3D Galileo Reference Antenna Pattern for Space Service Volume Applications

Abstract

There is an increasing demand for navigation capability for space vehicles. The exploitation of the so-called Space Service Volume (SSV), and hence the extension of the Global Navigation Satellite System (GNSS) from terrestrial to space users, is currently considered a fundamental step. Knowledge of the constellation antenna pattern, including the side lobe signals, is the main input for assessing the expected GNSS signal availability and navigation performance, especially for high orbits. The best way to define and share this information with the final GNSS user is still an open question. This paper proposes a novel methodology for the definition of a high-fidelity and easy-to-use statistical model to represent GNSS constellation antenna patterns. The reconstruction procedure, based on antenna characterization techniques and statistical learning, is presented here through its successful implementation for the "Galileo Reference Antenna Pattern (GRAP)" model, which has been proposed as the reference model for the Galileo programme. The GRAP represents the expected Equivalent Isotropic Radiated Power (EIRP) variation for the Galileo FOC satellites, and it is obtained by processing the measurements retrieved during the characterization campaign performed on the Galileo FOC antennas. The mathematical background of the model is analyzed in depth in order to better assess the GRAP with respect to different objectives such as improved resolution, smoothness and proper representation of the antenna pattern statistical distribution. The analysis confirms the enhanced GRAP properties and envisages the possibility of extending the approach to other GNSSs. The discussion is complemented by a preliminary use case characterization of the Galileo performance in SSV. The accessibility, a novel indicator, is defined in order to represent in a quick and compact manner, the expected Galileo SSV quality for different altitudes and target mission requirements. The SSV characterization is performed to demonstrate how simply and effectively the GRAP model can be inserted into user analysis. The work creates the basis for an improved capability for assessing Galileo-based navigation in SSV according to the current knowledge of the antenna pattern.

Keywords: GNSS; Galileo antenna pattern; accessibility index; antenna characterization; elastic-net regularization; high-orbit navigation; space service volume; spherical harmonic; statistical learning.

Figure 1

Rapresentation of Continuous Wave (CW) spherical scanning of the antenna pattern radiated field: different colors represent data samples collected at different central frequencies spaced 2.5 MHz apart.

Figure 2

Antenna Pattern Multi−step Reconstruction Procedure.

Figure 3

Distribution of $W_{{∆f}_n}^{PSD}$ for the different Galileo central frequencies.

Figure 4

Elastic Net Learning curve for E1 ${\lambda }_{min}$ determination.

Figure 5

Spherical Harmonic Parameter Space representation of the GRAP pattern: upper—E1 GRAP coefficients $\widehat{{\mathit{\beta }}_{\mathit{\mu }}}$, bottom—corresponding standard deviations.

Figure 6

Galileo E1 ${EIRP}_{E1,m,dBW}^R\left(\theta ,\phi \right)$ 3D representation (top) and correspondent polar plot (bottom).

Figure 7

Galileo E1 Laplacian for data sample mean (top) and reconstructed pattern (bottom).

Figure 8

E1 3D Constellation expected 95% variation: ${2\sigma }_{f,dB}^R\left(\theta ,\phi \right)$.

Figure 9

Galileo E1 Constellation pattern at different co-elevation and azimuth cuts (blue line) together with confidence bounds (red dotted line) vs measurement data (grey samples).

Figure 9

Galileo E1 Constellation pattern at different co-elevation and azimuth cuts (blue line) together with confidence bounds (red dotted line) vs measurement data (grey samples).

Figure 10

E1 Galileo GRAP stability and strength for SSV applications.

Figure 11

Space Service Volume simplified geometry for accessibility index definition.

Figure 12

Off- boresight angle antenna pattern spanned for different SV rising positions and user altitudes.

Figure 13

Receiving antenna off-boresight angles vs altitude and compatible teta (top) and receiving working region for reference high gain receiving antenna pattern (bottom).

Figure 14

$\left({\theta }_i,h_{rx}\right)$received signal power distribution for Galileo E1.

Figure 15

$\left({\theta }_i,h_{rx}\right)$carrier-to-noise ratio distribution for Galileo E1.

Figure 16

Accessibility chart for Galileo E1 for target received signal power.

Figure 17

Accessibility chart for Galileo E1 for target receiver sensitivity (${C/N_0}_{min})$.

Figure 18

Variation with respect to azimuth for three different tracking thresholds: 15, 20, 25 dB/Hz.