Parameter Estimation Employing a Dual-Channel Sine-Wave Model Under a Gaussian Assumption

The Cramer-Rao bound (CRB) is a lower bound on the error variance of any estimator. For a Gaussian scenario, the CRB is derived for a seven-parameter, dual-channel sine-wave model, which is a model relevant to applications such as impedance measurements and the estimation of particle size and velocity by laser anemometry. Four different parameterizations were considered: the common quadrature/in-phase and amplitude-phase models and two relative amplitude-phase models. The CRB indicated the achievable error variance of an unbiased estimator as a function of the signal-to-noise ratio (SNR), the number of samples, and noise power. A nonlinear least squares fit of the signal model to the collected data was employed. The problem at hand is separable and can be solved by a 1-D search followed by a linear least squares fit of the remaining parameters. The performance of the method was investigated with the aid of a simulation study, and the outcome was compared with that of the corresponding CRB and with a recently proposed seven-parameter fit. For high SNRs, the performance of the proposed method is close to optimal with an error variance close to the predictions made by the CRB.