Initial Parameter Estimation for Non-Linear Optimization – Trigonometric Function
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.
Mehr zum Titel
| Titel | Initial Parameter Estimation for Non-Linear Optimization – Trigonometric Function |
|---|---|
| Medien | TECHP 2026/01 |
| Herausgeber | Coburg University, Faculty of Electrical Engineering and Computer Science |
| Verfasser | Prof. Dr.-Ing. habil. Tilo Strutz |
| Seiten | 1-29 |
| Veröffentlichungsdatum | 11.03.2026 |
| Zitation | Strutz, Tilo (2026): Initial Parameter Estimation for Non-Linear Optimization – Trigonometric Function. TECHP 2026/01, 1-29. DOI: 10.48550/arXiv.2603.09784 |