On Parameter Mismatch for Hidden Markov Models Applied to Indoor Localization

Abstract

Hidden Markov Chains (HMCs) and, more recently, Hidden semi-Markov Chains (HsMCs) have been used by several groups of researchers to provide a model for indoor localization. A homogeneous HMC is completely determined by the state initial probability vector and the state transition probability matrix. This is also true for the HsMC provided the state duration probability is given. These parameters are often chosen heuristically but when sufficient measurement training data are available, they can be learned using the well-known Baum-Welch algorithm. Given the model parameters, approaches such as the forward-only algorithm, the forward-backwards algorithm and the Viterbi algorithm can be applied for state sequence inference under the HMC/HsMC framework. In indoor localization applications, there is often insufficient prior information to specify such parameters in advance of the application and they have to be learned from limited amounts of training data. In this paper, we endeavour to evaluate the parameter learning accuracy of the Baum-Welch algorithm using varying amounts of training data, and evaluate the influence of applying inaccurate model parameters on these typical state estimation algorithms under both the HMC and HsMC frameworks. All of the evaluations are based on received signal strength (RSS) for application to indoor localization.