ON THE REALISTIC STOCHASTIC MODEL OF GPS OBSERVABLES: IMPLEMENTATION AND PERFORMANCE

Abstract. High-precision GPS positioning requires a realistic stochastic model of observables. A realistic GPS stochastic model of observables should take into account different variances for different observation types, correlations among different observables, the satellite elevation dependence of observables precision, and the temporal correlation of observables. Least-squares variance component estimation (LS-VCE) is applied to GPS observables using the geometry-based observation model (GBOM). To model the satellite elevation dependent of GPS observables precision, an exponential model depending on the elevation angles of the satellites are also employed. Temporal correlation of the GPS observables is modelled by using a first-order autoregressive noise model. An important step in the high-precision GPS positioning is double difference integer ambiguity resolution (IAR). The fraction or percentage of success among a number of integer ambiguity fixing is called the success rate. A realistic estimation of the GNSS observables covariance matrix plays an important role in the IAR. We consider the ambiguity resolution success rate for two cases, namely a nominal and a realistic stochastic model of the GPS observables using two GPS data sets collected by the Trimble R8 receiver. The results confirm that applying a more realistic stochastic model can significantly improve the IAR success rate on individual frequencies, either on L1 or on L2. An improvement of 20% was achieved to the empirical success rate results. The results also indicate that introducing the realistic stochastic model leads to a larger standard deviation for the baseline components by a factor of about 2.6 on the data sets considered.