An Empirical Stochastic Model for GPS

Abstract

In addition to functional models, stochastic modeling of observations plays an important role in GPS data processing. The stochastic model has influence over several issues of coordinates determination with GPS, such as the covariance matrix of the observations (which leads to weighting scheme) and the estimated covariance matrix of the parameters. In this paper we present an empirical stochastic approach to create observation covariance matrices for GPS. Our approach aims to a more realistic and complete information about the stochastic behavior of GPS observations and an improvement in quality and quality control of estimated coordinates.

In the empirical approach the correlation functions and variances are computed using the observed data, instead. Therefore it is not necessary any a-priori assumption linking observables variances and correlations to elevation angle or time lags, usually given by formal models. The first step of this approach is a functional reduction of the observables, which is made according to the functional model used in the late adjustment. The objective of this first step is leading the observation time series to stationarity. An auto-regressive model is then adjusted, with the determination of its parameters and order. Parameters are estimated using least squares adjustment and the order determined by an assessment of residuals. Once all parameters of the stochastic model were determined empirically, it is used to create the observation covariance matrix to be used in the functional model.

In the present case study, GPS baselines were processed. Analyses were made in terms of obtained coordinates and their estimated covariance matrices, aiming at an improvement in GPS quality control. Improvements of at least 11 % in precision and accuracy were found when this empirical stochastic approach was used. Future research aims to the enhancement of the method until it is general enough to be used in any case of GPS data processing.