A Recursive Sparse Learning Method: Application to Jump Markov Linear Systems

This paper addresses the problem of identifying linear multi-variable models from the input-output data which is corrupted by an unknown, non-centered, and sparse vector error sequence. This problem is sometimes referred to as error correcting problem in coding theory and robust estimation problem in statistics. By taking advantage of some recent developments in sparse optimization theory, we present here a recursive approach. We then show that the proposed identification method can be adapted to estimate parameter matrices of Jump Markov Linear Systems (JMLS), that is, switched linear systems in which the discrete state sequence is a stationary Markov chain. Some numerical simulation results illustrate the potential of the new method.