Resonance parameter estimation from spectral data: Cramér–Rao lower bound and stable algorithms with application to liquid sensors

Abstract

A recently introduced method for robust determination of the parameters of strongly damped resonances is evaluated in terms of achievable accuracy. The method extracts and analyzes the locus of the resonant subsystem of noisy recorded complex spectra, such that the interfering influences of many environmental factors are eliminated. Estimator performance is compared to the absolute lower limit determining the Cramér–Rao lower bound (CRLB) for the variance of the estimated parameters. A generic model that is suitable for representation of a large class of sensors is used and analyzed. It is shown that the proposed robust method converges to the CRLB for low measurement noise.