Multitarget Tracking Problem

At each measurement time, noisy measurements are provided from multiple target detections. The measurements for each detection consist of a set of D estimated location and/or velocity parameters. Detections can correspond to either targets or false alarms. Missed detections will be accounted for. The probability of detection P_d will be assumed known, as will the density function for the number of false alarms per measurement time in the surveillance volume. We assume that K, the number of targets, is unknown. For theoretical development, we assume that K is constant over the processing interval. We then develop a processing algorithm for the estimation of K which allows variation of K over time.

We denote as ${\bf z}_{m,j}$ the j^th measurement vector at time m. Then, ${\bf Z}_m =\{ {\bf z}_{m,j}; j=1,2, ... , J_m \}$ is the set of J_m measurement vectors at time m, and ${\cal Z}^n = \{ {\bf Z}_1 , {\bf Z}_2 , ... , {\bf Z}_n \}$denotes the set of all measurement vectors up to time n.