改进高斯-牛顿法的位场向下延拓  

A Modified Gauss-Newton Method for Downward Continuation of Potential Field

作　　者：曾小牛[1,2] 刘代志[1] 牛超[1] 齐玮[3] 

机构地区：[1]第二炮兵工程大学907教研室,陕西西安710025 [2]清华大学信息科学技术学院自动化系,北京100084 [3]第二炮兵装备研究院,北京100085

出　　处：《测绘学报》2014年第1期37-44,共8页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金面上项目(40974037;41374154)

摘　　要：针对位场向下延拓的不适定问题,在分析最优化算法中高斯-牛顿法基本原理及滤波函数滤波特性的基础之上,提出基于正则参数指数递增计算方法和残差最小步长准则的改进高斯-牛顿法。基于理论重力模型和航磁实测数据的对比试验表明,改进后得到的自适应迭代法具有相对较高的位场向下延拓精度和很好的收敛性。For the ill-posed problem of potential field downward continuation, a novel improved iterative method is proposed based on the analysis of the basic principle and the filter characteristic of the filter function of the Gauss-Newton method. This novel improved method uses an incremental geometric regularization parameter adaptive choice method and the minimal residual criterion for the iterative step choice. The comparison analysis of gravity theoretical model and real geomagnetic data shows that the proposed iterative method has high downward continuation accuracy and good convergence.

关 键 词：位场 高斯一牛顿法 向下延拓 正则参数 残差最小准则 

分 类 号：P228[天文地球—大地测量学与测量工程]