Fritz K. Brunner

An extended weight model for GPS phase observations

Low elevation data may be included in the processing of small scale engineering GPS applications, in order to improve satellite geometry and reduce the required observation time. Careful weighting of the phase observations is needed then, because of increased noise and systematic errors. The measured carrier-to-noise-power-density ratio (C/N0) has proven to be an excellent tool for the estimation of the random errors of the phase observables. In this paper an extended weight model using robust estimation is presented, in particular the Danish Method. This model combines the information inherent in C/N0 and the residuals of the double differenced phase observations in order to model random errors and signal distortion effects.

Short static GPS sessions: robust estimation results

Least-squares estimation (LS) yields results of low accuracy in the presentce of GPS phase-corrupting environmental conditions. We present a robust estimator that clearly identifies outlying observations caused by obstacles like diagonal cables, branches, or leaves. It performs significantly better than standard LS and signal-to-noise ratio dependent weighting if unfavorable signal distortion occurs, and is equal to LS otherwise. The estimator is realized by an iterated LS algorithm using an equivalent weight matrix. It is a generalization of the Danish Method to heterogeneous and correlated observations. The excellent peformance of the estimator for processing short static sessions is demonstrated using data obtained from an investigation of GPS signal obstruction.