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Tighter lower bounds on the error variance of pole and residue estimates from impulse response data: An expository example

Abstract:

The estimation of nonrandom pole and residue parameters from impulse-response data is revisited. Specifically, for an expository example (a one-pole discrete-time system), the Hammersley-Chapman-Robbins lower bound (HCRB) on the estimation error variance is derived, and compared with the widely-used Cramer-Rao bound (CRB). The HCRB is found to be significantly tighter than the CRB over a range of parameter values. Simplifications of the HCRB which admit analytical expressions but are guaranteed to outperform the CRB are also derived. The results indicate that CRB-based confidence intervals for pole-residue estimates, which are being used in several mode monitoring applications, need to be examined with caution.