While implementing an Interacting Multiple Model tracking filter with one model being a constant turn rate model, I began questioning how the mix should behave while taking into account that some models are constrained.

For example, with three models - constant velocity CV, constant acceleration CA, and constant turn rate CTR, its clear that the acceleration is never mixed into the CV model state because that is a constrained model with acceleration being constrained to zero.

When it comes to the CTR model, I have acceleration constrained to be orthogonal to the velocity [as in Models and Algorithms for Target Tracking with Coordinated Turn Motion by Yuan, Lian, and Han]. One case considered there uses the kinematic constraint f a pseudo-measurement that forces a treatment of the non-orthogonal acceleration as an error in the innovation term of a Kalman filter.

So this leaves me wondering why I would want to update the CTR mixture in an IMM with any non-orthogonal acceleration term from any of the models. I'd like to see if anyone else has dealt with this, and what direction did you take. How was the non-orthogonal mix handled and how was the covariance matrix adjusted?


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