Iterated Recursive Wiener Fixed-Point Smoothing and Filtering Algorithms in Discrete-Time Stochastic Systems with Nonlinear Observation Mechanism

Seiichi Nakamori

Abstract


This paper, by maximizing the conditional probability density function of the state vector given the observed values, presents discrete-time suboptimal maximum a posteriori (MAP) estimators for the nonlinear observation equation with additive white Gaussian observation noise. This paper, at first, proposes two kinds of iterated recursive Wiener extended algorithms for the fixed-point smoothing and filtering estimates. One is regarded as the Newton-Raphson algorithm, since it uses the first derivative in the Hessian with respect to the state vector, of the nonlinear observation function, and the other as the Newton’s algorithm which uses up to the second derivative in the Hessian. Secondly, this paper proposes three kinds of extended recursive Wiener fixed-point smoothing and filtering algorithms in accordance with the medium-scale Quasi-Newton line search method, the Quasi-Newton (the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS)) method and the Nelder-Mead simplex direct search method, in the relation with the MATLAB optimization toolbox respectively.

 


Keywords


Discrete-Time Stochastic Systems, Iterated Extended Recursive Wiener Estimators, Filter, Fixed-Point Smoother, Nonlinear Observation Mechanism.

Full Text:

PDF

References


Li Liang-qun, Ji Hong-bing,Luo Jun-hui, The iterated extended Kalman particle filter, International

Symposium on Communications and Information Technologies 2005 (ISCIT 2005), pp.1172-1175, 2005.

E. A. Wan and R. van der Merwe, The Unscented Kalman Filter. In Kalman Filtering and Neural Networks, chapter 7. The Unscented Kalman Filter, (62 pages), edited S. Haykin, Wiley Publishing, New York, 2001.

D. M. Himmelblau, Applied Nonlinear Programming, McGraw-Hill, New York, 1972.

S. Nakamori, Design of extended recursive Wiener fixed-point smoother and filter in discrete-time

stochastic systems, Digital Signal Processing, Vol. 17, pp.360-370, 2007.

R. E. Blahut, Digital Transmission of Information, Addison-Wesley Publishing Company, MA 1990.

A.P. Sage and J.L. Melsa, Estimation Theory with Applications to Communications and Control, McGraw-Hill,

New York, 1971.

W. H. Press, W. H. Press, S. A. Teukolsky, W. T. Vetterling and Brian P. Flannery,

Numerical Recipes in C, The Art of Scientific Computing, Second Edition, Cambridge University Press, Cambridge, 2002.

H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part 1, Wiley New York, 1968.

S. Nakamori, Recursive estimation technique of signal from output measurement data in linear discrete-time

systems, IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences, E82-A, pp. 600-607, 1995.

S. Nakamori, Reduced-order estimation technique using covariance data of observed value in linear discrete-

time systems, Digital Signal Processing, 7, pp. 55-62, 1997.

H. Akaike, Stochastic theory of minimal realization, IEEE Trans. Automatic Control, 19, pp. 667-674, 1974.

D. Simon, Optimal State Estimation Kalman, H_∞, and Nonlinear Approaches, Wiley, New York, 2006.

P. S. Maybeck, Stochastic Models, Estimation, and Control, Vol. 2, Vol. 141-2 in Mathematics in Science and Engineering, A Series of Monographs and Textbooks, Edited by R. Bellman, Academic Press, New York, 1982.


Refbacks

  • There are currently no refbacks.


Copyright © 2018 Scholars Journal of Research in Mathematics and Computer Science. All rights reserved.

ISSN: 2581-3064

For any query/support contact us at sjrmcseditor@scischolars.com, ssroscischolars@gmail.com.