Combining Bispectral Analysis with the Levenberg–Marquardt Algorithm for Enhanced Non-linear Signal Processing in Astronomy

The understanding of intricate, non-linear phenomena within astronomical data is pivotal for the progression of our knowledge of the universe. This paper introduces an innovative method that merges bispectral analysis with the Levenberg–Marquardt (LM) algorithm for processing astronomical signals. The LM algorithm is renowned for its effectiveness in non-linear parameter estimation and model fitting. At the same time, bispectral analysis is adept at identifying and measuring non-linear interactions and phase coupling within signals. By integrating these two techniques, our approach facilitates a comprehensive analysis of astronomical signals, encompassing both modeled and unmodeled non-linearities. This integrated methodology is particularly advantageous in fields such as the exploration of pulsars, binary star systems, exoplanet detection, and active galactic nuclei, where non-linear dynamics exert significant influence. The findings illustrate that this collaborative approach amplifies the identification and delineation of non-linear processes, leading to more precise models and profound insights into complex astronomical phenomena.