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|Title:||Higher order sigma point filter: A new heuristic for nonlinear time series filtering|
|Keywords:||Moment matching;Nonlinear time series;Sigma point filters;State estimation|
|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  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.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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