Bayesian estimation for jump Markov linear systems with non-homogeneous transition probabilities |
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| Authors: | Shunyi Zhao Fei Liu |
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| Institution: | 1. Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;2. Computer, Electrical and Mathematical Science & Engineering Department, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;1. Beijing Engineering Research Center of Industrial Spectrum Imaging, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Department of Automation, TNList, Tsinghua University, Beijing 100084, China;1. College of Computer Science, Chongqing University, Chongqing 400044, China;2. School of Industrial and Systems Engineering, Georgia Institute of Technology, AT 30332, USA;1. Faculty of Electrical Engineering, University of Montenegro, 81000 Podgorica, Montenegro |
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| Abstract: | This paper considers the state estimation problem for a class of discrete-time non-homogeneous jump Markov linear systems (JMLSs), where the transition probability matrix (TPM) is assumed to be time-variant and takes value in a finite set randomly at each time step. To show the simplicity brought by the finite-valued hypothesis, the optimal recursion for the posterior TPM probability density functions conditioned on that the TPM belongs to a continuous set is firstly derived. Then, we naturally incorporate the proposed TPM estimation into the recursion of system state. Two interacting multiple-model (IMM)-type approximation stages are employed to avoid the exponential computational requirements. The resulting filter reduces to the IMM filter when the number of candidate TPMs is unity. A meaningful example is presented to illustrate the effectiveness of our method. |
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