GNSS Elevation-Dependent Stochastic Modeling and Its Impacts on the Statistic Testing

Only the correct stochastic model can be applied to derive the optimal parameter estimation and then realize the precision global navigation satellite system (GNSS) positioning. The key for refining the GNSS stochastic model is to establish the easy-to-use stochastic model that should capture the error characteristics adequately based on the estimated precisions from the real observations. In this paper, the authors study the GNSS elevation-dependent precision modeling and analyze its impact on the statistic testing involved in the adjustment reliability. With the zero-baseline dual-frequency Global Positioning System (GPS) data, the authors first estimate the elevation-dependent precisions and establish the stochastic models by fitting them with three predefined functions, including the unique precision function and the sine and exponential types of elevation-dependent functions. Three established models are then evaluated by their performance in the overall and w-statistic testing. The results indicated that the GNSS observation precisions are indeed elevation dependent, but this dependence differed from the observation types. The inadequate elevation-dependent model will result in the incorrect statistics and lead to larger wrong decisions, for instance, larger false alarms.