An Approach to GPS Analysis incorporating Wavelet Decomposition

The classical least-squares processing of GPS measurements generates residuals, which contains the signature of both unmodelled systematic biases and random measurement noise. It is desirable to extract (or minimise) the systematic biases contained within the GPS measurements. This would be relatively straightforward if there were some apriori knowledge of the phenomena related to these errors. Common ways of dealing with this problem include (i) changes to the stochastic modelling, and (ii) redefinition of the functional model. In this paper, we apply a method based on wavelets to decompose GPS double-differenced residuals into a low-frequency bias term and a high-frequency noise term. The extracted bias component is then applied directly to the GPS measurements to correct for this term. The remaining terms, largely characterised by the GPS range measurements and high-frequency measurement noise, are expected to give the best linear unbiased solutions from a leastsquares process. A robust VCV estimation, using the MINQUE procedure, controls the formulation of the stochastic model. The results show that this method can improve both the ambiguity resolution and the accuracy of the estimated baseline components.