Amplitude estimation with application to system identification

We investigate herein the problem of amplitude estimation of sinusoidal signals from observations corrupted by colored noise. A relatively large number of amplitude estimators are described which encompass Least Squares (LS) and Weighted Least Squares (WLS) methods. Additionally, lterbank approaches, which are widely used for spectral analysis, are extended to amplitude estimation. Speci cally, we consider the recently introduced MAtched-FIlterbank (MAFI) approach and show that, by appropriately designing the pre lters, the MAFI approach includes the WLS approach. The amplitude estimation techniques discussed in this paper do not model the noise, and yet they are all asymptotically statistically e cient. It is their di erent nite-sample properties that are of particular interest to this study. Numerical examples are provided to illustrate the di erences among the various estimators. Though amplitude estimation applications are numerous, we focus on system identi cation using sinusoidal probing signals.