Modeling Pseudo Range Multipath As An Autoregressive Process

Peter F. de Bakker

Abstract:	When modeling a physical process, one can choose to treat certain parameters in a functional or in a stochastic manner. In this contribution we will investigate multipath on GNSS pseudo range measurements as a stochastic process in the measurement domain. Multi frequency data collected with static receivers are used to form the multipath linear combinations. These time series are known to have strong time correlation at 1 Hz and in this contribution it will be shown that they can be modeled by a low order autoregressive (AR) process. To this end we will estimate the AR parameters with a least-squares adjustment and test the estimates for significance. The purpose is to characterize the multipath environment, the multipath properties of the GNSS receiver and antenna, and the quality of the resulting pseudo range measurements. Another useful application of the estimated models is the simulation of realistic artificial multipath time series, which can e.g. be used in a GNSS (software) simulator. Furthermore, the models may play a role in integrity monitoring to detect multipath errors on the GNSS measurements, and can be used in GNSS position filter algorithms to improve on the common white-noise treatment of multipath, by extending the state vector with additional entries. The estimated autoregressive parameters differ for each of the measured GNSS signals and receivers. For the two receivers considered in this paper the following trends were visible for all available signals: The estimated AR(1) parameter is significant to a very high level for almost all of the considered multipath time series, which indicates time correlation of these multipath time series. Estimation of an AR(1) model significantly reduces the least squares residuals compared to a white noise model (especially for low satellite elevation angles). This shows that an AR(1) model fits the multipath time series much better than does a white noise model. With increasing order the estimated AR parameters decrease in magnitude and become less significant. Also the reduction of the residuals is much less pronounced in each step.
Published in:	Proceedings of the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2011) September 20 - 23, 2011 Oregon Convention Center, Portland, Oregon Portland, OR
Pages:	1737 - 1750
Cite this article:	de Bakker, Peter F., "Modeling Pseudo Range Multipath As An Autoregressive Process," Proceedings of the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 1737-1750.
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