The continuous time roots of the Interacting Multiple Model filter

The Interacting Multiple Model (IMM) filter has become a benchmarking reference in discrete time filtering of Markov jump linear systems, and one of the most popular maneuvering target tracking approaches. Although the IMM filter is typically known in discrete time setting, it has originally been developed in a pure continuous time setting in a 1982 technical report. The resulting continuous time IMM equations have subsequently guided the development of the discrete time IMM filter for Markov jump linear systems, and its application to maneuvering target tracking. This paper presents the continuous time IMM filter and shows that this reveals the interaction behavior that has become known as the key characteristic of the discrete time IMM.