Discrete chirp-Fourier transform-based acquisition algorithm for weak global positioning system L5 signals in high dynamic environments

For the acquisition of weak global positioning system L5 signals in high dynamic environments, coherent integration time is necessarily extended for signal-to-noise ratio improvement. However, the incidental problems, such as high-rate sign transitions, tiered codes and particularly the concurrence of Doppler shift and Doppler rate, will bring challenges to the acquisition. This study proposes a novel acquisition algorithm based on the discrete chirp-Fourier transform (DCFT) to solve the problems above. The 1 ms complex correlation is modelled as a chirp signal to account for high dynamics effect. Then the DCFT is introduced to simultaneously estimate the Doppler shift and Doppler rate residuals. In this way, the 1 ms complex correlations are coherently post-integrated and a high processing gain can be obtained when both the primary and secondary code phases are aligned. Furthermore, the false alarm and detection probabilities are derived to statistically characterise the acquisition performance. Simulation results demonstrate that the proposed algorithm is tolerant of high dynamics and robust to noise. Specifically, it can acquire the L5 signal with up to 20 g acceleration and only 25 dB Hz carrier-to-noise ratio, which is impossible for the conventional fast Fourier transform scheme.