Judgement criterion for terrain false matching based on joint probability of multiple reference points
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摘要:
针对地形轮廓匹配（TERCOM）算法容易受高程测量误差和地形相似性等影响而出现误匹配的问题，以平均平方差（MSD）匹配准则为例，提出了一种相关面内多参照点联合概率误匹配在线判断准则。首先，对测量高程数据和基准高程数据做相关运算，获得待匹配区域内各点的MSD值，即相关面；其次，通过分析高程量测噪声的统计分布，建立待匹配点的MSD概率分布密度函数；最后，计算选取待匹配点为正确匹配点的多点联合概率，并通过阈值判定此待匹配点是否为正确匹配点。仿真结果表明，选取不同的匹配序列长度和测量噪声的情况下，当判定阈值设为0.9时，对正确匹配的判断正确率达到97%以上，且90%以上的正确匹配点都能被保留下来，可以极大程度地避免误匹配。
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关键词:
- 地形匹配 /
- 地形轮廓匹配(TERCOM)算法 /
- 误匹配 /
- 匹配概率 /
- 虚定位
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.
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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)
Figure 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)
Figure 5. Schematic diagram of MSD correlation plane and regional joint probability of corresponding extreme point (correct matching)
表 1 图 4相关面对应极值点区域联合概率
Table 1. Regional joint probability of extreme points corresponding to correlation plane of Fig. 4
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 
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表 2 图 5相关面对应极值点区域联合概率
Table 2. Regional joint probability of extreme points corresponding to correlation plane of Fig. 5
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
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表 3 遍历仿真试验结果
Table 3. Traversal simulation test results
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
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