Ill-posed problem in determination of coordinate transformation parameters with small area's data based on bursa model

Abstract

The application of GPS is often needed to transform coordinates. If the transformation parameters are solved with the GPS data in a small area, the precision of transformation parameters may be very poor, especially the translation parameters. The reason is that the translation parameters and rotation parameters are high correlated in this case, which causes the solution model to be ill-posed, and regularization solution is an efficient method in dealing with ill-posed model. This paper discusses the regularization solution in solving 3-dimensional coordinate transformation parameters with small area’s data, in order to improve the precision and extend the application range of the solved transformation parameters; a solution model only to regularize translation parameters is also derived in this paper.The model and algorithm are verified with 500 numerical simulated examples; and the results show that the precision of the transformed coordinates in peripheral area can be significantly improved by regularization; and will linearly decrease as the extension of extrapolating distance.