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Multiple Quadrature Kalman Filtering

Closas, Pau and Fernández-Prades, Carles and Vilà-Valls, Jordi Multiple Quadrature Kalman Filtering. (2012) IEEE Transactions on Signal Processing, 60 (12). 6125-6137. ISSN 1053-587X

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Official URL: https://doi.org/10.1109/TSP.2012.2218811

Abstract

Bayesian filtering is a statistical approach that naturally appears in many signal processing problems. Ranging from Kalman filter to particle filters, there is a plethora of alternatives depending on model assumptions. With the exception of very few tractable cases, one has to resort to suboptimal methods due to the inability to analytically compute the Bayesian recursion in general dynamical systems. This is why it has attracted the attention of many researchers in order to develop efficient algorithms to implement it. We focus our interest into a recently developed algorithm known as the Quadrature Kalman filter (QKF). Under the Gaussian assumption, the QKF can tackle arbitrary nonlinearities by resorting to the Gauss-Hermite quadrature rules. However, its complexity increases exponentially with the state-space dimension. In this paper we study a complexity reduction technique for the QKF based on the partitioning of the state-space, referred to as the Multiple QKF. We prove that partitioning schemes can effectively be used to reduce the curse of dimensionality in the QKF. Simulation results are also provided to show that a nearly-optimal performance can be attained, while drastically reducing the computational complexity with respect to state-of-the-art algorithms that are able to deal with such nonlinear filtering problems.

Item Type:Article
HAL Id:hal-03203276
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Universitat Politècnica de Catalunya - UPC (SPAIN)
Other partners > Centre Tecnològic de Telecomunicacions de Catalunya - CTTC (SPAIN)
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Deposited On:19 Apr 2021 14:29

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