Root / CYBERNETICS AND PHYSICS / Volume 15, 2026, Number 2 / LD-based parameter identification approach for the pairwise Markov models

LD-based parameter identification approach for the pairwise Markov models

Andrey Tsyganov, Julia Tsyganova

This paper addresses the problem of parameter identification in pairwise Markov models, where all system matrices may depend on an unknown vector parameter. A novel, numerically stable approach based on the LD decomposition of the error covariance matrices is proposed. The main theoretical result is formulated as a theorem that justifies the exact gradient evaluation using the LD factorization. Two efficient algorithms are presented: one for computing the identification criterion only, and another for the simultaneous computation of the identification criterion and its gradient. The proposed methods are implemented in MATLAB and validated through Monte Carlo studies. The first experiment considers a canonical pairwise model with a scalar parameter, while the second one demonstrates the identification of the wave speed in the one-dimensional wave equation discretized by a finite-difference scheme. The results confirm that the LD-based gradient-type parameter identification algorithm provides accurate parameter estimates with high numerical robustness. The approach can be applied for adaptive filtering and parameter estimation in distributed parameter systems.
CYBERNETICS AND PHYSICS, VOL. 15, NO. 2, 2026, 222–233
https://doi.org/10.35470/2226-4116-2026-15-2-222-233

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