Kalman’s paper introducing his now-famous filter was first published in 1960 , and its first practical implementation was for integrating an inertial navigator with airborne radar aboard the C5A military aircraft .
The application of interest here is quite similar. We want to integrate an onboard inertial navigator with a different electromagnetic ranging system (GPS). There are many ways to do this , but nearly all involve Kalman filtering.
The purpose of this chapter is to familiarize you with theoretical and practical aspects of Kalman filtering that are important for GPS/INS integration, and the presentation is primarily slanted toward this application. We have also included a brief derivation of the Kalman gain matrix, based on the maximum-likelihood estimation (MLE) model. Broader treatments of the Kalman filter are presented in Refs. 6, 30, 59, and 101; more basic introductions can be found in Refs. 48 and 218, more mathematically rigorous derivations can be found in Ref. 99; and more extensive coverage of the practical aspects of Kalman filtering can be found in Refs. 29 and 66.
The Kalman filter is an extremely effective and versatile procedure for combining noisy sensor outputs to estimate the state of a system with uncertain dynamics, where
The noisy sensors could be just GPS receivers and inertial navigation systems, but may also include subsystem-level sensors (e.g., GPS clocks or INS ...