位场向下延拓迭代法收敛性分析及稳健向下延拓方法研究

Analysis on convergence of iteration method for potential fields downward continuation and research on robust downward continuation method

地磁导航作为一种新的无源导航方式,具有重要的国防意义.构建空间地磁数据库是实现地磁导航的基础,位场延拓是解决地磁数据库构建的有效方法.积分-迭代法是一种解决位场大深度向下延拓的实用方法.本文着重对积分-迭代法的收敛性进行了分析,从数学角度证明积分-迭代法能够收敛到直接下延法理论解.同时对积分迭代法的抗干扰性进行了初步分析,当观测数据含有噪声时,积分-迭代过程中使得噪声得到累加,影响延拓数据的精度.本文利用正则化方法和递增型维纳滤波方法,提出了波数域位场向下延拓新算法.模型检验表明,新算法稳定、抗干扰能力强、计算速度快.

Geomagnetic navigation is a brand new navigation technology and has very important significance for national defence. Spatial geomagnetic database is a precondition when implementing geomagnetic navigation. Potential field continuation is an effective method for designing geomagnetic database. Integral iteration method is a kind of stable downward continuation method for potential fields. This paper focuses on convergence analysis of integral iteration method, and proves that the method is convergent mathematically. This paper also analyses the robust performance of integral iteration method, and it concludes that when observed data contain noise, noise may be accumulated during iteration. A new wave number domain downward continuation method is presented according to the idea of regulation method and incremental Wiener filer method. Model test shows that the new method is stable, robust and has a short computation time.