Non recursive Nonlinear Least Squares for periodic signal fitting

A non-recursive version of Nonlinear Least Squares Fitting for frequency estimation is presented. This problem yields a closed-form solution exploiting a Taylor's series expansion. Respecting some conditions, the computational complexity is reduced, but equally the method assures that the accuracy reaches the Cramer-Rao Bound. The proposed method requires a frequency pre-estimate. A series of simulations has been made to determine how accurate the pre-estimate should be in order to ensure the achievement of the Cramer-Rao Bound in various conditions for different periodic signals. The execution time of the proposed algorithm is smaller compared to a single iteration cycle of the standard approach. The proposed method is useful in applications that require a high accuracy fitting of periodic signals, especially when limited computational resources are available or a real-time evaluation is needed.