A parameter transformation and Crame´r-Rao bounds for estimating decay rates from exponential signals

Weighted sums of decaying exponentials characterize the response of many physical systems. Therefore, accurate decay rate estimation is a goal in many diverse disciplines. A parameter transformation which improves decay rate estimation is presented. Simulation results across a wide range of decay rates, signal-to-noise ratios, and ratios of decay rates show that nonlinear least squares estimation of the decay rates via the proposed parameter transformation provides estimates with smaller RMS errors and bias than can be obtained without the parameter transformation. In addition, it is shown that the parameter transformation provides decay rate estimates which are closer to achieving the Crame´r-Rao bound. Improvement in estimation performance for this class of signals has important ramifications in signal detection performance in several application areas.