I am currently reading a lot about Kalman Filtering and am especially interested in the IMM - Interactive Multiple Model Algorithm. In the literature (e.g. here), IMM is used for Kalman Filters with state vectors of different dimensionality. For example, the paper linked above combines a constant velocity (6 dimensions) with an constant acceleration (9 dimensions) Model. When looking at the math of the IMM, this doesn't seem to make sense: mixing the state estimates consists of taking a weighted sum of the state vector of each Filter (weighted by the probability of that Filter). But if those state vectors have different dimensions, this operation doesn't make sense. The same goes for the calculation of the covariance matrix.

Does anyone here now more about IMMs and how these are implemented? Does an IMM only track the dimensions common to every Filter and does one "extract" only those when mixing state estimates?

  • $\begingroup$ Why don't you inquire with the author? Then let us know what he says. $\endgroup$ – Mark L. Stone Sep 12 '18 at 23:14

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