Abstract
A novel fast Kalman filtering algorithm according to the polytopic linear differential inclusion (PLDI) was proposed in this paper to improve the real-time performance of positioning algorithms, and reduce the complexity of online programming in multi-mode satellite navigation systems (MSNS). Firstly, it is proved that the error system of a multi-mode satellite navigation system can be described by a PLDI system model, based on which the tensor product (TP) model transformation method is then used to transform the error system into a PLDI system. Then, linear filtering is performed for each PLDI vertex system, and the optimal estimation of the multi-mode satellite navigation error system is obtained by fusion of the estimates for each vertex system based on the global optimal estimation theory and data confusion method. Compared with the traditional nonlinear filtering method, the Fast Kalman Filer carries out linearization of nonlinear systems using a global linearization method, and the Jacobian matrices does not need to be updated online during filtering, which significantly reduces the complexity of online programming and computation. The effectiveness and reliability of the proposed method are verified by the simulation results, and a preferable estimate performance for the GPS/BD-2 integrated satellite navigation are obtained.
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Xu, Y., Wu, Q., Xiong, Y., Zhu, X., Wang, C., Hu, X. (2022). A Polytopic Linear Differential Inclusion-Based Novel Fast Kalman Filter for Multi-Mode Satellite Navigation Systems. In: Yan, L., Duan, H., Yu, X. (eds) Advances in Guidance, Navigation and Control . Lecture Notes in Electrical Engineering, vol 644. Springer, Singapore. https://doi.org/10.1007/978-981-15-8155-7_218
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DOI: https://doi.org/10.1007/978-981-15-8155-7_218
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