A score for correct data association in multi-target tracking

In the real-world multi-target tracking problem, there exists the possibility for many things to go wrong. Typical problems which arise include: too few tracks are formed; too many tracks are formed (false tracks); and inaccurate position, course, and speed estimates are reported. The above difficulties are often the result of incorrect allocation of data to individual tracks. Algorithms, while estimating the motion of a given target, inadvertently mix in clutter and/or measurements from another target. In order for correct allocation of data to a given track to be made, one must have an effective scoring formula; that is, some means of determining how likely a given assignment of data is. To be effective, a scoring formula must produce (on the average) a better score for correct assignments than for incorrect assignments. Information useful in the scoring process includes a priori intelligence data (such as initial target locations), models of target motion, models of the transmission channel, and expected moments of clutter for the sensor gain setting being used. Basically, the score is derived from the residuals which come out of the processing of a batch of data with the extended Kalman filter. This is used to evaluate the likelihood of potential tracks. Although the "likelihood" has an intuitive meaning, the term is used here to mean the probability density function p(??) of the track ??. The expected cost of a given assignment is derived with the theory of extremals being used to obtain the expected cost of adding a clutter point in a track. The resulting expected cost is then shown to behave in a quantitative fashion and this can be visualized from a geometric viewpoint.