水下地形匹配定位置信区间估计

Confidence Interval Estimation of Underwater Terrain Aided Position

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X^p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,X^p向某一点跳变的置信度小于α时,认为x~α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X^p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。

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 X^p 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,X^p 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, X^p 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.