Kalman Filtering: Theory and Practice with MATLAB — Grewal & Andrews

Mohinder S. Grewal & Angus P. Andrews, 4th Edition (IEEE Press / Wiley)

The standard bridge from estimation theory to running code. Linear dynamic systems and random processes, the discrete and continuous Kalman filter as the recursive minimum-mean-square-error estimator, the nonlinear extensions (extended and unscented Kalman filters), and — crucially for firmware — the numerical side: square-root and factorized implementations, observability/controllability, and the practical failure modes (divergence, ill-conditioning, tuning \(Q\) and \(R\)). The recursive, real-time counterpart to the Wiener filter, and the foundation of sensor fusion and state estimation on embedded targets.

Worked in Course 1 — Section 14, the optimal-estimation capstone of the signal-processing phase, where the probability and linear algebra of the earlier sections (Gaussian conditioning / MMSE estimation, least squares, conditioning) converge on the recursive Kalman filter. Chosen because every chapter carries a problem set; problems are worked by hand.

Used in Course 2 — the theory behind the real-time Kalman-filter / state-estimation lab (6.6), and the estimation-theory companion to the noise-floor/PSD and Wiener-filter labs.

Chapters

Notes and worked problems added as I work through each chapter.