Adaptive Polynomial Approximation for Gravimetric Geoid: A case study using EGM96 and EIGEN-GL04C Geopotential Development

In this paper, adaptive polynomial approximation method to model the gravimetric geoid is presented. The polynomial approximation model to arrange training of input is for adaptive system. Training data pairs (input and output) were compiled from latitude and longitude data sequences as input training, and an associated geopotential developments datum on each spatial position as output training. By preceded centering of latitude and longitude data, input training formed with following appropriate formula is the polynomial terms. Adaptation process used LMS (least mean square) algorithm in weight updating, and after training session, approximation of desired target was computed by reloading weights into the polynomial model. Model of assessment test used was to validate adaptive model by comparing residual distance of consecutive point from both geopotential developments data and respective adaptive model in geocentric coordinates system. Using geopotential developments data around of Merapi and Merbabu as a case study, the results show that the residual distance between geopotential developments data and respective adaptive model are about 0.0014417 m (in total absolute value with standard deviation is about 4.6906x10-5 m) using EGM96 geoid and about 0.0014468 m (in total absolute value with standard deviation is about 4.702x10-5 m) using EIGEN-GL04C geoid. Better result could be achieved by adding more training session with smaller gain factor.