Optimal allocation of tracking pulses for an array radar

The problem of assigning pulses of an array radar which is engaged in tracking a possibly large number of targets simultaneously is discussed. It is assumed that the various targets may follow different trajectories and that the tracks are initiated and completed at possibly different times in each case. An arbitrary but known configuration of targets is treated. The problem is first formulated as a discrete-time dynamic optimization problem with constraints. The applicability of the discrete-time maximum principle to this problem is established, and necessary conditions for optimality are derived. This results in a set of coupled matrix two-point boundary value problems. An algorithm is then suggested for the solution of these equations. Several examples are included to illustrate the application of the results.