Linear and nonlinear filtering

This paper provides a review of the theory of filtering for stochastic processes. In particular, the sequential theory of linear filtering is reviewed as well as the theory of nonlinear filtering.

[1]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications , 1949 .

[2]  H. W. Bode,et al.  A Simplified Derivation of Linear Least Square Smoothing and Prediction Theory , 1950, Proceedings of the IRE.

[3]  E. B. Dynkin Infinitesimal Operators of Markov Processes , 1956 .

[4]  OPTIMUM FINITE TIME FILTERS FOR A SPECIAL NONSTATIONARY CLASS OF INPUTS. , 1959 .

[5]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[6]  R. L. Stratonovich CONDITIONAL MARKOV PROCESSES , 1960 .

[7]  R. E. Kalman,et al.  On the general theory of control systems , 1959 .

[8]  Lectures on stochastic processes , 1961 .

[9]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[10]  D. Youla,et al.  On the factorization of rational matrices , 1961, IRE Trans. Inf. Theory.

[11]  W. Wonham Some applications of stochastic difierential equations to optimal nonlinear ltering , 1964 .

[12]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[13]  H. Kushner On the Differential Equations Satisfied by Conditional Probablitity Densities of Markov Processes, with Applications , 1964 .

[14]  R. Bucy Nonlinear filtering theory , 1965 .

[15]  A. Bryson,et al.  Linear filtering for time-varying systems using measurements containing colored noise , 1965 .

[16]  R. E. Odeh Studies in the theory of random processes , 1966 .

[17]  Peter L. Falb,et al.  Infinite-Dimensional Filtering: The Kalman-Bucy Filter in Hilbert Space , 1967, Inf. Control..

[18]  Jacques-Louis Lions,et al.  State Estimation for Infinite-Dimensional Systems , 1967, J. Comput. Syst. Sci..

[19]  H. Kushner Approximations to optimal nonlinear filters , 1967, IEEE Transactions on Automatic Control.

[20]  Richard S. Bucy,et al.  Optimal filtering for correlated noise , 1967 .

[21]  L. Silverman Inversion of multivariable linear systems , 1969 .

[22]  L. Silverman,et al.  Correlated noise filtering and invariant directions for the Riccati equation , 1970 .

[23]  A New Approach to Singular Discrete Time Filtering and Control , 1971 .

[24]  R. Bucy,et al.  Digital synthesis of non-linear filters , 1971 .