﻿ 一种改进的基于UKF的单站无源定位方法

# 一种改进的基于UKF的单站无源定位方法An Improved Algorithm Based on UKF for Single Station Passive Location

Abstract: Single station passive location is an important function of electronic reconnaissance device. However, the existing methods either refer to complicated nonlinear equations, or need the station to move long time. For the device which is restricted to real time response, low power dissipation, small volume, these methods are not suitable. Aim at this problem, an improved algorithm for single station passive location is proposed. First, triangulation is executed to acquire rough estimation, then optimizing the estimation based on UKF. Simulation results demonstrate that the proposed algorithm can get the location in time, and converge to real position.

1. 引言

2. 单站无源定位方法

2.1. 定位模型

Figure 1. Geometric diagram of passive positioning of single station

2.2. 三角交叉定位

$\left\{\begin{array}{l}\left({y}_{T}-{y}_{k-1}\right)tg{\theta }_{k-1}={x}_{T}-{x}_{k-1}\\ \left({y}_{T}-{y}_{k}\right)tg{\theta }_{k}={x}_{T}-{x}_{k}\end{array}$ (1)

$AX=Z$ (2)

$\begin{array}{l}A=\left[\begin{array}{cc}1& -tg{\theta }_{k-1}\\ 1& -tg{\theta }_{k}\end{array}\right],\\ X=\left[\begin{array}{c}{x}_{T}\\ {y}_{T}\end{array}\right],\\ Z=\left[\begin{array}{c}-{x}_{k-1}+{y}_{k-1}tg{\theta }_{k-1}\\ -{x}_{k}+{y}_{k}tg{\theta }_{k}\end{array}\right]\end{array}$ (3)

$X={\left({A}^{T}A\right)}^{-1}{A}^{T}Z$ (4)

2.3. UKF滤波

$\left[\begin{array}{c}{x}_{T,k}\\ {y}_{T,k}\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{T,k-1}\\ {y}_{T,k-1}\end{array}\right]$ (5)

${\theta }_{k}=\mathrm{arctan}\left(\frac{{y}_{T}-{y}_{k}}{{x}_{T}-{x}_{k}}\right)+{\eta }_{k}$ (6)

UT的具体过程如下：

1) 计算2n + 1个Sigma点及其权值：

$\begin{array}{l}{X}_{i}=\left\{\begin{array}{ll}\stackrel{¯}{X},\hfill & i=0\hfill \\ \stackrel{¯}{X}+\sqrt{\left(n+1\right){P}_{X}},\hfill & i=1,2,\cdots ,n\hfill \\ \stackrel{¯}{X}-\sqrt{\left(n+1\right){P}_{X}},\hfill & i=n+1,n+2,\cdots ,2n\hfill \end{array}\\ {w}_{i}^{m}=\left\{\begin{array}{ll}\frac{\lambda }{n+\lambda },\hfill & i=0\hfill \\ \frac{1}{2\left(n+\lambda \right)},\hfill & i=1,2,\cdots ,2n\hfill \end{array}\\ {w}_{i}^{c}=\left\{\begin{array}{ll}\frac{\lambda }{n+\lambda }+\left(1-{\alpha }^{2}+\beta \right),\hfill & i=0\hfill \\ \frac{1}{2\left(n+\lambda \right)},\hfill & i=1,2,\cdots ,2n\hfill \end{array}\end{array}$ (7)

2) 计算Sigma点通过非线性函数f()的结果：

${Y}_{i}=f\left({X}_{i}\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=0,1,\cdots ,2n$ (8)

$\begin{array}{l}\stackrel{¯}{Y}=\underset{i=0}{\overset{2n}{\sum }}{w}_{i}^{m}{Y}_{i}\\ {P}_{Y}=\underset{i=0}{\overset{2n}{\sum }}{w}_{i}^{c}\left({Y}_{i}-\stackrel{¯}{Y}\right){\left({Y}_{i}-\stackrel{¯}{Y}\right)}^{T}\end{array}$ (9)

2.4. 算法流程

1) 启动定位功能；

2) 平台移动一定距离后，进行三角交叉定位，获取初始定位点；

3) 以初始定位点作为UKF滤波起始估计值；

4) 由状态滤波估计值产生Sigma点；

5) 根据滤波方程，迭代更新目标状态估计，即目标位置估计值。

3. 仿真分析

(a) R = 30 km, σ = 1˚, T = 0.1 s, v = 50 m/s (b) θ = 60˚, σ = 1˚, T = 0.1 s, v = 50 m/s (c) R = 30 km, θ = 60˚, T = 0.1 s, v = 50 m/s (d) R = 20 km, θ = 60˚, σ = 1˚, T = 0.1 s

Figure 2. Analysis diagram of simulation

Figure 3. Estimated location of single-station target (1)

Figure 4. Estimated location of single-station target (2)

Figure 5. Estimated location of single-station target (3)

4. 结论

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