Consider a variation of the Kalman filter where the prior based on the previous time step is a

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Consider a variation of the Kalman filter where the prior based on the previous time step is a mixture of K Gaussians

K

P r ( w t | x 1 …t − 1 ) = , Norm w t [ µ + k , Σ + k ] .

k =1

What will happen in the subsequent measurement incorporation step? What will happen in the next time update step?