Explicit estimation-error-probability computation and sensor design for flag Hidden Markov Models

Hidden Markov Models (HMM) are used in a number of sensor networking applications. These applications often require performance evaluation and sensor design for HMM estimation algorithms. This article approaches the performance evaluation and design problems from a structural perspective. Specifically, for a special class of flag HMMs (where sensors accurately flag a subset of states), explicit formulae are derived for the average error probability of the maximum-likelihood estimate. These formulae are used to optimally place sensors, and to gain an understanding of the relationship between the HMMs structure and estimation error. Three examples, including a real-world case study on monitoring the elderly in a smart home, are presented.