Numerically stable Kalman filter implementations for estimating linear pairwise Markov models in the presence of Gaussian noise

Computational Technologies , 22(3) (2017), 45-60
http://www.ict.nsc.ru/jct/annotation/1802?l=eng

This paper studies numerical methods of Kalman filtering for vector state estimation of linear Gaussian pairwise models. The pairwise Markov model generalizes the hidden Markov model and it attracted an increasing attention in recent years. For instance, the use of the pairwise Markov models instead of hidden Markov models in segmentation problems allows for dividing the error ratio by two. This paper explores such effective state estimation methods as the square-root pairwise Kalman filtering algorithms, including their array implementations. These filtering methods and their performance are studied in detail. The new UD factorization-based pairwise Kalman filtering approach has been developed. Other filtering algorithms applicable to the linear pairwise Markov model are discussed and numerically compared to the newly developed method on two examples.