Determination, separation, and tracking of an unknown time varying number of maneuvering sources by Bayes joint decision-estimation

This paper proposes a solution for the problem of determination, separation, and tracking of an unknown time-varying number of maneuvering sources based on a mixture of signals received by some omnidirectional sensors located at different places. To our knowledge, this problem has not been addressed in its full range: what has been addressed is limited to some simplified versions (e.g., with a fixed known number of sources) or with sensor arrays, which is different from our case (with omnidirectional sensors). This problem has one decision and two estimation subproblems: determine the number of sources (decision), estimate signals of different sources (separation), and estimate state vector of the sources (tracking), while the number of sources can change with time and their dynamic models are uncertain. These three subproblems are highly interrelated that solving one requires solutions of the other two. Therefore, they have to be considered jointly. Optimal Bayes joint decision and estimation (JDE) based on a generalized Bayes risk can handle such problems. However, here we have several additional difficulties, including two interrelated estimation subproblems, dynamic model uncertainty, correlated states of different sources, dependent dynamic models of different sources, nonlinearity of observation model, and two involved Markov process types (one for the number of sources and the other for the dynamic model). An approximate linear minimum mean square error estimator is derived to deal with the interrelated estimation subproblems. Having considered all the aforementioned issues, Bayes JDE required terms are derived based on a recursive calculation of some key terms. The proposed method is theoretically solid and simple for implementation. It is examined by simulations.