Mitigating the Impact of Inaccurate State Variance-Covariance Matrix in Kalman Filtering for Real-Time PPP with Low-Cost GNSS Devices

Yan Zhang, Yang Jiang, Yang Gao

Peer Reviewed

Abstract:	Kalman filtering (KF) is widely used in real-time precise point positioning (PPP) systems. The stochastic models for the dynamic and measurement systems, however, are often inaccurately provided. As a result, they would result in incorrect, usually over optimistic state variance-covariance (SVC) matrix and subsequently a numerically unstable system. This inaccuracy, for instance, would cause the SVC matrix to become negative definite which then violates the KF principle. It further leads to degraded positioning solutions from the KF. Some improved GNSS stochastic modelling methods have been proposed but it is difficult to precisely model the measurements from low-cost GNSS devices widely employed in mass-market applications where there are signal blockages and multipath. Although alternative filtering schemes such as 2 particle filters have also been proposed, KF remains the most widely used approach due to significantly increased computational load and implementation complexity by other methods. In this study, we propose the use of SVC matrix modification approach to keep positive definiteness property of the SVC matrix in KF and subsequently improve the system stability and the positioning accuracy. We have applied and compared three methods for SVC matrix modification, including matrix reconstruction (MR), Hossein Jorjani’s (HJ) and Larry R. Schaeffer’s (LRS) methods. An experiment based on undifferenced uncombined PPP (UUPPP) with low-cost GNSS devices was conducted in suburban environments and the results indicate that the three methods have brought in an improvement of 6.8 cm (MR), 14.9 cm (HJ) and 18.2 cm (LRS), respectively, compared to the case without applying SVC matrix modification.
Published in:	Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023) September 11 - 15, 2023 Hyatt Regency Denver Denver, Colorado
Pages:	1801 - 1822
Cite this article:	Zhang, Yan, Jiang, Yang, Gao, Yang, "Mitigating the Impact of Inaccurate State Variance-Covariance Matrix in Kalman Filtering for Real-Time PPP with Low-Cost GNSS Devices," Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Denver, Colorado, September 2023, pp. 1801-1822. https://doi.org/10.33012/2023.19289
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