Estimating the state of a one-dimensional waveguide

Abstract

Methods for estimating the state of a one-dimensional waveguide are analyzed. The state is parameterized in terms of right-going and left-going traveling waves for applications in reflectometry and control. Traditional methods estimate the localized state at a single position in the waveguide. In many cases, the history of a simple estimator may serve as time-delayed or time-advanced estimates for the remainder of the waveguides state. The decomposition method estimates the traveling wave components at a point using integration and a spatial gradient approximation. The delay method, which involves implementing a single delay accurately, is shown to be equivalent to the causal Wiener filter least-squares optimal estimator. If sensors are spaced irregularly, then an optimization problem typical of beam forming applications may be solved to find an FIR filter-based localized estimator. On the other hand, when the estimator needs to estimate the entire waveguide state quickly, then either additional sensors or computation cycles are required. The Kalman filter requires much more computation in general, but with the help of a digital waveguide model, it can provide complete state estimates with less than one sample of delay using as few as one sensor. [Work supported by the Wallenberg Global Learning Network.]