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Low-Computation GNSS Acquisition Method for Sparse Doppler Frequency Hypotheses in High-Dynamic Environment

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Abstract

To acquire Global Navigation Satellite System (GNSS) signal in high-dynamic and long integration applications, the high dimensional search of this detection needs a high computational cost. To reduce the computations of parameters estimation, this paper proposes a low-computation GNSS acquisition method (LGAM) in the high-dynamic environment. Firstly, sparse Doppler frequency (SDF) process is performed for SDF hypotheses, and post-correlation signal model is derived based on SDF structure. Then, double-FFT based detection is proposed based on the post-correlation signal model for parameters estimation. The results demonstrate that due to the reduction of complex multiplications, the computational cost of LGAM is lower than that of the FFT based methods under the moderate signal to noise ratio.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. Consent for publication The manuscript does not contain any individual person’s data in any form (including individual details, images, or videos) and therefore the consent to publish is not applicable to this article.

Abbreviations

BPSK:

Binary phase shift keying

FAP:

False alarm probability

GNSS:

Global Navigation Satellite System

IT:

Integration times

LGAM:

Low-computation GNSS acquisition method

SDF:

Sparse Doppler frequency

SNR:

Signal to noise ratio

SDHT:

Synthesized Doppler frequency hypothesis testing

MAC:

Mean acquisition computation

DCFT:

Discrete chirp-Fourier transform

FFT:

Fast Fourier transform

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Acknowledgements

Not applicable.

Funding

This work was supported by Key Laboratory of Cognitive Radio and Information Processing, Ministry of Education (Guilin University of Electronic Technology) No.: CRKL220207, the National Natural Science Foundation of China under Grant 61901154 and Zhejiang Province Science Foundation for Youths under Grant LQ19F010006.

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Authors and Affiliations

  1. School of Communication Engineering, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, China

    Chao Wu

  2. Key Laboratory of Cognitive Radio and Information Processing, Guilin University of Electronic Technology, Guilin, 541004, Guangxi, China

    Chao Wu

Authors
  1. Chao Wu
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All authors made contributions in the discussions, analyses, and implementation of the proposed method solution.

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Correspondence to Chao Wu.

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Appendix: Derivation of Doppler Rate Resolution

Appendix: Derivation of Doppler Rate Resolution

Based on (10), \({\boldsymbol{\Delta }}_{\boldsymbol{\alpha }}=\frac{1}{{{\varvec{N}}}_{{\varvec{B}}0}{{\varvec{T}}}_{{\varvec{s}}}}\) represents Doppler rate resolution, and when \(\left|{\boldsymbol{\alpha }}_{{\varvec{k}}}\right|\le \frac{{\boldsymbol{\Delta }}_{\boldsymbol{\alpha }}}{2}\) in (12), the correct unit corresponding to Doppler rate should be detected. In order not to cause too much attenuation of the detected peak,

$$20\mathit{lg}\left|\mathit{sin}c\left(\pi \frac{{N}_{B}{T}_{s}}{{N}_{B0}}{N}_{B}\right)\mathit{sin}c\left(\pi \frac{{N}_{B}{T}_{s}}{{N}_{B0}}{N}_{B}{N}_{SB}\right)\right|\ge -6\hspace{0.33em}dB$$
(33)

So

$$\left|\mathit{sin}c\left(\pi \frac{{N}_{B}{T}_{s}}{{N}_{B0}}{N}_{B}\right)\mathit{sin}c\left(\pi \frac{{N}_{B}{T}_{s}}{{N}_{B0}}{N}_{B}{N}_{SB}\right)\right|\ge 0.5$$
(34)

Since \(\left|{\varvec{sin}}{\varvec{c}}\left({\varvec{\pi}}\frac{{{\varvec{N}}}_{{\varvec{B}}}{{\varvec{T}}}_{{\varvec{s}}}}{{{\varvec{N}}}_{{\varvec{B}}0}}{{\varvec{N}}}_{{\varvec{B}}}\right)\right|\ge \left|{\varvec{sin}}{\varvec{c}}\left({\varvec{\pi}}\frac{{{\varvec{N}}}_{{\varvec{B}}}{{\varvec{T}}}_{{\varvec{s}}}}{{{\varvec{N}}}_{{\varvec{B}}0}}{{\varvec{N}}}_{{\varvec{B}}}{{\varvec{N}}}_{{\varvec{S}}{\varvec{B}}}\right)\right|\), (34) can be simplified further as:

$$\left|\mathit{sin}c\left(\pi \frac{{N}_{B}{T}_{s}}{{N}_{B0}}{N}_{B}{N}_{SB}\right)\right|\ge \frac{1}{\sqrt{2}}$$
(35)

So based on Taylor expansion, (35) can be simplified further as:

$$\mathit{sin}\left(\pi \frac{{N}_{B}^{2}{N}_{SB}{T}_{s}}{{N}_{B0}}\right)\approx \left(\pi \frac{{N}_{B}^{2}{N}_{SB}{T}_{s}}{{N}_{B0}}\right)-\frac{{\left(\pi \frac{{N}_{B}^{2}{N}_{SB}{T}_{s}}{{N}_{B0}}\right)}^{3}}{6}\ge \frac{1}{\sqrt{2}}\pi \frac{{N}_{B}^{2}{N}_{SB}{T}_{s}}{{N}_{B0}}$$
(36)

When \({N}_{B}\)=20,

$${N}_{B0}\ge \frac{\pi {N}_{B}^{2}{N}_{SB}{T}_{s}}{\sqrt{6\left(1-\frac{1}{\sqrt{2}}\right)}}\approx {N}_{SB}$$
(37)

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Wu, C. Low-Computation GNSS Acquisition Method for Sparse Doppler Frequency Hypotheses in High-Dynamic Environment. Wireless Pers Commun 135, 1947–1963 (2024). https://doi.org/10.1007/s11277-024-10967-x

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