The statistical performance of state-variable balancing and Prony´s method in parameter estimation

This paper presents a statistical analysis of the state-variable balancing and Prony methods for estimating the parameters of exponential signals in the presence of additive noise. The case of frequency estimation for a single sinusoid is carried out in detail. Analytical expressions for the variances of the frequency estimates at high signal-to-noise ratios are derived. The calculated variances are compared to the Cramer-Rao bound. The results are validated by simulations over a wide range of signal-to-noise ratios. The analysis and simulations show that the state-variable balancing method can provide slightly more accurate frequency estimates while avoiding the problem of selecting the signal zeros of the Prony polynomial.