NDLI: Square-rooting approaches to accurate mixed-type continuous-discrete extended and fifth-degree cubature Kalman filters

Content Provider	IET Digital Library
Author	Kulikova, Maria V. Kulikov, Gennady Yu.
Abstract	The fifth-degree cubature Kalman filter (5D-CKF) has been recently developed for both the discrete- and continuous-time non-linear stochastic systems. In the published works, it has been mentioned that numerically stable square-root 5D-CKF implementations are not feasible to derive, although they are easily obtained for the third-degree CKF. The key problem of the underlying mathematical derivation is negative weight coefficients appeared in the fifth-degree cubature rule, which prevents the required square-root factorisation of the filters’ equations. The authors resolve this essential problem existed for the 5D-CKF methodology by utilising hyperbolic transformations instead of the usual ones traditionally used for square-rooting in the engineering literature. The authors’ solution is given within both the Cholesky and singular value decomposition (SVD) and is based on matrix calculus with the hyperbolic QR and SVD transformations involved. The theoretical results are illustrated in a case of the continuous-discrete mixed-type estimator ACD-EKF-5DCKF and can be applied to any other 5D-CKF strategy. Numerical experiments are also provided.
Starting Page	1671
Ending Page	1680
Page Count	10
ISSN	17518784
Volume Number	14
e-ISSN	17518792
Issue Number	Issue 11, Nov (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-rsn/14/11
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-rsn.2020.0161
Journal	IET Radar, Sonar & Navigation
Publisher Date	2020-06-19
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	5D-CKF Methodology 5D-CKF Strategy Algebra Authors Resolve This Essential Problem Fifth-degree Cubature Kalman Filter Fifth-degree Cubature Rule Filter Filtering Method in Signal Processing Gradient Method Interpolation And Function Approximation Kalman Filter Linear Algebra Mixed-type Estimator ACD-EKF-5DCKF Nonlinear Filter Numerical Analysis Numerically Stable Square-root 5D-CKF Implementations Required Square-root Factorisation Signal Processing Theory Singular Value Decomposition Square-rooting Approach Statistics Stochastic Linearised SCUC Stochastic System Third-degree CKF Underlying Mathematical Derivation
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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