﻿ 基于雷达/电视的自标校数据融合方法
 舰船科学技术  2017, Vol. 39 Issue (3): 140-144 PDF

A self-calibration method based on fusion of landing guidance radar and centerline camera
WANG Zhao-yi, LIU Ai-dong, GAO Bo
Naval Aeronautical and Astronautical University, Yantai 264001, China
Abstract: The true value measurement problem is researched against the background of the shore base calibration of aircraft carrier landing system, Based on Fusion of Landing Guidance Radar and Centerline Camera,a target location algorithm is proposed .Firstly,considering the equipments of the system measured the target in different frequency, the carrier movement and the coordinate systems are consistend simultaneously,the paper unified the time and space.Secondly,the transer model was derived for each device measurement error.At last,on the basis of the variance of the error acquired above-mentioned,the angle information of the landing guidance radar and the centerline camera was fused with the weighted average method,then provided the final location results.The simulation rsults show that the method owns high positioning accuracy in the case of well-functioning equipments.
Key words: landing guidance system     spatio-temporal matching     data fusion     error transfer
0 引　言

1 雷达/电视测量模型 1.1 建立坐标系 1.1.1 甲板固连坐标系

1.1.2 水平坐标系

1.2 着舰引导雷达测量模型

 $\left\{ \begin{array}{l}{r_R} = {r_R}^\prime + {n_{rR}}\text{，}\\{\alpha _R} = {\alpha _R}^\prime + {n_{\alpha R}}\text{，}\\{\beta _R} = {\beta _R}^\prime + {n_{\beta R}}\text{。} \end{array}\right.$ (1)

 $\left[ \begin{array}{l}{x_R}\\{y_R}\\{z_R}\end{array} \right] = \left[ \begin{array}{c}{r_R}\cos {\beta _R}\cos {\alpha _R}\\{r_R}\cos {\beta _R}\sin {\alpha _R}\\{r_R}\sin {\beta _R}\end{array} \right]\text{。}$ (2)

1.3 中线电视测量模型

 $\left\{ \begin{array}{l}{\alpha _T} = {\alpha _T}^\prime + {n_{\alpha T}}\text{，}\\{\beta _T} = {\beta _T}^\prime + {n_{\beta T}}\text{。}\end{array} \right.$ (3)

 $\left[ \begin{array}{l}{\alpha _T}^\prime \\\cos {\beta _T}^\prime \end{array} \right] = \left[ \begin{array}{l}\arctan \left( {\frac{{{y_T}}}{{{x_T}}}} \right)\\\arctan \left( {\frac{{{z_T}}}{{\sqrt {x_T^2 + y_T^2} }}} \right)\end{array} \right]\text{。}$ (4)

2 雷达/电视数据融合算法

2.1 雷达/电视数据的时空匹配 2.1.1 测量数据拟合算法

 $S\left( x \right) = {a_1}{\varphi _1}\left( x \right) + {a_2}{\varphi _2}\left( x \right) + \cdots {a_n}{\varphi _n}\left( x \right)\text{，}$ (5)

 $\begin{split}\left[ {\begin{array}{*{20}{c}} {\left( {{\varphi _1},{\varphi _1}} \right)}&{\left( {{\varphi _1},{\varphi _2}} \right)}& \cdots &{\left( {{\varphi _1},{\varphi _n}} \right)}\\{\left( {{\varphi _2},{\varphi _1}} \right)}&{\left( {{\varphi _2},{\varphi _2}} \right)}& \cdots &{\left( {{\varphi _2},{\varphi _n}} \right)}\\ \vdots & \vdots & \ddots & \vdots \\{\left( {{\varphi _n},{\varphi _1}} \right)}&{\left( {{\varphi _n},{\varphi _2}} \right)}& \cdots &{\left( {{\varphi _n},{\varphi _n}} \right)}\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{{a_1}}\\{{a_2}}\\ \vdots \\{{a_n}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{d_1}}\\{{d_2}}\\ \vdots \\{{d_n}}\end{array}} \right]\text{。}\end{split}$ (6)

2.1.2 测量数据空间转换

 $\left[ \begin{array}{l}{x_{RL}}\\{y_{RL}}\\{z_{RL}}\end{array} \right] = {{ T}_A}{{ T}_L}{ T}_R^{ - 1}\left[ \begin{array}{l}{x_R}\\{y_R}\\{z_R}\end{array} \right] + \left[ \begin{array}{l}{x_r}\\{y_r}\\{z_r}\end{array} \right]{\text{。}}$ (7)

 ${{T}_A} = \left[ {\begin{array}{*{20}{c}}{\cos {\varphi _c}}&{\sin {\varphi _c}}&0\\{ - \sin {\varphi _c}}&{\cos {\varphi _c}}&0\\0&0&1\end{array}} \right]\text{，}$
 $\begin{array}{l}{{T}_R} = \left[ {\begin{array}{*{20}{c}}{\cos {\gamma _R}}&{ - \sin {\gamma _R}}&0\\{\sin {\gamma _R}}&{\cos {\gamma _R}}&0\\0&0&1\end{array}} \right] \times\\ \left[ {\begin{array}{*{20}{c}}{\cos {\psi _R}}&0&{ - \sin {\psi _R}}\\0&1&0\\{\sin {\psi _R}}&0&{\cos {\psi _R}}\end{array}} \right] \cdot \left[ {\begin{array}{*{20}{c}}1&0&0\\0&{\cos {\theta _R}}&{ - \sin {\theta _R}}\\0&{\sin {\theta _R}}&{\cos {\theta _R}}\end{array}} \right]\text{。}\end{array}$

2.2 时空匹配后误差传递分析

1）着舰引导雷达、中线电视及理想着舰点处的局部基准给出的船体姿态信息无误差；

2）着舰引导雷达、中线电视及理想着舰点在理想着舰点坐标系下的相互位置已知；

3）斜角甲板中线与首尾线的在甲板面上的夹角不变。

 $\left[ \begin{array}{l}\Delta {x_{RL}}\\\Delta {y_{RL}}\\\Delta {z_{RL}}\end{array} \right] = M \cdot A \cdot \left[ {\begin{array}{*{20}{c}}{\Delta {r_R}}\\{\Delta {\alpha _R}}\\{\Delta {\beta _R}}\end{array}} \right]\text{。}$ (8)

 $\begin{array}{l}A\! = \!\left[ {\begin{array}{*{20}{c}}\!\!\!{\cos {\beta _R}\cos {\alpha _R}}\!\!\!&\!\!\!{ - {r_R}\cos {\beta _R}\sin {\alpha _R}}\\\!\!\!{\cos {\beta _R}\sin {\alpha _R}}\!\!\!&\!\!\!{{r_R}\cos {\beta _R}\cos {\alpha _R}}\\\!\!\!{\sin {\beta _R}}\!\!\!&\!\!\!0\end{array}} \right.\left. \begin{array}{l} \!\!\!- {r_R}\sin {\beta _R}\cos {\alpha _R}\\ \!\!\!- {r_R}\sin {\beta _R}\sin {\alpha _R}\\\!\!\!{r_R}\cos {\beta _R}\end{array}\right]\end{array}\!\!\!\!\text{，}$
 ${M} = {{T}_A} \cdot {{T}_L} \cdot {T}_R^{ - 1}\text{。}$

 $\left[ {\begin{array}{*{20}{c}}{\Delta {r_{RL}}}\\{\Delta {\alpha _{RL}}}\\{\Delta {\beta _{RL}}}\end{array}} \right] = B \cdot \left[ \begin{array}{l}\Delta {x_{RL}}\\\Delta {y_{RL}}\\\Delta {z_{RL}}\end{array} \right]\text{。}$ (9)

 $\begin{array}{l}B \!= \!\left[ \!\!\!\begin{array}{l}\frac{{{x_{RL}}}}{{\sqrt {x_{RL}^2 + y_{RL}^2 + z_{RL}^2} }}\\\frac{{ - {y_{RL}}}}{{x_{RL}^2 + y_{RL}^2}}\!\!\!\\\frac{{ - {x_{RL}}{z_{RL}}/\sqrt {x_{RL}^2 + y_{RL}^2} }}{{\left( {x_{RL}^2 + y_{RL}^2 + z_{RL}^2} \right)}}\end{array} \right.\left. {\begin{array}{*{20}{c}}{\frac{{{y_{RL}}}}{{\sqrt {x_{RL}^2 + y_{RL}^2 + z_{RL}^2} }}}\!\!\!\!&\!\!\!\!{\frac{{{z_{RL}}}}{{\sqrt {x_{RL}^2 + y_{RL}^2 + z_{RL}^2} }}}\!\!\!\!\\{\frac{{{x_{RL}}}}{{x_{RL}^2 + y_{RL}^2}}}\!\!\!\!&\!\!\!\!0\!\!\!\!\\{\frac{{ - {y_{RL}}{z_{RL}}/\sqrt {x_{RL}^2 + y_{RL}^2} }}{{\left( {x_{RL}^2 + y_{RL}^2 + z_{RL}^2} \right)}}}\!\!\!&\!\!\!{\frac{{\sqrt {x_{RL}^2 + y_{RL}^2} }}{{x_{RL}^2 + y_{RL}^2 + z_{RL}^2}}}\end{array}}\!\!\! \right]\end{array}\text{，}$

 $\left[ {\begin{array}{*{20}{c}}{\Delta {r_{RL}}}\\{\Delta {\alpha _{RL}}}\\{\Delta {\beta _{RL}}}\end{array}} \right] = {BMA}\left[ {\begin{array}{*{20}{c}}{\Delta {r_R}^\prime }\\{\Delta {\alpha _R}^\prime }\\{\Delta {\beta _R}^\prime }\end{array}} \right]\text{。}$ (10)

 ${{P}_{RL}} = {BMA}{{P}_R}{\left( {{BMA}} \right)^{\rm{T}}}\text{。}$ (11)

2.3 同步数据融合

 $\left\{ \begin{array}{l}{r_{RT}} = {r_{RL}}\text{，}\\[9pt]{\alpha _{TR}} = \sigma _{\alpha TR}^2\left( {\frac{{{\alpha _{TL}}}}{{\sigma _{\alpha TL}^2}} + \frac{{{\alpha _{RL}}}}{{\sigma _{\alpha RL}^2}}} \right)\text{，}\\[9pt]{\beta _{TR}} = \sigma _{\beta TR}^2\left( {\frac{{{\beta _{TL}}}}{{\sigma _{\beta TL}^2}} + \frac{{{\beta _{RL}}}}{{\sigma _{\beta RL}^2}}} \right)\text{，}\\[9pt]\sigma _{\alpha TR}^2 = \frac{{\sigma _{\alpha TL}^2\sigma _{\alpha RL}^2}}{{\sigma _{\alpha TL}^2 + \sigma _{\alpha RL}^2}}\text{，}\\[9pt]\sigma _{\beta TR}^2 = \frac{{\sigma _{\beta T}^2\sigma _{\beta R}^2}}{{\sigma _{\beta T}^2 + \sigma _{\beta R}^2}} \text{。}\end{array}\right.$ (12)
3 仿真分析

 图 1 中线电视处船体姿态信息 Fig. 1 The ship attitude information at the centerline camera

 图 2 着舰引导雷达测距/测角误差方差放大比例 Fig. 2 The variance amplification ratio of the landing guidance radar ranging and angle measurement error

 图 3 中线电视测角误差方差放大比例 Fig. 3 The variance amplification ratio of the centerline camera angle measurement error

 图 4 三种定位方法的均方根误差比较 Fig. 4 Comparison of root mean square error of three kinds of positioning methods

 图 5 极坐标下的数据融合目标定位性能 Fig. 5 Positioning performance of data fusion target in polar coordinates

4 结　语

 [1] ﻿PRICKETT A L, PARKES C J. Flight testing of the F/A-18E/F automatic Carrier landing system.[C]//IEEE Proceedings Aerospace Conference. Big Sky, MT, USA:IEEE Press, 2001, 5:2593–2612. [2] 王兆毅, 刘爱东, 高波, 等. 一种舰载机下滑道一致性指示数据产生方法[J]. 指挥控制与仿真, 2016, 38(2): 84–88. [3] 柴敏, 于慧, 宋卫红, 等. 光学无线电测量信息融合定位[J]. 光学学报, 2012, 32(12): 1–7. [4] 石晓荣, 王青, 张明廉, 等. 基于多传感器数据融合的激动目标跟踪自适应算法[J]. 系统仿真学报, 2002, 14(5): 631–636. [5] 朱志宇. 基于红外和雷达数据融合的激动目标跟踪方法[J]. 激光与红外, 2002, 37(2): 170–174. [6] 尹继豪, 崔炳喆. 雷达/红外数据融合的机动目标跟踪算法综述[J]. 航空兵器, 2009, 10(5): 39–43. [7] BLAIR S, ALOUANI A T.A Asynchronous data fision for target tracking with a multi-tasking radar and optical sensor[J]. Acquisition tracking and pointing. SPIEs, 1991, 1482: 234–245. [8] 梁凯, 潘泉, 宋国明, 等. 基于曲线拟合的多传感器时间对准方法研究[J]. 火力与指挥控制, 2006, 31(12): 51–53. [9] 王国宏, 毛士艺, 何友. 雷达与红外数据融合算法综述[J]. 火力与指挥控制, 2002, 27(2): 3–6. [10] 钟德安. 航天测量船测控通信设备标校与校飞技术[M], 北京: 国防工业出版社, 2009.