Fundamentals of Inertial Aiding

Navigation-grade inertial systems are characterized by so-called “free inertial” position error drift rates on the order of one nautical mile-per-hour of operation. Such performance implies a certain class of gyros and accelerometers and thus certain specifications on biases, scale factor errors and noise. For more than five decades, the Kalman filter has been the primary tool used to reduce inertial drift through the integration of various sensors. Specifically, the aiding sources (e.g., stellar, Doppler, GPS, etc) are used by the filter to estimate the errors in the free inertial processing. Thus, the heart of any aided-inertial Kalman filter is the inertial error model including, specifically, sensor errors. We will discuss these models and will proceed to explain how aiding source observations are then used by the filter, in conjunction with the models, to estimate the inertial errors. For example, a given aiding source may provide an independent measurement of position, yet somehow the filter is able to use this in order to estimate gyro biases in the inertial system. The daunting matrix mathematics involved in the full algorithm can be extremely intimidating to the newcomer. In this lecture, the basic concepts of estimation theory will be briefly reviewed and the Kalman Filter will be described first in terms of simple one-dimensional problems for which the full algorithm reduces to an approachable set of scalar equations. We will look at the performance of the filter in some simple case studies and by the end will have an intuitive feel for how the full filter operates. We will then apply the Kalman filter to the aiding of inertial systems. We will see how external sources of position and velocity (such as GPS) can be used first to measure inertial system error and then, with the aid of the Kalman filter, to estimate and correct inertial sensor error as well as system error.