Implementation of parallel least square algorithm for gravity field inversion

Abstract

The Gravity Recovery and Climate Experiment (GRACE) mission Launched in 2002 has provided accurate scientific products which help people gain new details on the Earth's gravity field. Meanwhile, this satellite mission also presents a computational challenge to analyze the large amount of data collected. To deal with this problem, much effort has been done to minimize the heavy computational burden (Gunter 2000; Han 2004). This paper focuses on applying parallel techniques in a straight forward way to estimate unknown geopotential coefficients. The gravity model is based on the energy conservative approach (Jekeli, 1999) that builds a direct connection between the in situ disturbed geopotential difference of two satellites and the position, velocity, range rate data obtained from the GPS, accelerometer and range instrument respectively carried aboard GRACE. The corresponding observation model is a simple linear equation which makes the construction of design matrix handy. Three major steps make up the whole processing procedures. The first is the creation of local contribution. The second is transformation of local information to global object. The last is Cholesky decomposition. We tested the implementations of two methods. The Normal Matrix Accumulation (NMA) method computes design matrix and normal matrix locally and accumulates them to global objects afterwards. The Design Matrix Accumulation (DMA) approach is to form small size of design matrix locally first and transfer to global scale, by matrix-matrix multiplication to obtain the global normal matrix. The creation of normal matrix occupies the majority of the whole wall time. Our preliminary results indicate that the NMA method is very fast but cannot be used to estimate very high degree and order coefficients due to the lack of memory. The DMA can solve for up to 120 degree and order in roughly 30 minutes.