Statistical analysis of state-space approach in harmonic retrieval

The author presents a statistical analysis of the performance of the state-variable balancing for estimating the parameters of exponential signals in the presence of additive noise. The case of frequency estimation for a single damped sinusoid is carried out in detail because the analysis can be presented more clearly; the formulas are simpler and provide insight; and the results are applicable in radar, sonar, communication, and data modelling. Analytical expressions for the variances of the frequency estimate at high signal-to-noise ratios is derived. Both analytical and experimental results are presented to illustrate the performance of the state-variable balancing method