Estimation of model-parameter errors
M. Roman Serbyn · The Journal of the Acoustical Society of America · 1999
The linear time-invariant two-port, characterized by four complex parameters, has established itself as a reliable model for a variety of physical systems. It has been studied in two aspects: as the ‘‘forward’’ problem (analysis) and the ‘‘inverse’’ problem (synthesis). The focus of the research here reported is on the latter, that is, on inferring the values of the model parameters from the results of measurements at the input and output ports. In particular, the goal of this investigation has been to quantify the relationship between uncertainties in the measured values and the resulting errors in the parameter estimates. Two physical systems have been used in the present study: an electrical circuit with known component values and an uncalibrated electromechanical transducer. Mathematically, each device was modeled as a Moebius transformation, w=(az+b)/(cz+d), whose parameters, (a,b,c,d), were estimated from least-squares fits to measured values of the variables (z,w). The a priori known electrical circuit provided a base line for checking the validity of the computation algorithms. maple, matlab, and spice programs were utilized. [Work supported by HUD Special Projects Grant No. B98SPMD0074.]