Initial Parameter Estimation for Non-Linear Optimization -- Trigonometric Function

TL;DR

This paper presents a new method for estimating initial parameters in nonlinear optimization of trigonometric functions, improving accuracy and computational efficiency especially in noisy and limited data scenarios.

Contribution

A novel NI-based initial parameter estimation strategy for trigonometric models that enhances optimization success in challenging data conditions.

Findings

Accurate initial parameter estimation achievable at low SNR of 1.4 dB.

Method outperforms Lomb-Scargle periodogram in computational cost.

Effective for data with few periods or high noise.

Abstract

Nonlinear optimisation techniques are commonly employed to minimise complex cost functions, with their effectiveness determined largely by the structure of the underlying error landscape. These methods require initial parameter values, and in the presence of multiple local minima, they are prone to becoming trapped in suboptimal regions. The likelihood of locating the global minimum increases substantially when the initialisation lies within its corresponding basin of attraction. Consequently, high-quality initial parameters are critical for successful optimisation. This technical report outlines a new strategy for selecting suitable initial parameters for a trigonometric model and unevenly sampled data, ensuring that the optimisation procedure starts sufficiently close to the global minimum. The proposed parameter estimation approach is strictly NI-based, interpretable, and explainable. It targets at complicated cases which include: samples with strong random noise, samples with only few covered periods, and samples which cover only a fraction of one period. Special attention is put on the frequency estimation. It can be shown that an estimation of initial parameters with sufficient accuracy is possible down to a signal-noise-ratio of 1.4 dB at much lower computational costs than the Lomb-Scargle-periodogram method requires.