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Title: Higher order sigma point filter: A new heuristic for nonlinear time series filtering
Authors: Ponomareva, K
Date, P
Keywords: Moment matching;Nonlinear time series;Sigma point filters;State estimation
Issue Date: 2013
Citation: Applied Mathematics and Computation, 221: 662 - 671, (15 September 2013)
Abstract: In this paper we present some new results related to the higher order sigma point filter (HOSPoF), introduced in [1] for filtering nonlinear multivariate time series. This paper makes two distinct contributions. Firstly, we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector, a specified covariance matrix, the average of specified marginal skewness and the average of specified marginal kurtosis. Both the sigma points and the probability weights are given in closed-form and no numerical optimization is required. Combined with HOSPoF, this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments. A numerical example on nonlinear, multivariate time series involving real financial market data demonstrates the utility of this new algorithm. Secondly, we show that HOSPoF achieves a higher order estimation accuracy as compared to UKF for smooth scalar nonlinearities. We believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications.
ISSN: 0096-3003
Appears in Collections:Dept of Mathematics Research Papers

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