﻿ 多参照点联合概率地形误匹配判断准则<sup>*</sup>
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Judgement criterion for terrain false matching based on joint probability of multiple reference points
ZHANG Kunwei, WANG Kedong
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2017-07-21; Accepted: 2017-10-27; Published online: 2017-12-18 13:17
Corresponding author. WANG Kedong.E-mail:wangkd@buaa.edu.cn
Abstract: Since the terrain contour matching (TERCOM) algorithm is easy to mismatch due to measurement error and terrain self-similarity, an on-line false matching judgement criterion based on the joint probability of multiple reference points in a correlation plane was proposed by taking mean square difference (MSD) as an example. Firstly, the MSD correlation plane was calculated by the correlation of the measured elevation data with the reference elevation data. Then, the MSD probability distribution density function of the candidate matching points was derived by analyzing the statistical distribution of elevation measurement error. Finally, the multi-point joint probabilities were calculated for all the candidate points in the correlation plane so that they are compared with a threshold to judge the matching of the point with the minimum MSD value false or not. The simulation results show that 97% false matching points can be detected and 90% correct matching points can be preserved when the threshold is set to 0.9, implying that false matching can be avoided to a great extent.
Key words: terrain matching     terrain contour matching (TERCOM) algorithm     false matching     matching probability     false positioning

1 TERCOM算法基本原理

TERCOM算法原理如图 1所示，飞行器在飞越航线上的地形匹配区时，利用雷达高度表和气压高度表等设备测量沿航线的地形高程序列，将测得的实时高程序列和预存的基准图高程序列进行相关，按最佳相关确定飞行器的地理位置。

 图 1 TERCOM算法原理图 Fig. 1 Schematic diagram of TERCOM algorithm

 (1)

2 参照点概率 2.1 正确匹配点概率分布

 (2)

 (3)

wi的分布和式(3)可得

 (4)

2.2 参照点概率分布

 (5)

 (6)

vi为均值为(hDEMihri)、与wi同方差的高斯噪声，即vi~N(hDEMihri, σ2)。此时有

 (7)

vi的分布和式(7)可得

 (8)

3 多参照点概率联合

1) 点选取。PDAF算法以惯性导航系统(Inertial Navigation System，INS)输出位置的匹配位置为中心确定待匹配窗口，求得该窗口内各待匹配点的MSD值，构成地形轮廓匹配算法的MSD相关面，并获得其中最小的m个极小值点{p1, p2, …, pm}。

2) 联合概率计算区域确定。针对获得的m个极小值点，以每个极小值点为中心、gr个地图网格间距为半径，对应的区域即为该极小值点的联合概率计算区域。

3) 区域内各点为正确匹配点的概率计算。针对每个极小值点对应计算区域内(2gr+1)2个点{a1, a2, …, a(2gr+1)2}，按式(4)分别计算每个点ai服从Γ分布[15]的概率值γai

4) 参照点的概率计算。取ai点上下左右间隔为d个网格间距的4个网格点作为ai联合概率计算的参照点{rref1, rref2, rref3, rref4}，按式(8)分别计算其服从非中心χ2分布的概率值{αref1, αref2, αref3, αref4}。

5) 区域联合概率计算。设βaiai点联合概率，则有

 (9)

 (10)

6) 选取区域为正确匹配区域的概率计算。第l个区域对应的极值点为正确匹配点的概率为

 (11)

4 仿真验证 4.1 仿真条件

 图 2 地形高程图 Fig. 2 Terrain elevation map
 图 3 三维地形图 Fig. 3 Three-dimensional terrain map
4.2 误匹配判断

 图 4 MSD相关面及其对应极值点区域联合概率示意图(误匹配) Fig. 4 Schematic diagram of MSD correlation plane and regional joint probability of corresponding extreme point (false matching)
 图 5 MSD相关面及其对应极值点区域联合概率示意图(匹配正确) Fig. 5 Schematic diagram of MSD correlation plane and regional joint probability of corresponding extreme point (correct matching)

 编号 极小值点坐标 MSD值 区域联合概率 1 (90, 90) 347.6 0.31 2 (111, 112) 351.4 0.69 3 (69, 9) 526.8 0 4 (127, 161) 546.9 0 5 (37, 142) 595.5 0 6 (147, 153) 685.3 0 7 (62, 181) 723.6 0 8 (103, 119) 767 0 9 (114, 63) 809.5 0 10 (135, 52) 947.2 0

 编号 极小值点坐标 MSD值 区域联合概率 1 (33, 49) 67.6 0.97 2 (108, 14) 93.5 0 3 (102，107) 130.7 0 4 (93, 1) 209.2 0 5 (48，169) 289.2 0 6 (63, 109) 303.5 0 7 (113, 144) 315.9 0 8 (38, 56) 358.7 0.03 9 (199, 200) 407.5 0 10 (129, 134) 458.9 0

4.3 阈值选取

 序列长度 σn/m 正确点保留率/% 匹配准确率/% 无阈值 阈值为0.6 阈值为0.9 无阈值 阈值为0.6 阈值为0.9 100 10 4.6 100 97.9 97.9 94.5 98.9 99.4 17 2.7 100 95.9 94.1 86 97 98.8 24 1.9 100 90.9 90.4 83.5 96.2 97.4 150 10 4.6 100 99 99 98 100 100 17 2.7 100 98.5 98.5 97.5 99.5 99.5 24 1.9 100 96.8 96.2 92.5 98.4 98.9 200 10 4.6 100 99.5 98.9 98.5 100 100 17 2.7 100 99 99 97.5 99.5 100 24 1.9 100 98.9 98.4 95.5 99.5 100

5 结论

1) 正确匹配判定准确率高。在不同仿真条件下，当联合概率阈值设为0.9时，判断准确率达到97%以上。

2) 正确匹配结果遗失少。选取不同的匹配序列长度和测量噪声的情况下，当概率阈值设为0.9时，依然保留了90%以上的正确匹配结果。

3) 匹配精度高。仿真中设定的正确匹配精度为不大于2个网格间距。

4) 适用于在线判定。判定结果仅基于单次匹配相关面给出，不需要额外信息。

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#### 文章信息

ZHANG Kunwei, WANG Kedong

Judgement criterion for terrain false matching based on joint probability of multiple reference points

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(7): 1562-1568
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0499