Hello, in the context of estimating the state of a Markovian switching or hybrid system, filtering and smoothing have the same meanings they usually do in state estimation. Filtering is the estimation of the state (continuous for dynamical state and discrete for the Markov chain state) based on the current and previous measurements. Smoothing is the estimation of the state given all measurements, past and previous. Smoothing can be formulated in at least 3 ways: fixed point, fixed lag and fixed interval. For definitions of these terms, please refer to a textbook like Optimal Filtering (Anderson & Moore). For a coverage of some aspects of hybrid systems, particularly for manoeuvring target tracking where they are frequently used, please refer to:

Technical Report A Survey of Manoeuvring Target Tracking Methods

If you find this answer useful, please recommend.

Thanks for the valuable answer

Komal Jindal ,

Filtering and Smoothing are basically inference problems that ask about the probability of one or more of the latent variables, given the model's parameters and a sequence of observations

Filtering in Hidden Markov Model is the task to compute, given the model's parameters and a sequence of observations, the distribution over hidden states of the last latent variable at the end of the sequence.

Smoothing is somewhat similar to filtering but asks about the distribution of a latent variable somewhere in the middle of a sequence.

Sourangshu Ghosh,

Thanks for the answer