A new signal-to-noise-ratio based stochastic model for GNSS high-precision carrier phase data processing algorithms in the presence of multipath errors
Institute of Navigation - 19th International Technical Meeting of the Satellite Division, ION GNSS 2006, 2006-9-26 ~ 2006-9-29, pp 276-285, 2006
Stochastic modelling is widely used to mitigate errors that are not completely modelled in the functional relationships used as the basis for modern GNSS phase processing algorithms. For short to medium baselines such relationships typically include corrections and/or parameters for multipath, ionospheric and tropospheric errors, and stochastic models therefore perform the role of remedying imperfections in these. Most simple stochastic models used in practice are primarily based on satellite elevation angle: as this angle decreases the weight of the measurement is decreased due to the assumption that the noise level of the functional model imperfections will increase. This generally works well for imperfections in the ionospheric and tropospheric models as the size of the total errors in both cases can be directly related to elevation angle, but imperfections in multipath error models are not always simply elevation angle dependent. This is because phase multipath errors are very sensitive to the exact satellite-reflector-antenna geometry. Even phase measurements to satellites with high elevation angles can have large multipath errors if there is a reflecting surface high above the antenna (e.g. in the case of a tall building) or if a reflector is tilted with respect to the antenna. Also changes in the satellite-reflectorantenna geometry (brought about either by antenna or satellite motion) produce cyclic rather than approximately linear changes in the size of the phase multipath error. For instance a change in the additional path length of a reflected signal of only half a wavelength (9.5cm for GPS L1) will lead to a phase shift (phase difference between the direct and reflected signals) of the same magnitude but opposite sign. Therefore, whilst elevation angle dependent stochastic models can be used to reduce the effect of ionospheric and tropospheric residuals on positioning solutions, they may not mitigate fully phase multipath errors. To counteract these problems there have been a number of investigations into the use of the signal-to-noise ratio (SNR) to drive GNSS phase processing stochastic models. This is because SNR is well-known to be correlated to multipath error. However time series plots of phase multipath errors and SNRs always show that there is an about 90° phase difference between the two, and existing methods do not take this into account leading to phase data without multipath sometimes being incorrectly down-weighted. This paper introduces and tests a new SNR-based stochastic modelling approach that does not suffer from this disadvantage. Two real data sets have been collected in well-controlled experimental sites, one in Laboratoire Central des Ponts et Chaussées (LCPC) near Nantes in France, and the other on campus of the University of Nottingham in UK. The data sets have been used to assess the performance of the proposed stochastic model in the presence of multipath errors. Positioning errors obtained with the proposed stochastic model are compared with those from standard least squares solutions. An improvement in accuracy of between 26% and 35% has been found with these data sets, with the level of improvement depending on the amplitudes and frequencies of multipath errors, and the phase coherence of SNRs and pseudorange multipath errors.