Convergence analysis of non‐linear filtering based on cubature Kalman filter
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This study analyses the stability of cubature Kalman filter (CKF) for non‐linear systems with linear measurement. The certain conditions to ensure that the estimation error of the CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Since adaptation law has a very important role in convergence, fuzzy logic is proposed to improve the versatility of the proposed adaptive noise covariance. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the modified CKF is compared to the CKF in two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF, while the MCKF is successfully able to estimate the states. In addition, the superiority of MCKF that uses fuzzy adaptation rules is shown.An outline of power quality and its analysis and detection methods is given; then basic principles of three kinds of Kalman filtering, i.e., traditional Kalman filtering, extended Kalman filtering and unscented Kalman filtering, are surveyed and the application of these methods in power quality analysis is summarized; the comparative analysis on advantages and disadvantages of these methods are performed; finally, the existing defects in Kalman filtering are pointed out and the development trend of Kalman filtering is prospected.
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An application of Kalman filtering theory in nonlinear systems is discussed.And the flaws of extended Kalman filtering applied to nonlinear systems are pointed out.On the basis of that,the Unscented filtering theory is analyzed,and the performance between the Unscented filtering and extended Kalman filtering is compared in this paper.At the last,the Unscented filtering's superiority over extended Kalman filtering is validated through an example.
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The problem of on-line calibration of dynamic traffic assignment (DTA) models is receiving increasing attention from researchers and practitioners. The problem can be formulated as a non-linear state-space model. Because of its nonlinear nature, the resulting model cannot be solved by the Kalman filter and therefore non-linear extensions need to be considered. In this paper, three extensions to the Kalman filter algorithm are presented: extended Kalman filter (EKF), limiting EKF (LimEKF), and unscented Kalman filter (UKF). The solution algorithms are applied to the calibration of the state-of-the-art DynaMIT-R DTA model and their use is demonstrated in a freeway network in Southampton, U.K. The LimEKF shows accuracy comparable to that of the best algorithm, but vastly superior computational performance
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Abstract : Contents: Linear estimation theory; Further comments on the derivation of Kalman filters; Computational techniques in Kalman filtering; Modeling errors in Kalman filters; Suboptimal Kalman filter techniques; Comparison of Kalman, Bayesian and maximum likelihood estimation techniques; Nonlinear filtering and comparison with Kalman filtering; Linear smoothing techniques (post-flight data analysis); Nonlinear smoothing techniques; General questions on Kalman filtering in navigation systems; Application of Kalman filtering theory to augmented inertial navigation systems; Application of Kalman filtering to Baro/inertial height systems; Application of Kalman filtering to the C-5 guidance and control system; Application of Kalman filtering techniques to the Apollo program; Some applications of Kalman filtering in space guidance; Application of Kalman filtering for the alighnment of carrier aircraft inertial navigation systems; Navigation at sea using the invariants form of Kalman filtering; Marine applications of Kalman filtering; Optimal use of redundant information in an inertial navigation; Application of Kalman filtering techniques to strapdown system initia-alignment; and A Kalman filter augmented marine navigation system.
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For Kalman filter-based data fusion in sensor networks, based on the weighted least squares (WLS) method, two distributed measurement fusion Kalman filtering algorithms are presented in terms of the average weighted measurements and the average inverse-covariance matrices, where the second algorithm is equivalent to the micro-Kalman filter (or μ-Kalman filter) derived from the centralized Kalman filter in sensor networks. Using the information filter, it is proved that they are functionally equivalent to the centralized fusion Kalman filtering algorithm, i.e. they give the Kalman estimators which are numerically identical to the centralized Kalman estimators. They not only have the global optimality, and but also can reduce the computational burden. Two numerical simulation examples verify their functional equivalence.
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In general conditions, Kalman filtering technique has been applied extensively. When there is uncertainty in dynamic model of the statistics of noise sources are not fully known or unavailable, the application of Kalman filtering is restricted. H_∞ filtering can solve the problems in the applications of Kalman filtering with high accuracy and robustness. In this paper, H_∞ filtering and Kalman filtering technique are introduced in brief, H_∞ robust filter and Kalman filter are designed, and their performances are compared and studied through three aspects.
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This chapter contains sections titled: Verifying Kalman filter performance Multiple-model estimation Reduced-order Kalman filtering Robust Kalman filtering Delayed measurements and synchronization errors Summary Problems
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