一种新的基于局部重力图逼近的组合匹配算法  

A new integrated gravity matching algorithm based on approximated local gravity map

作　　者：童余德[1,2] 边少锋[1,3] 蒋东方[1] 向才炳[1] 

机构地区：[1]海军工程大学导航工程系,武汉430033 [2]海岛(礁)测绘技术国家测绘局重点实验室,青岛266510 [3]中国科学院测量与地球物理研究所,武汉430077

出　　处：《地球物理学报》2012年第9期2917-2924,共8页Chinese Journal of Geophysics

基　　金：国家重点基础研究发展计划(2012CB719900);国家自然科学基金项目(40904018;41071295;61203193);海岛(礁)测绘技术国家测绘局重点实验室开放研究基金(2010B04);水下测控技术重点实验室延伸性发展基金(YSOC261102)资助

摘　　要：惯性导航系统定位误差随时间积累发散,利用重力场辅助惯性导航已成为组合导航领域的新方向,该技术对实现潜艇无源定位意义重大.首先利用二维高斯基函数对局部离散格网重力异常基准图进行逼近获取其解析表达式,在此基础上对传统相关极值匹配算法进行重新建模,采用拟牛顿BFGS非线性寻优方法对该模型进行解算,最终完成基于连续解析形式重力异常基准图的相关极值匹配算法设计.为进一步提高算法性能进行以下两点改进:(1)采用TERCOM算法进行预匹配以缩小寻优范围提高寻优速度;(2)采用差分法减小实测过程中Etvs效应对重力匹配的影响.最后在2′×2′卫星测高反演重力异常数据库基础上进行了三组对比仿真实验,从实验结果可以看出,在重力测量误差、系统误差及初始定位误差较大的情况下,通过该组合匹配算法获得的匹配定位仍能以较高的精度跟踪真实航迹,且其性能较传统单一匹配算法有较大提高.The gravity field aided inertial navigation has been applied to correct the drifting errors in the inertial navigation which are accumulated with time and it has become a new research direction in the integrated navigation technology which is significant to implement autonomous and passive navigation of submarines.Firstly,the algorithm to approximate the local grid gravity anomaly map with the 2-D Gauss spline function is proposed.The mathematical model of maximum correlation matching algorithm is redesigned based on this local continuous map and the BFGS method of Quasi-Newton is adopted to solve the non-linear model.Finally,the maximum correlation matching algorithm based on a continuous analytic form of gravity anomaly map is accomplished.Two improvements are used to further improve the efficiency of the new algorithm as follows：（1） TERCOM algorithm is applied to pre-match for the reduction of optimizing region and the enhancement of the optimizing speed;（2） The method of difference is used to reduce Etvs effect in measure process of gravity matching.Three contrast simulation experiments have been done based on 2′×2′ gravity anomaly database from satellite altimetry inversion.From the simulation results,we can see that the matching results of the new integrated algorithm can track the real positions with high precision in case of relatively big observation error,systematic error and initial position error and the performances of this algorithm are better than the conventional single matching algorithm.

关 键 词：惯性导航系统 重力图逼近 组合匹配算法 相关极值 

分 类 号：P223[天文地球—大地测量学与测量工程]