Non-linear instantaneous least squares and its high SNR analysis

A novel approach for signal parameter estimation, named the Non-Linear Instantaneous Least Squares (NILS) estimator, is proposed and a high SNR statistical analysis of the estimates is presented. The algorithm is generally applicable to deterministic signal in noise models. However, it is of particular interest in applications where the “conventional” non-linear least squares criterion suffers from numerous local minima. The key idea here is to apply a sliding window to estimate the instantaneous amplitude, which is then used in a separable least squares criterion-function. Hereby the radius of attraction of the global minimum is under the control of the user, which makes the NILS approach advantegous to use in practical applications. Numerical results using polynomial-phase signals validate the theoretical results.