Algorithmic Differentiation of the MWGS-Based Arrays for Computing the Information Matrix Sensitivity Equations within the Problem of Parameter Identification

The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The...

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Published inMathematics (Basel) Vol. 10; no. 1; p. 126
Main Authors Tsyganov, Andrey, Tsyganova, Julia
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2022
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ISSN2227-7390
2227-7390
DOI10.3390/math10010126

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Abstract The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The solution is based on the usage of special methods for the algorithmic differentiation of matrix MWGS transformation of two types: forward (MWGS-LD) and backward (MWGS-UD). The main result of the work is a new MWGS-based array algorithm for computing the information matrix sensitivity equations. The algorithm is robust to machine round-off errors due to the application of the MWGS orthogonalization procedure at each step. The obtained results are applied to solve the problem of parameter identification for state-space models of discrete-time linear stochastic systems. Numerical experiments confirm the efficiency of the proposed solution.
AbstractList The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The solution is based on the usage of special methods for the algorithmic differentiation of matrix MWGS transformation of two types: forward (MWGS-LD) and backward (MWGS-UD). The main result of the work is a new MWGS-based array algorithm for computing the information matrix sensitivity equations. The algorithm is robust to machine round-off errors due to the application of the MWGS orthogonalization procedure at each step. The obtained results are applied to solve the problem of parameter identification for state-space models of discrete-time linear stochastic systems. Numerical experiments confirm the efficiency of the proposed solution.
Author Tsyganov, Andrey
Tsyganova, Julia
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  fullname: Tsyganova, Julia
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SubjectTerms algorithmic differentiation
Algorithms
array algorithms
Arrays
Computation
Decomposition
Difference equations
Differentiation
Discrete time systems
information filter
information matrix
Kalman filters
Mathematics
Matrices (mathematics)
MWGS-orthgonalization
Noise
Parameter identification
Parameter sensitivity
Robustness (mathematics)
Roundoff error
Sensitivity
sensitivity equation
State space models
Stochastic systems
Transformations (mathematics)
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Title Algorithmic Differentiation of the MWGS-Based Arrays for Computing the Information Matrix Sensitivity Equations within the Problem of Parameter Identification
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