The acquisition of high-resolution GPS animal tracks has led to major advances in the discovery and understanding of movement patterns and strategies of animals. GPS tracks of marine birds can for instance be recorded at a temporal resolution up to one second (approximately a one-to-ten-meter spatial resolution). Such tracks typically depict a variety of patterns of interest, such as intensive and extensive search behaviors, with characteristic scales ranging from a few meters to several kilometers or even hundred of kilometers for large seabirds (e.g., wandering Alabatros). Here we propose two novel statistical schemes delivering a multiscale representation of the significant geometric patterns along a trajectory, namely loop-based representations and wavelet-based decompositions. We emphasize their relevance compared to previous work, including single-scale frameworks such as the FPT method that typically focus on a single scale range. We also consider an application to the determination of the characteristic scale ranges of movement tracks in relation to the time sampling of the GPS tag. This analysis stresses the requirement for considering high-resolution tracks (with sampling period from a few seconds to ten seconds depending on the species) to reveal all movement scales (especially characteristic scales lower than a few hundreds of meters).