Fast Nearly ML Estimation of Doppler Frequency in GNSS Signal Acquisition Process

Xinhua Tang,Emanuela Falletti,Letizia Lo Presti

doi:10.3390/s130505649

Xinhua Tang, Emanuela Falletti + Show 1 more

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https://doi.org/10.3390/s130505649

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Abstract

It is known that signal acquisition in Global Navigation Satellite System (GNSS) field provides a rough maximum-likelihood (ML) estimate based on a peak search in a two-dimensional grid. In this paper, the theoretical mathematical expression of the cross-ambiguity function (CAF) is exploited to analyze the grid and improve the accuracy of the frequency estimate. Based on the simple equation derived from this mathematical expression of the CAF, a family of novel algorithms is proposed to refine the Doppler frequency estimate with respect to that provided by a conventional acquisition method. In an ideal scenario where there is no noise and other nuisances, the frequency estimation error can be theoretically reduced to zero. On the other hand, in the presence of noise, the new algorithm almost reaches the Cramer-Rao Lower Bound (CRLB) which is derived as benchmark. For comparison, a least-square (LS) method is proposed. It is shown that the proposed solution achieves the same performance of LS, but requires a dramatically reduced computational burden. An averaging method is proposed to mitigate the influence of noise, especially when signal-to-noise ratio (SNR) is low. Finally, the influence of the grid resolution in the search space is analyzed in both time and frequency domains.

Highlights

The main purpose of the acquisition and tracking systems of a Global Navigation Satellite System (GNSS) receiver is to provide an estimate of the Doppler frequency fd, the code delay τ, and the phase of the carrier, φ, of the signal transmitted by each visible satellite
A system typically adopted by a GNSS receiver to reach this goal is a frequency lock loop (FLL), which is generally integrated within a phase lock loop (PLL)
With respect to that previous work, here we extend and complete all the mathematical derivations, extend the performance analysis with appropriate comparisons, derive and discuss the Cramer-Rao lower bound (CRLB) for the frequency estimator showing that the proposed approach is close to the CRLB, and include the theoretical analysis of other non-Additive White Gaussian Noise (AWGN) nuisances

Summary

Introduction

The main purpose of the acquisition and tracking systems of a Global Navigation Satellite System (GNSS) receiver is to provide an estimate of the Doppler frequency fd , the code delay τ , and the phase of the carrier, φ, of the signal transmitted by each visible satellite. The task of the acquisition is system a a to detect the visible satellites and to provide, for each detected satellite, a coarse estimate fd , τof fd and τ This parameter vector is passed to the tracking systems, whose task is to refine this estimate. The refinement of Doppler frequency estimate is generally performed by a classic phase lock loop (PLL), which requires an initial estimate much more accurate than the one provided by the acquisition system. An interpolation method is introduced in Reference [5] to estimate the true value of the Doppler frequency, but it is based on an empirical approximation

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