With the rapid development of satellite signal modulation technology in the field of Low Earth Orbit (LEO) satellite constellation, the acquisition of highly dynamic LEO satellite navigation signals has become a focal point in academia. The SNAP certified structured signal proposed by international scholars as the analysis target is selected, the applicability of an improved Fast Fourier Transform (FFT) algorithm for such highly dynamic signals is investigated, and a mathematical model for the SNAP signal time-division acquisition algorithm is established. The challenge of capturing signals with discontinuous code period during the acquisition process is specifically addressed, and the approach through Matlab simulations is validated. Simulation results demonstrate that, signals with Doppler shifts up to 100 kHz can be acquired at a SNR of -12 dB and a coherent integration time of 3 ms can effectively mitigate the coherent integration loss caused by bit transition. The findings provide valuable insights for the design of acquisition algorithm in next-generation LEO navigation receivers.