Kalman filter versus IMM estimator: When do we need the latter?

In this paper a performance comparison between a Kalman filter and the interacting multiple model (IMM) estimator is carried out for single-target tracking. In a number of target tracking problems of various sizes, ranging from single-target tracking to tracking of about a thousand aircraft for Air Traffic Control, it has been shown that the IMM estimator performs significantly better than a Kalman filter. In spite of these studies and many others, the condition under which an IMM estimator is desirable over a single model Kalman filter has not been quantified. The limits of a single model Kalman filter versus an IMM estimator are quantified here in terms of the target maneuvering index, which is a function of target motion uncertainty, measurement uncertainty, and sensor revisit interval. Using simulation studies, it is shown that above a certain maneuvering index an IMM estimator is preferred over a Kalman filter to track the target motion. These limits should serve as a guideline in choosing the more versatile, but somewhat costlier, IMM estimator over a simpler Kalman filter.