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.

Giarnetti, S., Leccese, F., Caciotta, M. (2017). Non recursive Nonlinear Least Squares for periodic signal fitting. MEASUREMENT, 103, 208-216 [10.1016/j.measurement.2017.02.023].

Non recursive Nonlinear Least Squares for periodic signal fitting

GIARNETTI, SABINO;LECCESE, Fabio;CACIOTTA, Maurizio
2017-01-01

Abstract

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.
Giarnetti, S., Leccese, F., Caciotta, M. (2017). Non recursive Nonlinear Least Squares for periodic signal fitting. MEASUREMENT, 103, 208-216 [10.1016/j.measurement.2017.02.023].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/317070
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