Effectiveness of the likelihood function in logic-based track formation

A logic-based track formation procedure was presented by C.B. Chang et al. (1984). In addition to the conventional gating logic, it utilized the negative log-likelihood function (goodness of fit or sum of residuals) to further reduce the false track acceptance probability. An analytical technique for the evaluation of the effectiveness of this reduction is presented. The exact solution in closed form and a Gaussian approximation are given and compared. It is shown that the goodness of fit provides an additional reduction of the false track acceptance probability by a factor of two to three