Identification, Estimation, and Learning
MIT OpenCourseWare offers this graduate-level course on the mathematical foundations of system identification, estimation, and learning. Topics include least squares estimation and its convergence properties, Kalman filters, noise dynamics, function approximation through neural nets, radial basis functions, wavelets, and Volterra expansions, plus the statistical theory behind estimation: persistent excitation, asymptotic variance, central limit theorems, maximum likelihood, the Cramer-Rao lower bound, the Kullback-Leibler distance, and Akaike's information criterion. The course also covers model structure selection, system order estimation, experiment design, and model validation. Materials come from MIT's OpenCourseWare initiative and are free to access, following the CC BY-NC-SA license, with no certificate offered. The course assumes strong prior grounding in probability and linear systems and suits students building rigorous tools for estimating models from noisy data.