Multi-Gnss Inter-System Model For Complex Environments Based On Optimal State Estimation

When calibrating inter-system biases (ISB), especially the fractional part of inter-system phase biases (F-ISPB), a multi-GNSS inter-system model can effectively improve positioning performance under a complex environment. Usually, the F-ISPB is estimated after fixing the intra-system ambiguities. However, this approach seems inapplicable when it is difficult to obtain intra-system ambiguities under a complex environment. A multi-dimensional particle filter (PF)-based F-ISPB estimate method has been proposed to overcome the problem. Nevertheless, the multi-dimensional PF involves a great quantity of computations. In this contribution, four state optimal estimate-based F-ISPB handling schemes are proposed: step-by-step PF, step-by-step particle swarm optimization (PSO), multi-dimensional PF, and multi-dimensional PSO-based F-ISPB estimate methods. Two baselines were selected to investigate the F-ISPB estimate performance in both open and complex environments. The results show that due to the potential of the wrong F-ISPB to bring about the maximum ratio for a long time during the initial stage, the step-by-step PF method can achieve better performance than step-by-step PSO. Besides, the two-dimensional results show that all of the F-ISPB still cannot be extracted under complex environments by multi-dimensional PSO. Furthermore, compared with step-by-step PF, the multi-dimensional PF method costs too much to obtain the right value. For example, in the two-dimensional case, the step-by-step PF searches 200 times for each epoch, while the two-dimensional PF requires 40 000 times for each epoch, so it is difficult for receivers to provide hardware support for this method. In addition, the step-by-step PF can obtain the right F-ISPB with about 100 epochs no matter what scenario. Thus, under challenging observation scenarios, a step-by-step PF method is recommended to extract the F-ISPB.