Multi-GNSS inter-system model for complex environments based on optimal state estimation

Abstract

With calibrating the inter-system biases (ISB), especially the fractional part of inter-system phase biases (F-ISPB), multi-GNSS inter-system model can effectively improve the positioning performance under complex environment. Usually the F-ISPB is estimated after fixing the intra-system ambiguities. However, this approach seems inapplicable when it difficult to obtain intra-system ambiguities under complex environment. A multi-dimensional particle filter (PF) based F-ISPB estimate method have 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 method. Two baselines were selected to investigate the F-ISPB estimate performance in both open and complex environments. The results shown that due to the wrong F-ISPB may bring about maximum ratio for a long time during initial stage, the step-by-step PF method can achieve better performance than step-by-step PSO. Besides, the two-dimensional results shown 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 cost too much to get the right value. For example, in the two-dimensional case, the step-by-step PF search 200 times for each epoch, while the two-dimensional PF needs 40000 times for each epoch, 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 scenarios. Thus, under challenging observation scenarios, a step-by-step PF method is recommended to extract the F-ISPB.