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On the convergence rate of the unscented transformation

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  • Kwang Ahn
  • Kung-Sik Chan

Abstract

Nonlinear state-space models driven by differential equations have been widely used in science. Their statistical inference generally requires computing the mean and covariance matrix of some nonlinear function of the state variables, which can be done in several ways. For example, such computations may be approximately done by Monte Carlo, which is rather computationally expensive. Linear approximation by the first-order Taylor expansion is a fast alternative. However, the approximation error becomes non-negligible with strongly nonlinear functions. Unscented transformation was proposed to overcome these difficulties, but it lacks theoretical justification. In this paper, we derive some theoretical properties of the unscented transformation and contrast it with the method of linear approximation. Particularly, we derive the convergence rate of the unscented transformation. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Kwang Ahn & Kung-Sik Chan, 2013. "On the convergence rate of the unscented transformation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 889-912, October.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:5:p:889-912
    DOI: 10.1007/s10463-013-0397-x
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    Cited by:

    1. Ahn, Kwang Woo & Chan, Kung-Sik, 2014. "Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 243-254.

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