Comparing Viterbi & Kalman Filters for Dynamic HMM

[EmmaSaunders1]

HI All,

Would someone be-able to clarify the key differences between the kalman filter (including smoothing) and Viterbi algorithm when modelling a dynamic hidden Markov chain from a results point of view.

I understand that the Viterbi algorithm will give the MAP estimate of hidden state variables given all observations, resulting in the single most likely state sequence. The kalman filter will give the individual most probable states given all observables which can be concatenated to give the most likely (in a MMSE sense) states given observations.

I am slightly confused as to which algorithm performs the best. The Viterbi algorithm is used in a discrete model, the Kalman will approach the same result as the Viterbi if the system is continuous, what if however the kalman filter you are using assumes a discrete state space but the underlying physical process is continuous?

Thanks for any help

 

[anorlunda]

It's just like anything else. How well does the discrete approximation represent the real process? You must answer that question first and foremost.

But also look at these related PF threads.
https://www.physicsforums.com/search/25857/?q=Viterbi++Kalman&o=relevance