© 1993

Nonlinear Filters

Estimation and Applications


Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 400)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Hisashi Tanizaki
    Pages 1-13
  3. Hisashi Tanizaki
    Pages 14-34
  4. Hisashi Tanizaki
    Pages 185-197
  5. Back Matter
    Pages 198-203

About this book


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.


Kalman Filter Nichtlineare Filter Nonlineare Filter Normal Transit econometrics estimator filtering integration measurement programming simulation Ökonom Ökonometrie

Authors and affiliations

  1. 1.Department of EconomicsKobe-Gakuin UniversityNishi-ku, KobeJapan

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