Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature: new computationally efficient methods are proposed for more accurately analyzing and modeling dynamic processes that are nonlinear and subject to non-Gaussian noise
Date
2007
Authors
Arasaratnam, I.
Haykin, S.
Elliott, R.
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Conference paper
Citation
Proceedings of the Institute of Electrical and Electronics Engineers (IEEE), 2007, vol.95, iss.5, pp.953-977
Statement of Responsibility
Ienkaran Arasaratnam, Simon Haykin and Robert J. Elliiott
Conference Name
IEEE Transactions on Automatic Control (1 May 2007
Abstract
In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression(SLR) through a set of Gauss–Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF)approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other nonlinear filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve nonlinear non-Gaussian filtering problems.
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© 2007 IEEE