Filtering and parameter estimation for a class of Hidden Markov Models with application to bubble-counting in microfluidics

Motivated by a practical problem, in this work we investigate the problem of simultaneous estimation of state and parameters of an Hidden Markov Model with a particular structure. The motivating application is the problem of automatic counting of bubbles or droplets flowing into a microfluidic channel, where the noisy output of a photodiode has to be processed in order to detect the transit of bubbles. The goal is achieved through the recursive computation of a pseudo-max-likelihood estimate.