Dimitrios Psychas, Department of Geoscience and Remote Sensing, Delft University of Technology, and Fugro Innovation & Technology B.V., The Netherlands; Sandra Verhagen, Department of Geoscience and Remote Sensing, Delft University of Technology, The Netherlands

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Abstract:

Integer ambiguity resolution (IAR) at a single-receiver precise point positioning (PPP) user is feasible by providing the user, next to satellite orbits and clocks, with information about the satellite phase and code biases. With a proper application of these corrections, the user’s ambiguities can be of double-differenced form, thereby recovering their integerness. This is crucial, since successful IAR can reduce the long convergence times experienced by the PPP users. However, in the absence of precise a priori information about the ionosphere, instantaneous centimeter-level positioning is not feasible, since the relatively weak ionosphere-float model, according to which unknown slant ionospheric delays need to be parameterized, will not allow successful IAR. Through the provision of precise a priori information on the ionosphere, the user’s model can be strengthened such that successful ambiguity resolution can be achieved in a single or a few epochs. Such corrections for the ionospheric delays of the user can be estimated in real-time through a spatial interpolation of the ionospheric delays of reference stations, which are estimated in a PPP-RTK network processing. Incorporating these stochastic user-specific ionospheric corrections allows one to extend one’s ionosphere-float model to its ionosphere-weighted variant, in which the ionospheric residuals can be weighted based on the ionospheric prediction error. It is well known that the ionosphere decorrelates with increasing inter-station distance, implying that the smaller a network is, the smaller the prediction error and the stronger the model are. Based on all of the above, it is concluded that the network dimension has an impact on the performance of the ionosphere-weighted PPP-RTK user solutions, which is the main topic of our work. This study presents an analysis of the ambiguity resolution and positioning performance of a PPP-RTK user in the presence of precise ionospheric corrections from networks with varying dimension. To investigate the impact of network dimension on the user’s ambiguity-resolved solution, we processed GPS dual-frequency code and phase data from four wide-area networks with inter-station spacings ranging from about 70 to 250 km in order to generate satellite clocks, satellite phase biases and user-specific least-squares-interpolated ionospheric corrections. The distance-dependent accuracy of the ionospheric corrections was empirically evaluated based on validation stations, the ionospheric delays of which were known from an ionosphere-float PPP-RTK processing. Based on this analysis, we demonstrate the relationship that the inter-station distance has with the precision of ionospheric corrections, which was taken into account in the ionosphere-weighted variant of our user’s stochastic model. Given the network corrections and data from several single-receiver users in the networks’ coverage, we computed a multitude of kinematic positioning error samples to get representative results for the positioning accuracy and convergence time that can be achieved with the ionosphere-weighted PPP-RTK user model. At the user side we used the uncombined functional and stochastic model, and the parameter solutions were estimated in emulated real-time using a Kalman-filter-based implementation treating the receiver phase biases and integer phase ambiguities as time-invariant parameters. Our numerical results showed that sub-decimeter positioning accuracy can be achieved almost instantaneously with partial ambiguity resolution by using ionospheric information from a 70 km spaced network of four receivers. It is also demonstrated that the user’s convergence times increase linearly with increasing inter-station distance, due to ionosphere decorrelation, with the user experiencing a 7 minutes convergence time to achieve 10 cm accuracy using corrections from a 250 km spaced 4-receiver network.