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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. |
URI: | http://www.sciencedirect.com/science/article/pii/S0096300313007339 http://bura.brunel.ac.uk/handle/2438/10046 |
DOI: | http://dx.doi.org/10.1016/j.amc.2013.06.084 |
ISSN: | 0096-3003 |
Appears in Collections: | Dept of Mathematics Research Papers |
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