An approach for computing approximate bounds of estimator time-lag for a typical homing PN guidance loop

The present paper proposes a scheme to compute the allowable bounds of time-lag of an estimator, indispensable in a typical homing guidance loop for ballistic target interception. The stringent specifications of miss distance can be achieved by employing an estimator which can adapt itself with the time varying bandwidth requirement of the guidance loop. However, the time-lag incurred in this process should be within a tolerable bound to avoid instability in the loop manifested in terms of unacceptably large miss. In available literature, no reference is found which provides an insight regarding the tolerable bounds of the estimator in loop or any method to compute such bounds. This paper attempts to provide the filter designer an idea of the time-varying bounds of time-lag of a first-order estimator from the stability point of view of the guidance loop. It has been established by Lipschitz formulation that the nonlinearities in the loop are restricted by the bounds of estimator time-lag. The analysis yields a time-varying bound of the estimator time-lag beyond which the loop becomes destabilized. These results are corroborated with numerical simulation.