The GPS data weight matrix: what are the issues?

C.C.J.M. Tiberius

Abstract:	GPS data are usually processed with algorithms based on the least-squares principle. In order to apply this principle one needs to specify both the observation equations and the observation weights. Much research effort has been, and is being made on the observation equations in particular for precise positioning. One may think of dealing with orbital errors and tropospheric and ionospheric delays. The observations' weight matrix has received consideraby less attention. This matrix has however a direct impact on key issues like quality control and carrier phase ambiguity validation. The choice of the weight matrix is optimal when it equals the inverse of the variance-covariance matrix of the observations. In that case the balance between the relative weights is such that the best possible precision is obtained for the computed least-squares solution. In order to specify the vc-matrix adequately, one needs to know the stochastic properties of the actual data. It is the purpose of this contribution to discuss the relevant issues and to show which factors may contribute to the variance-covariance components of GPS data. To this end the noise characteristics of GPS pseudorange and carrier phase data of (high end) dual frequency receivers are analyzed. Contributing factors that will be dealt with in the analysis are respectively, zero mean departure of residuals, satellite elevation dependence of observation noise, cross-correlation between observation types (between frequencies and between pseudorange and carrier phase), and finally time correlation. The results show that data taken by GPS receivers of different makes clearly possess different stochastic properties, and thus indicate that one should take care when specifying weight matrices for ones application.
Published in:	Proceedings of the 1999 National Technical Meeting of The Institute of Navigation January 25 - 27, 1999 Catamaran Resort Hotel San Diego, CA
Pages:	219 - 227
Cite this article:	Tiberius, C.C.J.M., "The GPS data weight matrix: what are the issues?," Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 1999, pp. 219-227.
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