ML Estimation of Transition Probabilities in Jump Markov Systems via Convex Optimization

A popular approach to track a maneuvering target is to model it as a jump Markov system (JMS) whereby a set of models can transit from one to another according to a Markov chain with known transition probabilities (TPs). In this paper, we consider a more practical case where the transition probability matrix (TPM) is unknown. We use an approximate likelihood function of the TPM derived in [5] and determine the TPM according to the maximum likelihood (ML) criterion. Since the problem can be formulated as a convex program, it can be solved efficiently and the global solution can be obtained. However, directly solving the program will be not only time-consuming, but also will result in unreasonable solutions when the measurement information is little. To solve these problems, we first derive an approximate likelihood function of each row similar to that in [5], based on which an alternative ML formulation is proposed. Using this ML formulation, we apply greedy strategy to get the estimate. Simulation results show that the proposed method is a good tradeoff between performance and computational cost.