SINUSOIDAL SIGNALS WITH RANDOM AMPLITUDE - LEAST-SQUARES ESTIMATORS AND THEIR STATISTICAL-ANALYSIS

The asymptotic properties of constrained and unconstrained least-squar es estimates of the parameters of a random amplitude sinusoid are anal yzed. An explicit formula for the asymptotic covariance matrix of the estimation errors is derived for both the constrained and unconstraine d estimators, Accuracy aspects are investigated with the following mai n results, For a certain weighting matrix, which is shown to be the sa me for the constrained and unconstrained methods, the estimation error s achieve their lower bounds, It is proven that in the optimal case, t he constrained method always outperforms the unconstrained method, It is also proven that the accuracy of the optimal estimators improves as the number of least-squares equations increases. A formula for the sa mple length needed for the asymptotic theory to hold is derived, and i ts dependence on the lowpass modulating sequence is stressed. Simulati ons provide illustrations of the difference between the constrained an d unconstrained estimators as well as the difference between the optim al and basic estimates. The influence of the number of least-squares e quations and the characteristics of the lowpass envelope on the estima tion accuracy is also investigated.