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

Author

Listed:
  • Andrey Tsyganov

    (Department of Mathematics, Physics and Technology Education, Ulyanovsk State University of Education, 432071 Ulyanovsk, Russia
    These authors contributed equally to this work.)

  • Julia Tsyganova

    (Department of Mathematics, Information and Aviation Technology, Ulyanovsk State University, 432017 Ulyanovsk, Russia
    Department of Academic Policy and Organization of Educational Activities, Innopolis University, 420500 Innopolis, Russia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Andrey Tsyganov & Julia Tsyganova, 2022. "Algorithmic Differentiation of the MWGS-Based Arrays for Computing the Information Matrix Sensitivity Equations within the Problem of Parameter Identification," Mathematics, MDPI, vol. 10(1), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:126-:d:716253
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