Online Bayesian Estimation of Hidden Markov Models with Unknown Transition Matrix and Applications to IEEE 802.11 Networks

Abstract

We develop online Bayesian signal processing algorithms to estimate the state and parameters of a hidden Markov model (HMM) with unknown transition matrix. The first online estimator is based on the sequential Monte Carlo (SMC) technique and uses a set of sufficient statistics to carry the information about the transition matrix. A deterministic variant of the SMC estimator is then developed, which is simpler to implement and offers superior performance. Finally, a novel approximate maximum a posteriori (MAP) algorithm is proposed. These algorithms offer a solution to the problem of estimating the number of competing terminals in an IEEE 802.11 network where better performance can be expected if the backoff parameters are adapted to the number of active users. Realistic simulations using the ns-2 network simulator are provided to demonstrate the excellent performance of the proposed estimators.