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

摘要

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.