A formal dynamic stochastic model for single-frequency precise point positioning constrained by global ionosphere map

Abstract

Single-frequency precise point positioning (SF-PPP), having few redundant observations, needs a long convergence time to achieve a positioning accuracy level of decimetres to centimetres. An analytic use of external ionospheric information can improve the positioning performance of SF-PPP. However, it will instead deteriorate the SF-PPP performance, if the stochastic characteristics of the ionospheric pseudo-observations are determined incorrectly. In this contribution, a method for determining a formal dynamic stochastic model is proposed for ionosphere-constrained SF-PPP using ionospheric information from global ionosphere map. First, a temporal loosening constraint is adopted for ionospheric pseudo-observations, to gradually decrease their contributions to SF-PPP solutions over time. Second, for each epoch, a search algorithm based on the principle of minimizing the standard deviation of the unit weight is used to find the optimal variances of the ionospheric pseudo-observations. Experiments based on 7d of Global Positioning System observation data from 44 Multi-Global Navigation SatelliteSystem experimental stations were carried out to validate the proposed stochastic model, using positioning performance and tropospheric delay retrieval. The results indicate that ionosphere-constrained SF-PPP with a conventional stochastic model exhibits little improvement and even worse positioning performance, compared to traditional ionosphere-free-half (IFH) SF-PPP. Nevertheless, ionosphere-constrained SF-PPP with the proposed stochastic model significantly improves positioning performance, compared with IFH SF-PPP. The use of the proposed model can reduce the convergence time by 89.2%, 34.2%, and 0.0% in the static mode and 57.3%, 50.6%, and 24.1% in the kinematic mode for the east, north, and up directions, respectively, and increase the positioning accuracy by 41.1%, 29.6%, and 23.7% in the static mode and 45.5%, 38.4%, and 30.6% in the kinematic mode for the three directions, respectively. For tropospheric-delay retrieval, the zenith total-delay-estimation accuracy of ionosphere-constrained SF-PPP with the conventional stochastic model is much poorer than that of IFH SF-PPP, while that of the ionosphere-constrained SF-PPP with the proposed stochastic model is comparable to IFH SF-PPP.