Endgame Guidance and Relative Navigation of Strategic Interceptors with Delays

This paper is concerned with endgame guidance and relative navigation of strategic missiles equipped with divert thrusters to intercept nonmaneuvering reentry vehicles. The paper has three objectives: 1) demonstrate superiority of predictive guidance to pulsed proportional navigation guidance; 2) devise compensation for a onesample delay in arrival of line-of-sight (LOS) angle measurements at Kalman-filter module and another one-sample delay in communication of LOS rate estimates to the guidance module; and 3) develop a Kalman filter insensitive to modeling errors for relative navigation. A hybrid Kalman filter is developed for relative navigation with angle measurements—hybrid because relative position and velocity vectors are propagated in Cartesian coordinates, whereas the error covariance is propagated, and updated at the time of measurement, in spherical coordinates. For spherical computations, a time-to-go dependent transition matrix and a time-to-go dependent process noise matrix are formulated. It is shown that these time-to-go dependent matrices reduce the miss distance and its sensitivity to modeling errors. With this Kalman filter, it is shown that the closed-loop predictive guidance yields smaller miss distance, consumes less fuel, and requires fewer divert firings than the pulsed proportional navigation guidance does. The delay compensation is accomplished in two steps: first, the high-frequency stream of ∆V measurements from an accelerometer is stored and synchronized with the delayed LOS angle measurement from the seeker; second, the delayed LOS rate estimate from the Kalman filter is propagated forward using the measured ∆V that transpires during the delay. The miss distance of the zero-delay level and robustness to modeling errors is shown to be almost recovered.