Parameter Estimation by Parameter Signature Isolation in the Time-Scale Domain

Abstract

It is shown that output sensitivities of dynamic models can be better delineated in the time-scale domain. This enhanced delineation provides the capacity to isolate regions of the time-scale plane, coined as parameter signatures, wherein individual output sensitivities dominate the others. Due to this dominance, the prediction error can be attributed to the error of a single parameter at each parameter signature so as to enable estimation of each model parameter error separately. As a test of fidelity, the estimated parameter errors are evaluated in iterative parameter estimation in this paper. The proposed parameter signature isolation method (PARSIM) that uses the parameter error estimates for parameter estimation is shown to have an estimation precision comparable to that of the Gauss–Newton method. The transparency afforded by the parameter signatures, however, extends PARSIM’s features beyond rudimentary parameter estimation. One such potential feature is noise suppression by discounting the parameter error estimates obtained in the finer-scale (higher-frequency) regions of the time-scale plane. Another is the capacity to assess the observability of each output through the quality of parameter signatures it provides.