Determination of the Transition Probabilities for the Interacting Multiple Model Probabilistic Data Association Estimator

Zvonko Radosavljević

The problem of state estimation for Markovian switching systems with an unknown transition probability matrix (TPM) of the embedded Markov chain governing the switching is presented in this paper. Under the assumption of constant TPM, an approximate recursion of the TPM’s posterior probability density function is obtained. The exponential distribution of TPM is proposed and tested with the recursive algorithm for the Minimum Mean-Square Error (MMSE) estimation. The calculated initial TPM is incorporable into a typical Interacting Multiple Model with Probabilistic Data Association (IMMPDA) estimation scheme. Moreover, simulation results of TMP-adaptive algorithms for a maneuvering target tracking is shown. The results obtained test the scenario with two aircraft: military and civilian. The simulation shows that the proposed computation method increases the target tracking efficiency. The drawback of the simulation is that only one single target is assumed. The paper reports the preliminary results of an ongoing study and further investigation is under way.

Key words: target tracking, maneuvering target, hybrid system, state estimator, transition probability, probability determination, Markov chain.