A Sequential Monte Carlo framework for the system identification of jump Markov state space models

We propose a Maximum Likelihood-based method that combines the Expectation Maximization algorithm with Sequential Monte Carlo methods to estimate fixed parameters and transition probabilities for a general class of nonlinear jump Markov systems in state space form. This method is an extension to a previous method originally proposed by T. B. Schön, A. Wills, and B. Ninness for identifying the parameters of a class of nonlinear systems that are not dependent on a Markov chain. In this work, we detail an extension of this method to jump Markov systems and illustrate it through its application to identifying the parameters of the logistic map driven by white Gaussian noise with variance governed by a discrete Markov process.