Analysis of the Cramér-Rao Lower Bounds for Unbiased Parameter Estimators of Noisy Damped Sinusoids

In this paper the Cramér-Rao Lower Bounds (CRLBs) for unbiased estimators of the parameters of complex-valued noisy damped sinusoid are comprehensively analyzed assuming that enough samples are acquired in an interval duration equal to the signal time constant. At first accurate, but simple, expressions for the CRLBs are derived. Then, even simpler expressions are obtained assuming that the observation duration is either enough smaller or enough greater than the signal time constant. Leveraging on the derived expression, constraints on the number of analyzed samples that allow the optimization of the tradeoff between estimation accuracy, estimation delay, and processing effort are derived. They can be useful to optimize measurement procedures aimed at estimating unknown signal parameters. The accuracies of the derived results are verified through computer calculations and the application of a state-of-the-art almost unbiased and statistically efficient algorithm.