Problem Formulation

In this section we introduce the tracking problem, and we develop notation required to describe the Bayesian estimation approach and the trellis structure upon which the proposed generalized Viterbi algorithm is based.

In the Radar multitarget surveillance problem, the objective is to track multiple target trajectories over time. At each measurement time, measurements are provided from multiple target detections. The measurements for each detection consist of a set of D estimated location and/or velocity parameters. We assume that K, the number of targets, is unknown and constant over the processing time. Detections can correspond to either targets or false alarms. Missed detections will be accounted for. The probability of detection P_d is assumed known, as is the density function for the number of false alarms in the surveillance volume per measurement time. The problem we address here is to estimate K, as ${\hat K}$, while associating the measurements into ${\hat K}$ tracks. The algorithm proposed here, is sequential in that at each measurement time m an estimate ${\hat K}$ and ${\hat K}$ tracks (up to time m) are computed utilizing results from computations of estimates at previous times.

We denote as ${\bf z}_{m,j}$ the j^th the 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.