Tracking with text-based messages

A fuzzy MHT algorithm applied to text-based information tracking

“…Hypothesis , i.e., the th hypothesis that includes the observations , is built by means of appropriately appending some permutation, , of the new measurements to the hypothesis from the previous time. Thus (1) Let denote the set of measurements until time instant ; it consists of (2) The goal is to obtain (3) that is, to calculate the probability of the th active hypothesis after associating the observations collected until time instant . Using Bayes rule, this probability can be shown to be proportional to the product of the following three probabilities (4) The last term of this equation is the probability of the parent hypothesis and is, therefore, available from the previous iteration.…”

“…The first factor of equation (4) is directly used since vehicle dynamics are assumed known; the third factor does not need any change either; the second factor, on the other hand, is understood as a vehicle compatibility measurement, i.e., how likely it is that an observer reports a car for example and the association is made to a track in which the vehicle is, possibly, different from a car (a jeep, a small van or others). The authors demonstrated in [1] that an MHT-like algorithm so built, will eventually reach a correct solution in a worst case scenario under a very mild condition, specifically, provided that the probability of reporting vehicle when vehicle is the actual vehicle is greater than the probability of reporting any other type of vehicle with .…”

“…TEXTTRACK, described in [1], is a software system whose goals are to apply advanced signal processing tracking concepts to natural language processing. TEXTTRACK addresses the problems of correlating and tracking observations of multiple moving vehicles reported by natural language messages that are generated by multiple observers asynchronously over time.…”

“…Since the purpose is to model natural language ambiguity, linguistic variables (i.e., computing with words in Zadeh's terminology [24]) are a natural choice for this purpose. However, [1] does not include a rigorous analytical study of the TEXTTRACK system. That work presented an intuitive argument for the system's effectiveness and was illustrated with several working examples.…”

“…In this paper, we give the fuzzy MHT algorithm originally developed in [1] a solid theoretical foundation by analytically characterizing the FIE on which the algorithm is based. Due to the fact that its mathematical characterization is application-independent, a natural byproduct of this paper is the broadening of the range of possible applications of the text-based MHT philosophy.…”