Multiple-model estimation with heterogeneous state representation

How to fuse/combine state estimates that are obtained based on different models (e.g., a CV model, a CA model, and a CT model)? This paper provides a theoretical solution to such problems and beyond. Conventional multiple-model estimation methods use models defined in a common state space. In this paper, we discuss the advantage of using heterogeneous state space for different models in the multiple-model methods and deal with the consequent difficulties. Our algorithm is built mainly based on interacting multiple-model (IMM) due to its simplicity and popularity. Extensions to some other MM estimation methods, e.g., GPBn, are straightforward. For IMM with heterogeneous state, the model-conditioned estimates are converted to a common space for mixing and fusion. The reinitialization part is formulated as an optimization problem, which has an analytical solution. Our IMM with heterogeneous state is applied to a target tracking problem in a 2-dimensional scenario. Numerical results are provided to validate our method and demonstrate its performance compared with conventional IMM filters.