Elements of probability theory - random variables - Gaussian distribution - stochastic processes characterizations and properties - Gauss-Markov processes - Brownian motion process - Gauss-Markov models - Optimal estimation for discrete-time systems - fundamental theorem of estimation - optimal prediction.

Optimal filtering - Weiner approach - continuous-time Kalman Filter - properties and implementation - steady-state Kalman Filter - discrete-time Kalman Filter - implementation – sub optimal steady-state Kalman Filter - Extended Kalman Filter - practical applications.

Optimal smoothing - Optimal fixed-interval smoothing - optimal fixed-point smoothing - optimal fixed-lag smoothing - stability - performance evaluation.

Same as Reference

1. M.D.Srinath, P.K. Rajasekaran and R. Viswanathan: Statistical Signal Processing with Applications, PHI, 1996.

2. D.G.Manolakis, V.K. Ingle and S.M. Kogon: Statistical and Adaptive Signal Processing, McGraw Hill,2000.

3. S.M.Kay:Modern Spectral Estimation, Prentice Hall,1987.

4. H.V.Poor,"An Introduction to Signal Detection and Estimation",Springer,2/e,1998.

5. S.M.Kay, "Fundamentals of Statistical Signal Processing: Estimation Theory", Prentice Hall PTR,1993.

6. M.S.Grewal, A.P. Andrews, “Kalmanfiltering : Theory and Practice”, Second edition, John Wiley & Sons, 2001.

7. C.K.Chui, G. Chen, “Kalman Filtering with Real‐Time Applications”, Third edition, Springer‐Verlag,1999.

8. R.G.Brown, Y.C. Hwang, “Introduction to Random Signals and Applied Kalman Filtering”, Second edition, John Wiley & Sons, 1992.