1 Introduction to estimation and filtering theory.- 1.1 Basic notions of probability theory.- 1.2 Introduction to estimation theory.- 1.3 Examples of estimation problems.- 1.4 Estimation and filtering: similarity and distinction.- 1.5 Basic notions of filtering theory.- 1.6 Appendix: Proofs of Lemmas and Theorems.- 2 Optimal filtering of stochastic processes in the context of the Wiener-Kolmogorov theory.- 2.1 Linear filtering of stochastic processes.- 2.2 Filtering of stationary processes.- 2.3 Recursive filtering.- 2.4 Linear filters maximizing a signal to noise ratio.- 2.5 Appendix: Proofs of Lemmas and Theorems.- 2.6 Bibliographical comments.- 3 Abstract optimal filtering theory.- 3.1 Random elements.- 3.2 Linear stable estimation.- 3.3 Resolution space and relative finitary transformations.- 3.4 Extended resolution space and linear transformations in it.- 3.5 Abstract version of the Wiener-Kolmogorov filtering theory.- 3.6 Optimal estimation in discrete resolution space.- 3.7 Spectral factorization.- 3.8 Optimal filter structure for discrete time case.- 3.9 Abstract Wiener problem.- 3.10 Appendix: Proofs of Lemmas and Theorems.- 3.11 Bibliographical comments.- 4 Nonlinear filtering of time series.- 4.1 Statement of nonlinear optimal filtering problem.- 4.2 Optimal filtering of conditionally Gaussian time series.- 4.3 Connection of linear and nonlinear filtering problems.- 4.4 Minimax filtering.- 4.5 Proofs of Lemmas and Theorems.- 4.6 Bibliographical comments.- References.- Notation.
