ECE652: Estimation and Filtering Theory

ECE652: Estimation and Filtering Theory

Time & Location: TR 8:00pm-9:15am, Engr E206
Instructor: Ali Pezeshki, Engr C103J, Tel. 970-491-3242, {Instructor's Last Name}@engr.colostate.edu
Office Hours: TR 9:30am-10:30am

Syllabus and Course Information (PDF)

Suggested Textbook:

L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Times Series Analysis, Prentice Hall, 1991.

Papers and Reading Material:

Sufficient Statistics and Unbiased Estimation:

R. A. Fisher, "On the mathematical foundations of theoretical statistics," Philosophical Transactions of the Royal Society of London, Series A 222, pp. 309?368, 1922. [doi:10.1098/rsta.1922.0009]

S. M. Stigler, "Studies in the History of Probability and Statistics. XXXII: Laplace, Fisher and the Discovery of the Concept of Sufficiency," Biometrika, vol. 60, no. 3, pp. 439?445, Dec. 1973. [JSTOR 2334992]

E. L. Lehmann and H. Scheffé, "Completeness, similar regions, and unbiased estimation. I," Sankhy?, vol. 10, Part 4, pp. 305-340, 1950. [JSTOR 25048038]

E. L. Lehmann and H. Scheffé, "Completeness, similar regions, and unbiased estimation. II," Sankhy?, vol. 15, Part 3, pp. 219-236, 1955. [JSTOR 25048243]

D. Blackwell, "Conditional expectation and unbiased sequential estimation," Annals of Mathematical Statistics, vol. 18, no. 1, pp. 105?110, 1947. [doi:10.1214/aoms/1177730497]

Maximum Likelihood:

History

S. M. Stigler, "The epic story of maximum likelihood.” Statistical Science, vol. 22, no. 4, pp. 598-620, Nov. 2007. [arxiv]

Consistency and asymptotics:

A. Wald, "Note on the consistency of the maximum likelihood estimate," Ann. Math. Statist., vol. 20, no. 4, pp. 595-601, 1949. [article]

Estimation of Structured Covariances:

T. W. Anderson, "Statistical inference for covariance matrices with linear structure," Multivariate Analysis--II, P. R. Krishnaiah, Ed., Academic Press, NY, 1969.

J. P. Burg, D. G. Luenberger, and D. L. Wenger, "Estimation of structured covariance matrices," IEEE Proc., vol. 70, pp. 963-974, Sep. 1982.

D. R. Fuhrmann and M. I. Miller, "On the existence of positive definite maximum likelihood estimates of structured covariance matrices," IEEE Trans. Inform. Theory, vol. 34, pp. 722-729, Jul. 1988.

D. R. Fuhrmann, "Correction to "On the existence of positive-definite maximum-likelihood estimates of structured covariance matrices"," IEEE Trans. Inform. Theory, vol. 43, no. 3, pp. 1094-1096, May 1997.

Asymptotic Behavior of Bayes' Estimates:

J. Fabius, "Asymptotic behavior of Bayes' estimates," Annals of Mathematical Statistics, vol. 35, no. 2, pp. 846-856, Jun. 1964. [article]

D. A. Freedman, "On the asymptotic behavior of Bayes' estimates in the discrete case," Annals of Mathematical Statistics, vol. 34, no. 4, pp. 1386-1403, 1963. [article]

Reduced-rank Linear Filtering:

L. L. Scharf, "The SVD and reduced-rank signal processing," Signal Process., vol 25, pp. 113-133, 1991.

L. L. Scharf and J. T. Thomas, "Wiener filters in canonical coordinates for transform coding, filtering, and quantizing," IEEE Trans. Signal Process., vol. 46, pp. 647-654, Mar. 1998.

L. L. Scharf and C. T. Mullis, "Canonical coordinates and the geometry of inference, rate, and capacity," IEEE Trans. Signal Process., vol. 48, no. 3, pp. 800-808, Mar. 2000.

Y. Hua, M. Nikpour, and P. Stoica, "Optimal reduced-rank estimation and filtering," IEEE Trans. Signal Process., vol 49, pp. 457-469, Mar. 2001.

A. Pezeshki, L. L. Scharf, M. R. Azimi-Sadjadi, and Y. Hua, "Two-channel constrained least squares problems: Solutions using power methods and connections with canonical coordinates," IEEE Trans. Signal Processing, vol. 53, pp. 121-135, Jan. 2005.

Geometry of Canonical Coordinates:

M. L. Eaton, Multivariate Statistics: A Vector Space Approach, New York: Wiley, 1983, ch. 10.

L. L. Scharf and C. T. Mullis, "Canonical coordinates and the geometry of inference, rate, and capacity," IEEE Trans. Signal Process., vol. 48, no. 3, pp. 800-808, Mar. 2000.