Optimization of a Generalized Velocity-Inertial System

In this paper the variational calculus techniques of the Wiener-Kolmogoroff optimum filter theory are employed to develop the statistically optimum form of a generalized hybrid velocity-inertial system. A velocity-inertial system is considered which is general in both form and application. The form of the system encompasses pure inertial, pure Doppler, and a large family of Doppler- inertial hybrid systems including the present-day second-and thirdorder Doppler inertial navigation and stabilization systems. The system may be used for a wide range of applications including any linear combination of acceleration, velocity, or vertical-reference sensing. The general system form is developed by employing an unspecified filter to mix the inertially derived signal with the signal from the auxiliary velocity sensor. As a result of utilizing this general system form, a single general error equation is found which represents the system error for each of the above system forms and applications. Using a linear analysis and the minimum mean-square error criteria, an optimum system form is found for the complete range of possible system applications.