Higher order sigma point filter: A new heuristic for nonlinear time series filtering

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.

Demand uncertainty in modelling WDS: scaling laws and scenario generation

“…moments. These methods can in turn follow two different paths (Ponomareva and Date [16] and Ponomareva et al [17]). In the first path the statistical properties of the joint distribution are specified in terms of moments, usually including the covariance matrix.…”

A New Method for Generating Sigma Points and Weights for Nonlinear Filtering

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Unscented predictive variable structure filter for satellite attitude estimation with model errors when using low precision sensors

“…With a view to cope with these problems, some conventional estimation methods are the Kalman filter and its extended forms [3][4][5], the unscented Kalman filter (UKF) [6][7][8], cubature Kalman filter (CKF) [9][10] have shown to be very useful in the wide range of applications including the attitude estimation. However, the model errors in the dynamic model of attitude estimation system are treated as "process noise" according to the essential characteristics of the Kalman filter.…”