﻿ 船舶远距离目标跟踪的数据融合算法
 舰船科学技术  2023, Vol. 45 Issue (12): 144-147    DOI: 10.3404/j.issn.1672-7619.2023.12.028 PDF

Research on data fusion algorithm for ship long distance target tracking
YU Jian-guo
Zhengzhou University of Aeronautics-School of Intelligent Engineering, Zhengzhou 450046, China
Abstract: The long-range target detection and tracking technology of ships at sea has a wide range of applications in both military and civilian fields, such as long-range target reconnaissance, ship management and so on. The long-range target detection and tracking technology usually relies on shipborne radar. In recent years, in order to improve the accuracy of ship radar's target detection and tracking. Radar array technology and multi - sensor technology are widely used. Aiming at the target tracking scene under the ship's multi-radar detector, this paper focuses on introducing a remote target tracking data fusion algorithm based on Kalman filter algorithm. Through the multi-sensor data fusion technology, the ship's remote target tracking accuracy can be improved, which has important application value.
Key words: target tracking     radar     Kalman filter     data fusion
0 引　言

1）针对分布式阵列雷达与目标物体的相对运动关系，建立舰船分布式阵列雷达的方位坐标系，在坐标系的基础上进行远距离目标探测的数学建模；

2）介绍一种卡尔曼滤波算法，针对舰船阵列雷达的信号采集进行滤波和预测；

3）介绍舰船阵列雷达远距离目标探测过程的目标融合算法，通过多个雷达传感器的数据融合，提高远距离目标的探测精度。

1 船舶分布式阵列雷达系统远距离目标探测的坐标系建模

 图 1 远距离目标的阵列雷达坐标系统 Fig. 1 Array radar coordinate system for long-range targets

i时刻该坐标系统下，船舶航向角为 $\theta$ ，船舶速度为 ${v_T}$ ，远距离目标的移动速度为 $\left( {{v_x},{v_y}} \right)$ ，当前位置远距离目标相对于船舶雷达的方位角[4] ${\theta _t}$ ，可得远距离目标的速度关系式：

 $\left\{ {\begin{array}{*{20}{l}} {{v_x} = {v_T}\sin \left( {{\theta _t} - \theta } \right)}，\\ {{v_y} = {v_T}\cos \left( {{\theta _t} + \theta } \right)} 。\end{array}} \right.$

 $\begin{array}{*{20}{l}} {{X_t} = \left( {{\lambda _t} - {\lambda _0}} \right)\cos {\varphi _t}} ，\\ {{Y_t} = {\varphi _t} - {\varphi _0}} 。\end{array}$

 $\begin{array}{*{20}{l}} {{R_i} = \sqrt {X_t^2 + Y_t^2} }，\\ {{\alpha _i} = \arctan \frac{{{X_t}}}{{{Y_t}}} - {\varphi _0}} 。\end{array}$

O-XYZ坐标系下观测到远距离目标的坐标为 $\left( {{x_0},{y_0},{z_0}} \right)$ ，则可以得到位置配准模型为：

 ${\left( {{x_0},{y_0},{z_0}} \right)^{\rm{T}}} = \left[ \begin{gathered} \cos {\theta _t} \\ 1 \\ \sin {\theta _{}} \\ \end{gathered} \right] \times {\left( {{v_x},{v_y}} \right)^{\rm{T}}} \times \left[ \begin{gathered} {R_i} \\ {\alpha _i} \\ \end{gathered} \right] 。$
2 基于卡尔曼滤波算法的船舶雷达远距离目标跟踪数据融合算法 2.1 卡尔曼滤波算法

 图 2 卡尔曼滤波算法的应用流程图 Fig. 2 Application flow chart of Kalman filter algorithm

 $\begin{gathered} X(k + 1) = \varPhi \left( k \right)X\left( k \right) + \varGamma \left( k \right)u\left( k \right) + {\rm{G}}\left( k \right)V\left( k \right)，\\ Z\left( k \right) = {\rm{H}}\left( k \right)X\left( k \right) + W\left( k \right) 。\end{gathered}$

 \left\{ {\begin{aligned} & {EV(k) = 0,EV(k){V^{\rm T}}(j) = Q(k){\delta _{ij}}}，\\ & {EW(k) = 0,EW(k){W^{\rm T}}(j) = R(k){\delta _{ij}}}，\\ & {EW(k){V^{\rm T}}(k) = 0} 。\end{aligned}} \right.

${\delta _{ij}}$ 为dirichlet函数[2]，符合：

 ${\delta _{ij}} = \left\{ \begin{array}{*{20}{l}} {0,i = j} ，\\ {1,i \ne j} 。\end{array} \right.$

 $\hat X(k + 1/k) = \varPhi (k)\hat X(k/k) + \varGamma (k)u(k) \text{，}$

 $\hat Z(k + 1/k) = H(k + 1)\hat X(k + 1/k) \text{，}$

 $P(k + 1/k) = \varPhi (k)P(k/k) + G(k)Q(k)G{(k)^{\rm{T}}} \text{，}$

 $s(k + 1) = H(k + 1)P(k + 1/k){H^{\rm{T}}}(k + 1) \text{，}$

 $K(k + 1) = P(k + 1/k){H^{\rm{T}}}(k + 1){S^{ - 1}}(k + 1) 。$

 $v(k + 1) = Z(k + 1) - H(k + 1)\hat X(k + 1/k) \text{，}$

 $\hat X(k + 1/k + 1) = \hat X(k + 1/k) + K(k + 1)v(k + 1) 。$
2.2 船舶远距离目标探测雷达与AIS系统信号处理

AIS系统对船舶的定位采用地球坐标系，如图3所示。原点为地心，OZ轴指向北极，OX轴指向赤道，OY轴由地心指向赤道，雷达系统的坐标系如前文所述，可以用极坐标形式表示[3]

 图 3 雷达极坐标系和AIS地球坐标系的示意图 Fig. 3 Schematic diagram of radar polar coordinate system and AIS earth coordinate system

 $\left\{ \begin{gathered} x = \rho \sin {\theta _t} ，\\ y = \rho \cos {\theta _t}。\\ \end{gathered} \right.$

 $\begin{gathered} {\sigma _l} = {\sigma _0}\cos {\theta _t} + \rho \sin {\theta _t} ，\\ {\sigma _s} = {\sigma _0}\sin {\theta _t} + \rho \cos {\theta _t}。\\ \end{gathered}$

 ${\left( {{x_0},{y_0},{z_0}} \right)^{\rm{T}}} = \left[ \begin{gathered} \cos {\theta _t} \\ 1 \\ \sin {\theta _t} \\ \end{gathered} \right] \times {\left( {\rho ,{\theta _t}} \right)^{\rm{T}}} \times \left[ \begin{gathered} {\sigma _l} \\ {\sigma _s} \\ \end{gathered} \right] 。$
2.3 船舶远距离目标探测的雷达信号建模

 图 4 船舶雷达系统的远距离目标跟踪原理图 Fig. 4 Long-range target tracking schematic of ship radar system

 ${s_i}(t) = {k_i}(t){e^{j2 \text{π} {f_e}t}} \text{，}$

 $\int {} {k_i}(t){k_j}(t - \tau ){\rm{d}}t = 0 \text{，}$

N个雷达天线的回波信号为：

 $R = \left\{ {\begin{array}{*{20}{l}} {{\zeta _t}{K_t}\sqrt {\displaystyle\frac{E}{t}} {Q_r} + {n_t}}，& {{S_1}} ，\\ {{n_t}}，& {{S_0}}。\end{array}} \right.$

 $f(t) = \exp \left[ {j2\pi \left( {\frac{1}{2}\mu {t^2} + {f_0}t} \right)} \right] 。$

 $H(k,t) = \sqrt {\frac{{{E^2} \cdot {\xi _t}}}{{{{(4 \text{π} )}^3} \cdot {r^4}{E_0}}}} \cdot \exp \left\{ {2 \text{π} \left[ {{f_d}t + \frac{1}{2}r{{\left( {t - {\tau _i}} \right)}^2}} \right]} \right\} 。$

2.4 基于卡尔曼滤波的船舶远距离目标跟踪数据融合算法设计

 图 5 基于卡尔曼滤波算法的目标跟踪数据融合算法原理 Fig. 5 Principle of target tracking data fusion algorithm based on Kalman filter algorithm

 ${\sigma ^2} = E\left[ {{{(X - \hat X)}^2}} \right] = E\left\{ {\sum\limits_{i = 1}^n {W_i^2} {{\left( {X - {X_i}} \right)}^2}} \right\} 。$

 图 6 融合观测与常规观测的目标探测数据方差对比 Fig. 6 Contrast of target detection data variance between fusion observation and conventional observation
3 结　语

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