A fuzzy MHT algorithm applied to text-based information tracking
We carry out a detailed analysis of a fuzzy version of Reid's classical multiple hypothesis tracking (MHT) algorithm. Our fuzzy version is based on well-known fuzzy feedback systems, but the fact that the system we describe is specialized for likelihood discrimination makes this study particularly novel. We discuss several techniques for rule activation. One of them, namely the sum-product, seems particularly useful for likelihood management and its linearity makes it tractable for further analysis. Our analysis is performed in two stages: 1) we demonstrate that, with appropriately chosen rules, our system can discriminate the correct hypothesis; and 2) the steady-state behavior with a constant input is characterized analytically. This enables us to establish the optimality of the sum-product method and it also gives a simple procedure to predict the system's behavior as a function of the rule base. We believe this fact can be used to devise a simple procedure for fine-tuning the rule base according to the system designer's needs. The application driving our fuzzy MHT implementation and analysis is the tracking of natural language text-based messages. This application is used as an example throughout the paper.