Kalman Filtering
Mohinder S. Grewal, Angus P. Andrews, Chris G. Bartone · 2020
This chapter provides a working familiarity with Kalman filtering – both the theoretical and practical aspects of it. It focuses on those features essential for global navigation satellite system (GNSS) navigation, inertial navigation performance analysis and performance analysis of integrated GNSS/INS navigation. Kalman played a major role in a mid-twentieth century paradigm shift in engineering mathematics for estimation and control problems – from probability theory and spectral characteristics in the frequency domain to linear first-order differential equations in “state space” (Euclidean space) and matrix theory. The chapter presents an overview of the mathematical origins of that transformation and demonstrates the special properties of Gauss's linear least mean squares estimator that have been inherited by Kalman filtering. It discusses a method for assessing the magnitude of linearization errors. The chapter also presents some nonlinear implementations and approximation methods that have been used in Kalman filtering with relative success.