Monte Carlo Markov chain methods for tracking
Andrew R. Runnalls · 1995
Sets out the Bayesian formulation of a typical tracking problem. To keep things simple, we suppose that exactly one target is known to be present in the field of surveillance, but the same approach can be used in principle for multiple target tracking problems. The question we want to answer is: given the sequences of outputs of one or more target sensors, what is the probability distribution (conditional on these sensor data) of the various possible tracks of the target? Bayes' theorem tells us that the probability density we are interested in is given by: f(Track|Sensor data)=k×f(Sensor data|Track)×f(Track), where k is such that ∫all possible tracksf(Track|Sensor data) dTrack=1. The Bayesian approach to tracking can be summed up as follows: (1) Characterise the pattern of target motion that we expect to see by means of a probability density function f(Track); (2) Characterise the target sensor(s) by means of a conditional probability density f(Sensor data|Track). To do this, for each possible track Track, we must be able to answer the following question: if we knew the target's track was Track, but had not yet observed any data from the tracking sensors, what sequences of sensor data would we expect, and with what relative probabilities? These steps give us both of the probability densities on the right-hand side of the equation. (3) Given particular sequences of observed data from our sensors, we substitute the observed data values into the equation and solve it to obtain f(Track|Sensor data). We illustrate this approach by an example. (4 pages)