Biases and accuracy of, and an alternative to, discrete nonlinear filters |
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Authors: | Peiliang Xu |
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Institution: | (1) Disaster Prevention Research Institute, Kyoto University at Uji, Kyoto 611-0011, Japan e-mail: pxu@rcep.dpri.kyoto-u.ac.jp; Fax: 81 774 38 4239, JP |
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Abstract: | The biases and accuracy of the extended Kalman filter (EKF) and a second-order nonlinear filter (SONF) are discussed from
the point of view of a frequentist; these are often derived by applying the relevant conditional quantities to the linear
Kalman algorithm under the Bayesian framework. The EKF and the SONF are biased, although the SONF has been derived in the
hope of improving first-order filters. Unfortunately the biases of the SONF may be magnified further, because the second-order
terms of the relevant Bayesian conditional quantities have never been properly used to derive the SONF from the frequentist
point of view. The variance–covariance matrix of the SONF given in the literature is proven to be incorrect up to the second-order
approximation, and the correct one is derived. Finally, also from the point of view of a frequentist, an alternative, almost
unbiased SONF is proposed, if the randomness of partials is neglected.
Received: 12 July 1997 / Accepted: 5 October 1998 |
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Keywords: | , Nonlinear dynamical and nonlinear measurement system,Nonlinear filters,Bias and accuracy analysis,Almost unbiased second-order nonlinear filter |
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