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GNSS direction of arrival tracking using the rotate-to-zero direction lock loop

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Abstract

Array signal processing is attractive for Global Navigation Satellite System (GNSS) applications, as the desired reception environments for GNSS are becoming more challenging, while users’ demands for high-accuracy positioning are growing. One goal of array signal processing is to find the direction of arrival (DOA) of the signal source. Several advanced techniques have been proposed to estimate the DOA, with the direction lock loop (DiLL) being a representative method. However, applying the DiLL in GNSS receivers is not straightforward. One reason for this is the low sensitivity of the utilized spatial correlation function in the angular region close to broadside within a linear antenna array. In order to address this problem, an improved DOA tracking technique is presented building on the traditional DiLL, i.e., the rotate-to-zero direction lock loop (RZ-DiLL). Simulations and live data validations show that the proposed RZ-DiLL avoids the low sensitivity issue of the traditional DiLL. Moreover, the experimental results show that compared to a single-antenna GNSS receiver, the RZ-DiLL-implemented GNSS array signal receiver provides an improved carrier-to-noise ratio and, in turn, improved position solutions.

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Acknowledgements

The authors are grateful to Dr. Pai Wang from the University of Colorado Boulder for her help. This work has been partially supported by the China Scholarship Council.

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Correspondence to Nagaraj Channarayapatna Shivaramaiah or Jiaolong Wei.

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Appendix: Geometrical relationship between satellites and antenna placement

Appendix: Geometrical relationship between satellites and antenna placement

For a 2-element antenna array, the DOA is determined by the satellite position and antenna placement, as shown in Fig. 11. The projection of the satellite is \(a\), the antenna array position is \(c\), the satellite position is \(d\), the vertex of the perpendicular line from satellite projection \(a\) to the antenna array extending line is \(b\), \(\theta_{\text{el}}\) is the elevation angle of the satellite, and \(\theta_{{{\text{az}} - {\text{shift}}}}\) is the difference between the antenna array direction and the satellite azimuth angle.

Fig. 11
figure 11

Schematic of the relationship between the DOA, azimuth, elevation, and azimuth shift angles

Thus, the lengths of \(dc\), \(db\), and \(cb\) can be denoted as

$$\begin{aligned} dc & = \frac{ac}{{\cos \theta_{\text{el}} }} \\ db & = ac\sqrt {\sin^{2} \left( {\theta_{{{\text{az}} - {\text{shift}}}} } \right) + \tan^{2} \left( {\theta_{\text{el}} } \right)} \\ cb & = ac\cos \theta_{{{\text{az}} - {\text{shift}}}} \\ \end{aligned}$$
(16)

Then, the DOA angle \(\theta_{\text{DOA}}\) from a satellite to a 2-element antenna array can be expressed by

$$\begin{array}{*{20}c} {\uptheta_{DOA} = \arccos \left( {\frac{{\frac{1}{{\cos^{2} \theta_{el} }} + \sin^{2} \left( {\theta_{\text{az - shift}} } \right) + \tan^{2} \left( {\theta_{\text{el}} } \right) - \cos^{2} \left( {\theta_{\text{az-shift}} } \right)}}{{\frac{{2\sqrt {\sin^{2} \left( {\theta_{\text{az-shift}} } \right) + \tan^{2} \left( {\theta_{\text{el}} } \right)} }}{{\cos \theta_{\text{el}} }}}}} \right) } \\ \end{array}$$
(17)

Note that when \(\theta_{\text{az-shift}} = 0\), which is a special case in which the antenna direction is the same as the azimuth angle of the satellite, \(\theta_{\text{DOA}} = \frac{pi}{2} - \theta_{\text{el}}\).

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Wang, B., Shivaramaiah, N.C., Akos, D.M. et al. GNSS direction of arrival tracking using the rotate-to-zero direction lock loop. GPS Solut 24, 39 (2020). https://doi.org/10.1007/s10291-020-0952-x

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