ISSN:
1432-1394
Keywords:
Key words. Nonlinear dynamical and nonlinear measurement system
;
Nonlinear filters
;
Bias and accuracy analysis
;
Almost unbiased second-order nonlinear filter
Source:
Springer Online Journal Archives 1860-2000
Topics:
Architecture, Civil Engineering, Surveying
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s001900050216
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