一种卫星重力梯度数据的ARMA最优滤波模型构建方法

由于卫星重力梯度观测的有色噪声特性和海量观测特征，在利用直接法进行重力场模型的最小二乘求解时，观测值的协方差阵为超大型的非对角阵，这给数值求解带来了极大困难.本文提出了一种基于先验误差功率谱密度的最优ARMA滤波模型构建方法，结合法方程的分块求解策略，可实现对卫星重力梯度观测值的高效滤波处理.数值仿真结果表明，利用最优ARMA滤波器进行时域滤波后，法方程的态性得到了明显改善，重力梯度观测值中的有色噪声得到了有效的"白化"处理，大地水准面精度得到了显著提升.

A method for constructing the optimal ARMA filtering model on the satellite gravity gradiometry data

Due to the colored noise in the massive satellite gravity gradiometry observations, when determining the least square solution of the gravity field model using the direct method, the covariance matrix of the observations is a huge non-diagonal matrix, which brings great difficulties to numerical computation. To solve this problem, this work proposes a method of constructing the optimal ARMA filtering model based on the prior error power spectrum density, which realizes the efficient filtering of satellite gravity gradiometry observations combined with the block solving strategy. The numerical simulation analyses show that after the processing in the time domain with the optimal ARMA filter, the state of the normal equation matrix is improved obviously, and the colored noises mixed into the gravity gradiometry measurements are whitened efficiently, while the accuracy of the geoid increases significantly.