A novel system identification algorithm for nonlinear Markov jump system

Abstract

System identification of nonlinear Markov jump systems (NMJSs) is crucial in modeling complex systems that contain unknown continuous and discrete states. In this system, the dynamics of continuous states is governed by the discrete states, which means the system can operate among different modes. The existing studies primarily identify the mode transition probability and noise model, whereas the parameters concerning the nonlinear continuous state transition function and observation function are commonly not considered. To identify all the parameters, a novel NMJSs identification algorithm based on a new particle system is proposed. The hidden state inference is implemented via an extended smoother that embodies the new particle system and Rao-Blackwellized particle Gibbs ancestor sampling kernel. The smoother not only estimates hidden state but also enables parameter update of the nonlinear functions. After inferencing the hidden states’ posterior density, a log-likelihood-based loss function is utilized to reduce the uncertainty of identifying the parameters related to the continuous state transition function. Then expectation–maximization and gradient descent are adopted to update the parameters. Finally, different experiments are conducted to verify the proposed algorithm. The results show that the proposed algorithm can approximate the parameter that well describes the data, and outperform other related approaches.