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

Andrey Tsyganov and Julia Tsyganova
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Andrey Tsyganov: Department of Mathematics, Physics and Technology Education, Ulyanovsk State University of Education, 432071 Ulyanovsk, Russia
Julia Tsyganova: Department of Mathematics, Information and Aviation Technology, Ulyanovsk State University, 432017 Ulyanovsk, Russia

Mathematics, 2022, vol. 10, issue 1, 1-16

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.

Keywords: algorithmic differentiation; information matrix; information filter; MWGS-orthgonalization; array algorithms; sensitivity equation; parameter identification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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