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Estimating Both Reflection Coefficients of 2×2 Linear Hyperbolic Systems with Single Boundary Measurement

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Résumé

An adaptive scheme for estimating both boundary reflection coefficients of 2×2 linear hyperbolic systems, using only a single boundary measurement, is presented. The design consists first of mapping the system into a target system via a Volterra integral transformation. Using this target system, the output signal is written in regressor form linear in the unknown coefficients, and modified least-squares with forgetting factor is implemented to estimate them. Next, it is demonstrated how a similar approach can be applied to estimate the specific boundary acoustic impedances of a cylindrical metal tube open at both ends. By writing the linearised tube acoustics model as a linear hyperbolic 2×2 system, a regressor form with identical parametrization to the former case but with a different signal vector is found. The same adaptive scheme is then applied to estimate the acoustic impedances.
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Dates et versions

hal-03231380 , version 1 (20-05-2021)

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Nils Christian A. Wilhelmsen, Florent Di Meglio. Estimating Both Reflection Coefficients of 2×2 Linear Hyperbolic Systems with Single Boundary Measurement. 2020 59th IEEE Conference on Decision and Control (CDC), Dec 2020, Jeju, South Korea. pp.658-665, ⟨10.1109/CDC42340.2020.9304413⟩. ⟨hal-03231380⟩
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