Trainable Synchrosqueezed Chirplet Transform for IF-Crossover Signals With Very Close Chirp-Rates

In positioning, navigation and timing (PNT) systems based on low earth orbit satellites (LEO-PNT), extracting frequency information from densely deployed LEO satellites is a challenging task that requires processing two signals with crossover instantaneous frequency (IF) curves and very close chirp-rates. Existing methods, such as generalized linear chirplet transform and synchrosqueezed chirplet transform (SCT), are limited by a 'bubble phenomenon' caused by slow decay along the chirp-rate axis, which distorts the time-frequency-chirp rate (TFC) representation near crossovers and invalidates conventional local search and fixed-threshold strategies. To overcome this challenge, we propose a trainable SCT (TSCT) framework, which first utilizes adaptive detection techniques to dynamically generate noise spectra and detection thresholds, and then incorporates supervised learning for the decision-making task in high-dimensional parameter reassignment. Additionally, an improved version of the SCT frequency estimation operator based on dual spectral centroid method is designed to improve the stability of the algorithm. Through numerical simulations and validation with measured Starlink data, the proposed method demonstrates excellent performance in handling signals with complex intersecting IFs.