Second Order Interacting Multiple Model Algorithm for Systems With Markovian Switching Coefficients

An important problem is the estimation of the state of a linear system with Markovian switching coefficients. In this problem, the dynamics of the system is represented by multiple models which are hypothesized to be correct. The Interacting Multiple Model (IMM) algorithm is a novel approach to merging the different model hypotheses. In the IMM algorithm, the state estimate is computed under each possible model hypothesis over the most recent sampling period with each model using a different combination of previous model-conditioned estimates. In this paper, the second order Interacting Multiple Model (IMM2) algorithm is developed for estimating the state of a linear system with Markovian switching coefficients. In the IMM2 algorithm, the state estimate is computed under each possible model hypothesis over the two most recent sampling periods with each model hypothesis using a different combination of the previous model-conditioned estimates. Simulation results are given for a target tracking example to demonstrate the performance of the IMM2 algorithm relative to that of the IMM and second order Generalized Pseudo-Bayesian algorithms.