State Space Approach for Precise Real Time Positioning in GPS Reference Networks

Gerhard Wübbena，Stefan Willgalis
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Overview – Networks of GPS reference stations are set up to provide carrier phase corrections for precise real time positioning for an increasing number of applications ranging from legal and geodetic control surveys to geodynamics and hydrography. To exploit the potential of real time multistation positioning the parameterisation of GPS errors in the state space domain is applied. If the state of each GPS error component can be modelled the estimation of ambiguities will be faster and more reliable even over longer interstation distances. Most important is the individual modelling of the three distance dependent error components orbit, ionosphere, and troposphere. For the state space approach the use of undifferenced observations is recommended, since this allows the estimation of clock parameters as well as the separation of error components. It also makes the modelling of error processes easier compared to approaches based on double differences.
Since the current RTCM standard allows only for carrier phase corrections in the observation domain, the state vector needs to be represented by a simplified model, e.g. Area Correction Parameters (FKP) or Virtual Reference Stations (VRS). Both representations yield comparable results. The use of either methods merely depends on the communication infrastructure between the mobile user and the GPS reference network service provider. For the future it should be accomplished to transmit the state parameters to the mobile user, who is then enabled to operate in an absolute positioning mode. The behaviour of network coefficients is analysed. Selected positioning results of measurements within the reference network of Lower Saxony, Northern Germany, are presented.