Analytic study of biased proportional navigation

Proportional navigation has proved to be a useful guidance technique in several surface-to-air and air-to-air missile systems for interception of airborne targets. An analytic study of the biased proportional navigation with varying closing speed and maneuvering target is presented in this article. A specific target maneuver is considered that is proportional to the closing rate for effective escape during intercept period. The closed-form solutions are completely derived, and some important characteristics related to the system performance are discussed. The effects of the bias factor and target escape factor on the capture criterion and cumulative velocity increment are investigated in detail. In this scheme, the line-of-sight rate approaches a nonzero value, which is beyond the dead-zone of the system. But intercept still can be achieved with a cost of additional energy, and the capture area will be decreased due to the effect of bias.