水下地形匹配定位置信区间估计

王汝鹏, 李晔, 马腾, 丛正, 贡雨森, 张强

王汝鹏, 李晔, 马腾, 丛正, 贡雨森, 张强. 水下地形匹配定位置信区间估计[J]. 武汉大学学报 ( 信息科学版), 2019, 44(6): 830-836, 916. DOI: 10.13203/j.whugis20170281
引用本文: 王汝鹏, 李晔, 马腾, 丛正, 贡雨森, 张强. 水下地形匹配定位置信区间估计[J]. 武汉大学学报 ( 信息科学版), 2019, 44(6): 830-836, 916. DOI: 10.13203/j.whugis20170281
WANG Rupeng, LI Ye, MA Teng, CONG Zheng, GONG Yusen, ZHANG Qiang. Confidence Interval Estimation of Underwater Terrain Aided Position[J]. Geomatics and Information Science of Wuhan University, 2019, 44(6): 830-836, 916. DOI: 10.13203/j.whugis20170281
Citation: WANG Rupeng, LI Ye, MA Teng, CONG Zheng, GONG Yusen, ZHANG Qiang. Confidence Interval Estimation of Underwater Terrain Aided Position[J]. Geomatics and Information Science of Wuhan University, 2019, 44(6): 830-836, 916. DOI: 10.13203/j.whugis20170281

水下地形匹配定位置信区间估计

基金项目: 

国家重点研发计划 2017YFC0305700

国家自然科学基金 51879057

中央高校基本科研业务费 HEUCFG201810

详细信息
    作者简介:

    王汝鹏, 博士生, 主要从事水下机器人自主定位导航与环境地图构建方面的研究。wangrupeng@hrbeu.edu.cn

    通讯作者:

    李晔, 博士, 教授。liyeheu103@163.com

  • 中图分类号: P229

Confidence Interval Estimation of Underwater Terrain Aided Position

Funds: 

The National Key Research and Development Program of China 2017YFC0305700

the National Natural Science Foundation of China 51879057

the Fundamental Research Business Funds for the Central Universities HEUCFG201810

More Information
    Author Bio:

    WANG Rupeng, PhD candidate, specializes in autonomous positioning and navigation of underwater vehicles and environmental map construction. E-mail:wangrupeng@hrbeu.edu.cn

    Corresponding author:

    LI Ye, PhD, professor. E-mail:liyeheu103@163.com

  • 摘要: 地形匹配定位(terrain aided position,TAP)的似然函数反映了AUV(autonomous underwater vehicle)的位置在空间中的分布概率,由于地形的强非线性、随机性以及测量误差的非高斯分布使得似然函数也表现出非高斯分布的特点。TAP的误差与局部地形特征和地形测量误差密切相关,由于现有的方法未考虑局部地形特征,仅考虑了测量误差的统计置信区间,使得TAP置信区间的估计结果明显偏小。为解决TAP置信区间的估计问题,建立了TAP定位点的跳变模型。设TAP定位点Xp可以向搜索区间内任一点跳变,且向某一点的跳变概率与该点的似然函数值正相关,Xp向某一点跳变的置信度小于α时,认为xα不会向该点跳变,该点设为置信区间的边界点。另外,设地形匹配定位点的置信区间内匹配残差平方和函数为二次曲面,而Xp视为该曲面的待估计参数,则可以通过曲面参数的置信区间估计方法获得1-α置信度下的置信区间。新方法得到的置信区间范围大于现有的估计方法,试验结果表明,测量波束较少时,置信区间估计会出现异常,增加测量波束可以提高潮差和测量误差的估计精度,从而提高置信区间的估计精度,但测量误差非高斯分布条件下的补偿方法仍然需要进一步研究。
    Abstract: The TAP(terrain aided position) likelihood function reflects the probability of the position of AUV (autonomous underwater vehicle) in space. Due to the strong nonlinearity and randomness of the terrain and the non-Gauss distribution of the measurement error, the likelihood function also shows the characteristics of non-Gauss. The error of TAP is closely related to the local topographic and measurement error. Because the existing method does not consider the local topographic features, the statistical confidence interval of the measurement error is only established, so the estimation results of the TAP are obviously smaller. In this paper, a jump model of the TAP position Xp is established. It can jump to any point in the searching interval, and the probability jumping to any point is positively correlated with the likelihood function of the point. When the confidence of the jump to a certain point is less than α, Xp will not jump to this point and this point is called the boundary point of the confidence interval. Assumed the sum of squares of the matched residuals in the confidence interval of the TAP is quadric surface, Xp is regarded as the parameter of the quadric surface, and the confidence interval of TAP with confidence 1-α can be obtained by the confidence interval estimation method of the surface parameters. The confidence interval obtained by new estimate method is larger than the existing method. The experimental results show that the confidence interval estimation will be abnormal when the measuring beam is less. The increase of the measurement beam can improve the estimation accuracy of the tidal and measurement errors, thus can promote the estimation accuracy of the confidence interval, but the compensation method under the condition of non-Gauss distribution of measurement error is still needed in further work.
  • 图  1   多波束声纳单Ping下的测量模型

    Figure  1.   Multi-beam Sonar Measurement Model Under Single Ping

    图  2   由面观测模型转化为点测量模型

    Figure  2.   Transform from Surface Observation Model to Point Measurement Model

    图  3   地形匹配定位点的跳变区间和边界点

    Figure  3.   Jumping Interval and Boundary Points of TAP Position

    图  4   实验航线上的MTM的地形粗糙度

    Figure  4.   Terrain Roughness of MTM on Experimental Route

    图  5   本文方法和文献[3]方法得到的定位置信区间比较

    Figure  5.   Comparison of Two Confidence Intervals Using Our Proposed Method and Reference [3]

    图  6   本文方法和文献[3]方法得到的定位置信区间大小比较

    Figure  6.   Size of Two Confidence Intervals Using Our Proposed Method and Reference [3]

    图  7   测量波束为10 Ping时17~21号匹配点的似然函数、GPS定位点、TAP定位点和置信区间

    Figure  7.   Likelihood Function, GPS Positioning Point, TAP Positioning Point and Confidence Interval of Matching Point 17-21 at 10 Ping

    图  8   测量波束为10 Ping时地形匹配定位点的测量误差和潮差估计

    Figure  8.   Measurement Error and Tidal Range Estimation of TAP Points at 10 Ping

    图  9   测量波束为10 Ping时匹配点的残差序列和直方图统计结果

    Figure  9.   Residual Sequence and Histogram Statistics at TAP Position at 10 Ping

    图  10   测量波束为20 Ping时地形匹配定位点的测量误差和潮差估计

    Figure  10.   Measurement Error and Tidal Range Estimation of TAP Points at 20 Ping

    图  11   测量波束为30 Ping时21号匹配点的残差直方图统计

    Figure  11.   Residual Histogram Statistics of TAP Point 21 at 30 Ping

    图  12   测量波束为30 Ping时17~21号匹配点的似然函数、GPS定位点、TAP定位点和置信区间

    Figure  12.   Likelihood Function, GPS Positioning Point, TAP Positioning Point and Confidence Interval of Matching Points 17-21 at 30 Ping

    表  1   测量波束增加时测量误差对比

    Table  1   Comparison of Measurement Errors when Measuring Beam Increase

    测量波束/Ping 估计序列均值 估计序列标准差 与10 Ping结果比较/%
    均值 标准差
    10 0.181 5 0.089 8
    20 0.220 3 0.090 6 ↑21.38 ↑0.89
    30 0.233 8 0.087 6 ↑28.80 ↓2.45
    下载: 导出CSV

    表  2   测量波束增加时潮差估计对比

    Table  2   Estimation of Tidal when Measured Beam Increase

    测量波束/Ping 估计序列均值 估计序列标准差 与10 Ping结果比较/%
    均值 标准差
    10 2.553 8 0.163 7
    20 2.539 0 0.113 5 ↓0.58 ↓30.60
    30 2.528 0 0.121 6 ↓1.01 ↓25.72
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-12-06
  • 发布日期:  2019-06-04

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