This paper considers a number of related inverse filtering problems for hidden Markov models (HMMs). In particular, given a sequence of state posteriors and the system dynamics; i) estimate the corresponding sequence of observations, ii) estimate the observation likelihoods, and iii) jointly estimate the observation likelihoods and the observation sequence. We show how to avoid a computationally expensive mixed integer linear program (MILP) by exploiting the algebraic structure of the HMM filter using simple linear algebra operations, and provide conditions for when the quantities can be uniquely reconstructed. We also propose a solution to the more general case where the posteriors are noisily observed. Finally, the proposed inverse filtering algorithms are evaluated on real-world polysomnographic data used for automatic sleep segmentation.
Robert Mattila (KTH Royal Institute of Technology)
Cristian Rojas (KTH Royal Institute of Technology)
Cristian R. Rojas was born in 1980. He received the M.S. degree in electronics engineering from the Universidad Técnica Federico Santa María, Valparaíso, Chile, in 2004, and the Ph.D. degree in electrical engineering at The University of Newcastle, NSW, Australia, in 2008. Since October 2008, he has been with the Royal Institute of Technology, Stockholm, Sweden, where he is currently an Associate Professor of the Automatic Control Lab, School of Electrical Engineering. His research interests lie in system identification and signal processing. Dr. Rojas is a member of IEEE since 2013, and of the IFAC Technical Committee TC1.1. on Modelling, Identification, and Signal Processing since 2013. He is Associate Editor for the IFAC journal Automatica and for the IEEE Control Systems Letters.