {{{V}}^j}\left( k \right)\text{。}$ (2)

IMM算法滤波可分为几步：

1）模型交互作用

 ${\mu ^{i/j}}(k - 1|k - 1) = \frac{{\mathop p\nolimits_{ij} \mathop \mu \nolimits^i \left( {k - 1} \right)}}{{{{\overline C }_j}}},$ (3)
 ${\overline C _j} = \sum\limits_{i = 1}^n {\mathop p\nolimits_{ij} \mathop \mu \nolimits^i \left( {k - 1|k - 1} \right)} ,$ (4)
 $\mathop {\hat {{x}}}\nolimits^{0j} (k - 1|k - 1) = \sum\limits_{i = 1}^n {\mathop \mu \nolimits^{{i / j}} (k - 1|k - 1)} \mathop {\hat {{x}}}\nolimits^i (k - 1|k - 1),$ (5)
 $\begin{split} {{{P}}^{0j}}\left( {k \!-\! 1|k \!-\! 1} \right) \!=\! & \sum\limits_{i = 1}^n {\mathop \mu \nolimits^{{i / j}} } \left( {k \!-\! 1|k \!-\! 1} \right)\left[ {\mathop {{P}}\nolimits^i \left( {k \!-\! 1|k \!-\! 1} \right)} \right. +\\ &\left( {\mathop {\hat {{x}}}\nolimits^i \left( {k - 1|k - 1} \right) - \mathop {\hat {{x}}}\nolimits^{0j} \left( {k - 1|k - 1} \right)} \right) \cdot\\ &\left. {{{\left( {\mathop {\hat {{x}}}\nolimits^i \left( {k \!-\! 1|k \!-\! 1} \right) \!-\! \mathop {\hat {{x}}}\nolimits^{0j} \left( {k \!-\! 1|k \!-\! 1} \right)} \right)}^T}} \right] \text{。} \end{split}$ (6)

2）模型条件滤波

 $\mathop {{{\hat x}}}\nolimits^j \left( {k|k - 1} \right) = \mathop {{\Phi }}\nolimits^j \mathop {{{\hat x}}}\nolimits^{0j} \left( {k - 1|k - 1} \right),$ (7)
 $\mathop {{P}}\nolimits ^j \left( {k|k - 1} \right) = \mathop {{\Phi }}\nolimits ^j \mathop {{P}}\nolimits ^{0j} \left( {k|k - 1} \right){{\mathop {{\Phi }}\nolimits ^j} ^{\rm T}} + \mathop {{G}}\nolimits ^j \mathop {{Q}}\nolimits ^j {{\mathop {{G}}\nolimits ^j} ^{\rm T}}\text{。}$ (8)

 $\mathop {{S}}\nolimits^j \left( k \right) = \mathop {{H}}\nolimits^j \left( k \right)\mathop {{P}}\nolimits^j \left( {k|k - 1} \right)\mathop {{H}}\nolimits^j {\left( k \right)^{\rm T}} + \mathop {{R}}\nolimits^j \left( k \right),$ (9)
 $\mathop {{K}}\nolimits^j \left( k \right) = \mathop {{P}}\nolimits^j \left( {k|k - 1} \right)\mathop {{H}}\nolimits^j {\left( k \right)^{\rm T}}\mathop {{S}}\nolimits^j {\left( k \right)^{ - 1}},$ (10)
 $\mathop {{\nu }}\nolimits^j \left( k \right) = {{Z}}\left( k \right) - \mathop {{H}}\nolimits^j \left( k \right)\mathop {{{\hat x}}}\nolimits^j \left( {k|k - 1} \right),$ (11)
 $\mathop {{{\hat x}}}\nolimits^j \left( {k|k} \right) = \mathop {{{\hat x}}}\nolimits^j \left( {k|k - 1} \right) + \mathop {{K}}\nolimits^j \left( k \right)\mathop {{\nu }}\nolimits^j \left( k \right),$ (12)
 $\mathop {{P}}\nolimits^j \left( {k|k} \right) = \left[ {{{I}} - \mathop {{K}}\nolimits^j \left( k \right)\mathop {{H}}\nolimits^j \left( k \right)} \right]\mathop {{P}}\nolimits^j \left( {k|k - 1} \right)\text{。}$ (13)

3）模型概率更新

 $\mathop {{\Lambda }}\nolimits^j \left( k \right) = \frac{1}{{\sqrt {\left| {\mathop {2\text{π} {{S}}}\nolimits^j \left( k \right)} \right|} }}\exp \left\{ { - \frac{1}{2}\mathop {{\nu }}\nolimits^j {{\left( k \right)}^T}\mathop {{S}}\nolimits^j {{\left( k \right)}^{ - 1}}\mathop {{\nu }}\nolimits^j \left( k \right)} \right\},$ (14)

 $\mathop \mu \nolimits^j \left( {k|k} \right) = \frac{1}{C}\mathop {{\Lambda }} \nolimits^j \left( k \right){\overline C _j},$ (15)
 $C = \sum\limits_{i = 1}^n {\mathop {{\Lambda }}\nolimits^{\bf{i}} \left( k \right)} {\overline C _j}\text{。}$ (16)

4）交互模型输出

 $\hat {{x}}\left( {k|k} \right) = \sum\limits_{j = 1}^n {\mathop \mu \nolimits^j \left( {k|k} \right)\mathop {\hat {{x}}}\nolimits^j \left( {k|k} \right)},$ (17)
 $\begin{split} \hat {{P}}\left( {k|k} \right) =& \sum\limits_{i = 1}^n {\mathop \mu \nolimits^{{i / j}} } \left( {k|k} \right)\left[ {\mathop {{P}}\nolimits^i \left( {k|k} \right)} \right. +\\ &\left( {\hat {{x}}\left( {k|k} \right) - \mathop {\hat {{x}}}\nolimits^i \left( {k|k} \right)} \right) \cdot \left. {{{\left( {\hat {{x}}\left( {k|k} \right) - \mathop {\hat {{x}}}\nolimits^i \left( {k|k} \right)} \right)}^{\rm T}}} \right] \text{。}\end{split}$ (18)
3 仿真与结果分析

 ${{x}}(1|1) = \left[ {\begin{array}{*{20}{c}} {{Z_x}(1)} \\ {\dfrac{{{Z_x}(1) - {Z_x}(0)}}{T}} \\ {{Z_y}(1)} \\ {\dfrac{{{Z_y}(1) - {Z_y}(0)}}{T}} \end{array}} \right],$ (19)
 ${{P}}(1|1) = \left[ {\begin{array}{*{20}{c}} {{r_{11}}}&{\dfrac{{{r_{11}}}}{T}}&0&0 \\ {\dfrac{{{r_{11}}}}{T}}&{\dfrac{{2{r_{11}}}}{{{T^2}}}}&0&0 \\ 0&0&{{r_{22}}}&{\dfrac{{{r_{22}}}}{T}} \\ 0&0&{\dfrac{{{r_{22}}}}{T}}&{\dfrac{{2{r_{22}}}}{{{T^2}}}} \end{array}} \right],$ (20)

 ${{{\Phi}} ^1} = {{{\Phi}} ^2} = \left[ {\begin{array}{*{20}{c}} 1&0&T&0 \\ 0&1&0&T \\ 0&0&1&0 \\ 0&0&0&1 \end{array}} \right],$ (21)

 ${{{G}}^1} = 0,$ (22)
 ${{{G}}^2} = \left[ {\begin{array}{*{20}{c}} {{T^2}/2}&0 \\ 0&{{T^2}/2} \\ T&0 \\ 0&T \end{array}} \right]\text{。}$ (23)

 图 2 仿真中添加的测距与测向误差 Fig. 2 Measuring errors of range and bearing added in simulation

 图 3 真实目标、镜像目标与平台位置关系（左舷） Fig. 3 The location relationship between the real target, mirror target and platform（on the port）

 图 4 两跟踪器目标速度输出对比（左舷） Fig. 4 The contrast of target velocity between the two trackers（on the port）

 图 5 真实目标、镜像目标与平台位置关系（右舷） Fig. 5 The location relationship between the real target, mirror target and platform（on the starboard）

 图 6 两跟踪器目标速度输出对比（右舷） Fig. 6 The contrast of target velocity between the two trackers（on the starboard）
4 结　语

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