Discussion
Which situation defeats the Kalman filter's assumptions?
Answer: A
A Gaussian has one mode, so a belief that is genuinely split between two possibilities cannot be represented at all, which is the classic case for particle filtering. High dimension is expensive but tractable, irregular timing is handled by adjusting the transition, and large noise merely widens the covariance. Identifying the failure as representational rather than computational is what makes the choice of filter principled.
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