Hammersley-Chapman-Robbins lower bounds on pole and residue estimates from impulse response data

The estimation of nonrandom pole and residue parameters from impulse-response data is studied. Specifically, the Hammersley-Chapman-Robbins lower bound (HCRB) on the estimation error variance is analyzed for single-input single-output systems with multiple but distinct poles. The HCRB is compared with the widely used Cramer-Rao lower bound (CRB) in examples. The HCRB is found to be significantly tighter than the CRB when noise levels are high compared to the impulse response signal, while the bounds become close for small noise levels (equivalently, large residues).