EE 381K-6 Estimation Theory

Optimality of Kalman filter in linear dynamical systems with Gaussian inputs:

Richard J. Meinhold and Singpurwalla N. D., "Understanding the Kalman-Filter," The American Statistician, May 1983, 37, 2, 123-127.

M. Welling, "The Kalman Filter," class notes.

T. P. Minka, "From Hidden Markov Models to Linear Dynamical Systems," MIT Technical Report TR#531, 2000. (See Section 3).

Particle filtering tutorials:

P. Djuric et. al., "Particle Filtering",IEEE Signal Processing Magazine, vol. 20, no. 5, September 2003, pp: 19-38.

S. Arulampalam et. al., "A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking," IEEE Transactions on Signal Processing, vol. 50, no.2, February 2002, pp. 174-188.

On Cramer-Rao lower bound:

D. Johnson, "Cramer-Rao Bound," brief tutorial on cnx.org, 2003.

Markov Chain Monte Carlo (MCMC):

B. Walsh, "Markov Chain Monte Carlo and Gibbs Sampling,"Lecture notes, 2004.

P. Djuric et. al., "Perfect Sampling: A Review and Applications to Signal Processing,"IEEE Transactions on Signal Processing, vol. 50, no. 2, February 2002, pp. 345-356.

Expectation-maximization algorithm:

S. Borman, "The expectation-maximization algorithm: A short tutorial."

Arthur P Dempster, Nan M Laird and Donald B Rubin, "Maximum likelihood from incomplete data via the EM algorithm," Journal of the Royal Statistical Society. Series B (Methodological), Vol. 39, No. 1. (1977), pp.1-38

Unscented Kalman filter:

S. J. Julier and J. K. Uhlmann, "A new extension of the Kalman filter to nonlinear systems."

E. A. Wan and R. Van Der Merwe, "The unscented Kalman filter."

Further links:
Sequential Monte Carlo Methods (at Cambridge University).