Performance analysis of familiar elevation-dependent stochastic models with error variance compensation and posteriori unit weight in GPS/BDS precise point positioning

With global networking of BeiDou Navigation Satellite System (BDS) in July 2020, multi-constellation Precise Point Positioning (PPP) with Global Positioning System (GPS) and BDS has become a more accurate global positioning technique. In multi-constellation PPP, a suitable stochastic model can accurately describe observation noises of different satellites to help estimate accurate positioning parameters. To balance the unit weight between GPS and BDS, the posteriori unit weight is adopted between GPS and BDS constellation by using least-squares variance component estimator (LS-VCE). Under the error variance compensation and posteriori unit weight, the positioning performances of stochastic models using four familiar elevation-dependent functions are compared in terms of obtaining small positioning error and convergence with the GPS and BDS constellations. The positioning experiments were conducted to verify the positioning performances of different elevation dependent stochastic models in multi-constellation PPP with GPS and BDS at 55 stations over an 8 day period. The results show that all stochastic models have the similar positioning accuracy and precision, the differences are sub-millimeter level. But compared with second-best stochastic models, the mean convergence time reduces by more than 4.2% and the convergence stability increases by more than 10.0% in the stochastic model using the exponential function. While its mean convergence time reduces by 10.0% and its convergence stability increases by 29.1%, compared with the worst stochastic model. The stochastic model using exponential function is the most suitable under the error variance compensation and posteriori unit weight in static PPP with GPS and BDS, compared with the other familiar elevation dependent stochastic models.