Doppler Frequency Estimation in GNSS Receivers Based on Double FFT

Abstract

This paper presents an innovative Doppler frequency estimation technique, which is particularly suited for global navigation satellite system (GNSS) receivers operating in vehicular scenarios. Mass-market and commercial navigation devices are being increasingly exploited for in-car navigation and for vehicular applications based on positioning. However, the low computational burden that can be afforded by such devices requires the implementation of low-complexity algorithms, allowing real-time and on-demand processing. This is the case, for instance, for open-loop architectures and of maximum likelihood estimation (MLE)-based techniques, which estimate the frequency component of the GNSS signal through a discrete Fourier transform. A state of the art of such methods is first carried out, outlining their benefits, regarding robustness and stability, and their limitations, mainly concerning the accuracy. Successively, an innovative refinement technique is introduced, based on the computation of a frequency correction term. Further enhancements are then proposed to solve particular issues, such as the estimation of the sign of the correction term and the impact of the initial frequency error. In particular, zero forcing and a double fast Fourier transform (FFT), which represent the main contribution of this paper, are proposed to increase the accuracy without increasing the computational load. A complete analytical derivation and theoretical description is provided, along with a detailed performance assessment. Finally, a performance comparison with existing techniques and with the Cramer–Rao lower bound (CRLB) for frequency estimation is given, confirming the excellent behavior of the proposed algorithm for the signal conditions and strengths that are typical of a vehicular scenario and in the presence of frequent interruptions.