﻿ 基于机动检测的水下目标自适应跟踪算法
 舰船科学技术  2001, Vol. 44 Issue (6): 114-120    DOI: 10.3404/j.issn.1672-7649.2022.06.023 PDF

Adaptive tracking algorithm for underwater target based on maneuver detection
MEI Peng, SUN Zhen-xin, MA Sha-sha
Jiangsu Automation Research Institute, Lianyungang 222061, China
Abstract: Aiming at the defect that the adaptive Gaussian model and algorithm have strong dependence on maneuver frequency when tracking underwater targets, an improved algorithm based on maneuver detection is proposed. Utilizing the characteristics of the continuous change of the heading angle of the target when turning and maneuvering, construct statistics to estimate the maneuvering and non-maneuvering points of the target, and then adaptively adjust the maneuvering frequency of the model to achieve accurate tracking of the underwater target. The simulation results show that the maneuver detection algorithm based on the heading change rate has a good detection effect on underwater targets with different speeds and different maneuvering intensities, the improved model and algorithm based on maneuver detection have good detection results for both non-maneuverable targets and steering maneuvering targets.
Key words: underwater target tracking     maneuver frequency     maneuver detection
0 引　言

1 自适应高斯模型及其局限性分析

1.1 目标运动模型

 ${x_{k + 1}} = {\varPhi _{k + 1,k}}{x_k} + {U_k}{\bar a_k} + {w_k}，$ (1)

 ${x}_{k}={({x}_{k},{\dot{x}}_{k},{\ddot{x}}_{k})}^{{\rm{T}}}\text{，}{\overline{a}}_{k}={({\overline{a}}_{k},{\dot{\overline{a}}}_{k})}^{{\rm{T}}}，$ (2)
 ${\varPhi _{k + 1,k}} = \left( {\begin{array}{*{20}{c}} 1&T&{(\alpha T - 1 + {e^{ - \alpha T}})/{\alpha ^2}} \\ 0&1&{(1 - {e^{ - \alpha T}})/\alpha } \\ 0&0&{{e^{ - \alpha T}}} \end{array}} \right)，$ (3)
 ${U_k}{\text{ = }}\left( {\begin{array}{*{20}{c}} { - T + \displaystyle\frac{{\alpha {T^2}}}{2} + \displaystyle\frac{{1 + {e^{ - \alpha T}}}}{\alpha }}&{( - T + \displaystyle\frac{{\alpha {T^2}}}{2} + \displaystyle\frac{{1 + {e^{ - \alpha T}}}}{\alpha })/\alpha } \\ {\alpha T - 1 + {e^{ - \alpha T}}}&{T - \displaystyle\frac{{1 - {e^{ - \alpha T}}}}{\alpha }} \\ {\alpha (1 - {e^{ - \alpha T}})}&{1 - {e^{ - \alpha T}}} \end{array}} \right)。$ (4)

 ${{\boldsymbol{Q_k}}}{\text{ = 2}}\alpha {\sigma _a}^2\left( {\begin{array}{*{20}{c}} {{q_{11}}}&{{q_{12}}}&{{q_{13}}} \\ {{q_{21}}}&{{q_{22}}}&{{q_{23}}} \\ {{q_{31}}}&{{q_{32}}}&{{q_{33}}} \end{array}} \right)。$ (5)

 ${z_k} = {{\boldsymbol{H_k}}}{x_k} + {v_k},$ (6)

 ${{\text{v}}_k}{\text{ = }}{{\text{z}}_k} - {{\boldsymbol{H_k}}}[{\Phi _{k + 1,k}}{x_k} + {U_k}{\bar a_k}]。$ (7)

 ${\tau _k}{\text{ = v}}_k^{\text T}{\boldsymbol{S_k}}^{ - 1}{v_k},$ (8)

 $\left\{ \begin{split} &{\bar a}_k = {{\hat {\ddot x}}}_k \hfill, \\ &{\dot {\bar a}}_k = {{\dot {\hat {\ddot x}}}}_k = ({{{{\hat {\ddot x}}}}_k} - {{{\hat {\ddot x}}}}_{k {\text{- 1}}})/T \hfill。\\ \end{split} \right.$ (9)

 ${\sigma _a}= \frac{{{{{{\dot {\hat {\ddot x}}}}}_k}}}{b}，$ (10)

1.2 模型局限性分析

 图 1 不同机动频率下，原模型对非机动目标的跟踪误差 Fig. 1 The tracking error of the model to non-maneuvering targets under different maneuvering frequencies

 图 2 不同机动频率下，原模型对机动目标的跟踪误差 Fig. 2 The tracking error of the model to the maneuvering target under different maneuvering frequencies

2 基于机动检测的自适应高斯模型 2.1 机动检测算法

 ${\theta _v}= \arctan \left( {{{\hat {\dot y}}_k}/{{\hat {\dot x}}_k}} \right)，$ (11)

 $\left\{ \begin{array}{*{20}{c}} {\dot{ \hat {\dot x}}}_k = ({\hat {\dot x}}_{k +1} - {\hat {\dot x}}_k)/T，\\ {\dot {\hat {\dot y}}}_k = ({\hat {\dot y}}_{k + 1} - {\hat {\dot y}}_k)/T。\end{array} \right.$ (12)

 $\dot \theta _{\rm v} = \frac{{\hat {\dot y}}_k{\dot {\hat {\dot x}}}_k - {\hat {\dot x}}_k{{\dot {\hat {\dot y}}}_k}}{\sqrt {\hat {\dot x}_k^2 + \hat {\dot y}_k^2} } = \frac{{{{\hat {\dot y}}_k}({{\hat {\dot x}}_{k +1}}} - {{\hat {\dot x}}_k}) - {{\hat {\dot x}}_k}({{\hat {\dot y}}_{k + 1}} - {{\hat {\dot y}}_k})}{\sqrt {\hat{ \dot x}_k^2 + \hat {\dot y}_k^2} }。$ (13)

 ${\varepsilon _k} = \frac{\left|{\displaystyle\sum\limits_{i = 1}^N {{{\dot \theta }_{\text{v}}}} }\right|}{{\displaystyle\sum\limits_{i = 1}^N {|{{\dot \theta }_{\text{v}}}|} }}。$ (14)

 $P\left\{ {{\tau _k} \leqslant {\tau _{\max }}} \right\} = 1 - \alpha。$ (15)

 图 3 机动检测算法流程图 Fig. 3 Flow chart of maneuver detection algorithm
2.2 改进的自适应高斯模型

 ${\hat x_{k + 1,k}} = {\varPhi _{k + 1,k}}{\hat x_{k,k}} + {U_k}{\bar a_k}；$ (16)

 ${P_{k + 1,k}} = {\varPhi _{k + 1,k}}{P_{k,k}}\varPhi _{k + 1,k}^{\rm{T}} + {U_k}{\bar a_k} + {Q_k}；$ (17)

 ${K_{k + 1}} = {P_{k + 1,k}}H_{k{\text{ + 1}}}^{\text {T}}{\left[ {{H_{k + 1}}{P_{k + 1,k}}H_{k{\text{ + 1}}}^{\text {T}} + {R_{k + 1}}} \right]^{ - 1}}；$ (18)

 ${\hat x_{k + 1,k + 1}} = {\hat x_{k + 1,k}} + {K_{k + 1}}\left[ {{z_{k + 1}} - H{{\hat x}_{k + 1,k}}} \right]；$ (19)

 ${P_{k + 1,k + 1}} = \left[ {I - {K_{k + 1}}{H_{k + 1}}} \right]{P_{k + 1,k}}；$ (20)

 $\left\{ \begin{split} &{\bar a}_{k+1} = {\hat {\ddot x}}_{k + 1,k + 1} \hfill，\\ &{\dot {\bar a}}_{k + 1} = ({\hat {\ddot x}}_{k + 1,k + 1} - {\hat {\ddot x}}_{k,k})/T \hfill；\\ \end{split} \right.$ (21)

 ${a}_{k+1}\text=\left\{\begin{split}&{a}_{1},({\epsilon }_{k}\geqslant \delta )\&({\tau }_{k} > {\tau }_{\rm{max}})，\\ &{a}_{2},{\rm{others}}；\end{split} \right.$ (22)

 $\sigma _a^2= ({{{\hat {\ddot x}}}_{{{k + 1,k + 1}}}}/b{)^2}；$ (23)

 ${Q_{k{\text{ + }}1}} = 2\alpha \sigma _a^2\cdot{Q_i}；$ (24)

 $k\text=\left\{\begin{split}&{c}k-n,{\scriptsize{机动发生或机动停止}}，\\& k+1,{{\rm{others}}}。\end{split} \right.$ (25)
3 仿真验证 3.1 机动检测算法性能验证

 图 4 传统算法对水下目标的机动检测效果 Fig. 4 Maneuvering detection effect of traditional algorithms on underwater targets

 图 5 改进算法对水下目标的机动检测效果 Fig. 5 Maneuvering detection effect of improved algorithms on underwater targets

 图 6 目标机动检测仿真航路 Fig. 6 Simulation route for target maneuver detection

 图 7 对不同转弯率的低速目标，检测延迟与滑窗宽度的关系 Fig. 7 For low-speed targets with different turning rates, the relationship between detection delay and sliding window width

 图 8 对不同转弯率的高速目标，检测延迟与滑窗宽度的关系 Fig. 8 For high-speed targets with different turning rates, the relationship between detection delay and sliding window width

 图 9 对不同转弯率的低速目标，虚警率与滑窗宽度的关系 Fig. 9 For low-speed targets with different turning rates, detect the relationship between the false alarm rate and the width of the sliding window

 图 10 对不同转弯率的高速目标，虚警率与滑窗长度的关系 Fig. 10 For high-speed targets with different turning rates, detect the relationship between the false alarm rate and the length of the sliding window

 图 11 对不同量测误差的低速目标，检测延迟与转弯率的关系 Fig. 11 For low-speed targets with different measurement errors, detect the relationship between delay and turning rate

 图 12 对不同量测误差的高速目标，检测延迟与转弯率的关系 Fig. 12 For high-speed targets with different measurement errors, detect the relationship between delay and turning rate

3.2 自适应跟踪算法性能验证

 图 13 目标理想轨迹和量测轨迹 Fig. 13 Ideal trajectory and measurement trajectory of the target

 图 14 机动检测效果图 Fig. 14 Maneuvering inspection renderings

 图 15 改进算法前后目标运动轨迹对比图 Fig. 15 Comparison chart of target trajectory before and after the improved algorithm

 图 16 改进算法前后距离均方根误差对比图 Fig. 16 Comparison of distance root mean square error before and after the improved algorithm

4 结　语

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