Nonlinear Filters
Estimation and Applications
Hisashi Tanizaki(Author)
Springer (Publisher)
Published on 5. July 1993
Book
Paperback/Softback
XII, 203 pages
978-3-540-56772-1 (ISBN)
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Description
For a nonlinear filtering problem, the most heuristic and
easiest approximation is to use the Taylor series expansion
and apply the conventional linear recursive Kalman filter
algorithm directly to the linearized nonlinear measurement
and transition equations. First, it is discussed that the
Taylor series expansion approach gives us the biased
estimators. Next, a Monte-Carlo simulation filter is
proposed, where each expectation of the nonlinear functions
is evaluated generating random draws. It is shown from
Monte-Carlo experiments that the Monte-Carlo simulation
filter yields the unbiased but inefficient estimator.
Anotherapproach to the nonlinear filtering problem is to
approximate the underlyingdensity functions of the state
vector. In this monograph, a nonlinear and nonnormal filter
is proposed by utilizing Monte-Carlo integration, in which a
recursive algorithm of the weighting functions is derived.
The densityapproximation approach gives us an
asymptotically unbiased estimator. Moreover, in terms of
programming and computational time, the nonlinear filter
using Monte-Carlo integration can be easily extended to
higher dimensional cases, compared with Kitagawa's nonlinear
filter using numericalintegration.
easiest approximation is to use the Taylor series expansion
and apply the conventional linear recursive Kalman filter
algorithm directly to the linearized nonlinear measurement
and transition equations. First, it is discussed that the
Taylor series expansion approach gives us the biased
estimators. Next, a Monte-Carlo simulation filter is
proposed, where each expectation of the nonlinear functions
is evaluated generating random draws. It is shown from
Monte-Carlo experiments that the Monte-Carlo simulation
filter yields the unbiased but inefficient estimator.
Anotherapproach to the nonlinear filtering problem is to
approximate the underlyingdensity functions of the state
vector. In this monograph, a nonlinear and nonnormal filter
is proposed by utilizing Monte-Carlo integration, in which a
recursive algorithm of the weighting functions is derived.
The densityapproximation approach gives us an
asymptotically unbiased estimator. Moreover, in terms of
programming and computational time, the nonlinear filter
using Monte-Carlo integration can be easily extended to
higher dimensional cases, compared with Kitagawa's nonlinear
filter using numericalintegration.
More details
Series
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (UK-trade)
Illustrations
12 illustrations, 36 tables
Dimensions
Height: 24.4 cm
Width: 17 cm
Weight
320 gr
ISBN-13
978-3-540-56772-1 (9783540567721)
DOI
10.1007/978-3-662-22237-9
Schweitzer Classification
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Content
1 Introduction.- 2 State-Space Model in Linear Case.- 3 Nonlinear Filters Based on Taylor Series Expansion.- 4 Nonlinear Filters Based on Density Approximation.- 5 Comparison of Nonlinear Filters: Monte-Carlo Experiments.- 6 An Application of Nonlinear Filters: Estimation of Permanent Consumption.- 7 Summary and Directions for Further Research.- References.