Polynomial LMMSE estimation: A case study

This paper investigates the potential of the polynomial LMMSE estimation for nonlinear/nongaussian estimation problems. This is done by a case study: the estimation of the frequency of a sinusoidal signal with unknown amplitude and phase. We give analytical formulas to calculate the second order moments which are needed for the polynomial LMMSE estimation and we study the performance for varying orders of observations. Variable selection is used to identify the most relevant observations. It turns out that only a small number (less than one percent) of all available variables gives nearly the same mean squared error.