Statistical filter theory for time-varying systems

The guidance and control accuracy of most aerodynamic and space vehicles is limited primarily by the noise disturbances which enter the guidance system. Present theory for the minimization of these noise effects does not take into account the forced kinematic time variations, such as is due to time-varying range, which occur in most guidance problems. Such time variations occur in interplanetary flight, satellite rendezvous, interception of missiles or bombers, and so forth. In this paper an analytical approach is presented for the optimization of systems which are forced both to be time varying and to operate with inputs contaminated with noise. Two objectives are the establishment of the theoretical optimum performance and a method of synthesizing the optimum control system. Effects of restrictions on the capability of the output element in addition to the noise and the forced time variation are considered. Although an exact analytical solution of the problem does not appear feasible, it is shown how approximate solutions utilizing time-varying control systems can be found. The method is illustrated by a hypothetical example of a homing missile attacking a bomber.