The special feature of the interacting multiple model (IMM) estimator that distinguishes it from other suboptimal multiple model (MM) estimators is the “mixing/interaction” between its “mode-matched” base state filtering modules at the beginning of each cycle. This note shows that the same feature is exactly what it has in common with the optimal estimator for hybrid (MM) systems and this can be seen as the main reason for its success.@en

The reversion in time of a stochastic difference equation in a hybrid space with a Markovian solution is presented. The reversion is obtained by a Martingale approach, which previously led to reverse time forms for stochastic equations with Gauss-Markov or diffusion solutions. The reverse time equations follow from a particular noncanonical Martingale decomposition, while the reverse time equations for Gauss-Markov and diffusion solutions followed from the canonical Martingale decomposition. The need for this noncanonical decomposition stems from the hybrid state space situation. Moreover, the non-
Gaussian discrete time situation leads to reverse time equations that incorporate a Bayesian estimation step. The latter step is carried out for linear systems with Markovian switching coefficients, and the result is shown to provide the solution to the problem of fixed-interval smoothing. For an application of this smoothing approach to a trajectory with sudden maneuvers, simulation results are given to illustrate the practical use of the reverse time equations obtained.@en

WO maneuvering target tracking techniques are compared in this note. The first, called input estimation, models the maneuver as constant unknown input, estimates its magnitude and onset time and then corrects accordingly the state estimate. The second models the maneuver as a switching of the target state model, where the various state models can be of different dimension and driven by process noises of different intensities, and estimates the stale according to the interacting multiple model (IMM) algorithm While the first requires around 20 parallel filters, it is shown how the latter, implemented in the form of the IMM, performs equally or better with 2 or 3 fillers.@en

An important problem in filtering for linear systems with Markovian switching coefficients (dynamic multiple model systems) is the one of management of hypotheses, which is necessary to limit the computational requirements. A novel approach to hypotheses merging is presented for this problem. The novelty lies in the timing of hypotheses merging. When applied to the problem of filtering for a linear system with Markovian coefficients this yields an elegant way to derive the interacting multiple model (IMM) algorithm. Evaluation of the IMM algorithm makes it clear that it performs very well at a relatively low computational load. These results imply a significant change in the state of the art of approximate Bayesian filtering for systems with Markovian coefficients.@en