STATISTICAL ESTIMATION IN INERTIAL NAVIGATION SYSTEMS

Abstract

Although navigation systems have generally been developed by solving exactly the dynamic equations of motion, in reality the navigation problem is a statistical one since there are unpredictable errors in the measurements. The advent of very powerful navigation computers makes it possible by using statistical filtering techniques to retrieve more of the information contained in the navigation measurements. The navigation system is thus developed here as an information-filtering problem rather than a simulation of a deterministic physical system. The Kalman optimum linear filter is found to apply to the navigation problem if some technique is used to account for possible non-Gaussian maneuver accelerations. A major problem in the application of statistical techniques is the tremendous amount of computation required. Two methods are suggested which greatly reduce the amount of computation with a minimum degradation in the performance of the system. In one method, physical considerations are used to divide the total filter into smaller, simpler filters. In the other method, the optimum gains are precomputed and approximated by simple functions in the flight computer. The details are given for the alignment and calibration of an inertial platform using statistical filtering.