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 in | Mathematics (Basel) Vol. 10; no. 1; p. 126 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.01.2022
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| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/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. |
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| 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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| Cites_doi | 10.1109/CDC.2016.7798725 10.1002/9780470890042 10.1134/S0005117911090141 10.1109/TAC.1971.1099816 10.1007/978-3-540-68942-3_4 10.1002/0471200719 10.1016/0005-1098(80)90078-3 10.1109/CDC.2014.7040033 10.1109/TAC.2013.2259093 10.1007/BF01385717 10.1137/S0895479897330182 10.1016/j.ifacol.2018.11.483 10.1007/978-1-4612-1208-9_6 10.1137/S0036142993247311 10.23919/ECC.2019.8795648 10.1109/TAC.2008.2010989 10.1109/TAC.1974.1100714 10.1007/BF01934122 10.1016/j.ejcon.2020.02.001 |
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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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