A Baseband MLE for Snapshot GNSS Receiver Using Super-Long-Coherent Correlation in a Fractional Fourier Domain

Abstract

Low-cost global navigation satellite system and global positioning system(GPS) receivers require reliable baseband processing to guarantee accurate positioning. However, classic baseband performance is limited in challenging cases due to the characteristics of traditional loop filters. Accordingly, a snapshot baseband maximum likelihood estimator (MLE) using super-long coherent integration (S-LCI) in a fractional Fourier domain (FrFD) is proposed to upgrade the traditional frequency/phase/delay lock loop tracking algorithms. First, applying the S-LCI correlation in an FrFD increases the accuracy of a weak and dynamic signal estimation. Tolerance of the initial guess error in the snapshot baseband processing is then relaxed by the MLE. Finally, a gradient descent algorithm accelerates the convergence of signal estimation. Moreover, we derive the Cramer-Rao lower bound for the proposed MLE. Both numerical simulations and real-world experiments based on this GPS receiver prototype verify the effectiveness of its high-accuracy estimations of weak signals, strong tolerance for large initial guess errors, and prompt responses to converging.