Inside GNSS Media & Research

JUL-AUG 2019

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Page 56 of 67 J U L Y / A U G U S T 2 0 1 9 Inside GNSS 57 Table 1 summarizes the number of satellites and the trans- mission band of each constellation. Figure 2 depicts a snapshot of the upcoming Starlink con- stellation, while Figure 3 is a heat map of the number of visible Starlink LEO satellites above an elevation mask of 5 degrees. Figure 5 is a heat map showing the position dilution of preci- sion (PDOP) for the Starlink constellation, while Figure 5 is a heat map showing the logarithm of the Doppler position dilu- tion of precision (DPDOP). Figure 2 through Figure 5 together with Table 1 demonstrate the potential of using LEO satellite signals for PNT and imply that the commercial space industry is inadvertently creating new PNT sources, which could be utilized by future vehicles to make the vehicle's PNT system more resilient and accurate. For exam- ple, a Tesla connected to Starlink satellites could dually provide a passenger with internet access, as designed, while also enabling the vehicle to navigate in GNSS-challenged environments. ere are several challenges that need to be addressed to exploit LEO satellites for navigation. First, their positions and velocities must be known. e position and velocity of any satellite may be parameterized by its Keplerian elements. ese elements are tracked, updated once daily, and made publicly available by the North American Aerospace Defense Command (NORAD) [see North American Aerospace Defense Command, Additional Resources]. However, these elements are dynamic and will deviate from their nominally available val- ues due to several sources of perturbing forces, which include non-uniform Earth gravitational field, atmospheric drag, solar radiation pressure, third-body gravitational forces (e.g., gravity of the Moon and Sun), and general relativity (Vetter, Additional Resources). ese deviations can cause errors in a propagat- ed satellite orbit as high as 3 kilometers if not accounted for with corrections. Second, LEO satellites are not necessarily equipped with an atomic clock, nor are they precisely synchro- nized. Subsequently, their clock error must be known along- side their position and velocities. In contrast to GNSS, where corrections to the orbital elements and clock errors are peri- odically transmitted to the receiver in the navigation message, such orbital element and clock corrections may not be available for LEO satellites; in which case they must be estimated along with the receiver's states. ird, ionospheric delay rates become significant for LEO satellites, particularly the ones transmit- ting in the very high frequency (VHF) band. FIGURE 2 Snapshot of the Starlink LEO constellation. FIGURE 3 Heat map showing the number of visible Starlink LEO satellites above a 5-degree elevation mask. System Number of satellites Frequency band Orbcomm 36 VHF Globalstar 48 S and C Iridium 66 L and Ka OneWeb 882 Ku and Ka Boeing 2956 V and C SpaceX 11943 Ku, Ka, and V Samsung 4600 V Table 1: Existing and future LEO constellations: number of satellite and transmission bands. FIGURE 4 Heat map showing PDOP for the Starlink LEO constellation above a 5-degree elevation mask. FIGURE 5 Heat map showing log 10 [DPDOP] for the Starlink LEO constellation above a 5-degree elevation mask.

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