Inside GNSS Media & Research

JUL-AUG 2019

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www.insidegnss.com J U L Y / A U G U S T 2 0 1 9 Inside GNSS 59 to the receiver. Moreover, LEO satellites are not necessar- ily equipped with high-quality atomic clocks. From what is known about the existing LEO constellations, LEO satellites are equipped with oven-controlled crystal oscillators (OCXOs). Practically, the navigating receiver will be equipped with a lower quality oscillator, e.g., a temperature-compensated crys- tal oscillator (TCXO). To visualize the magnitude of the clock errors in the satellite and receiver clocks, Figure 7 depicts the time evolution of the bound of the clock bias and dri of a typical OCXO and a typical TCXO, obtained from the so- called two-state clock model (Brown and Hwang, Additional Resources). It can be seen from Figure 7 that the satellite and receiver clock bias and dri may become very signifi cant; therefore, they must be accounted for appropriately. D. IONOSPHERIC DELAY ERRORS Most broadband LEO constellations reside above the iono- sphere, which in turn will induce delays into their signals. Although LEO satellite signals propagate through the tropo- sphere, its eff ect is less signifi cant compared to ionospheric propagation. e magnitude of the ionospheric delay rate is (i) inversely proportional to the square of the carrier frequen- cy and (ii) proportional to the rate of change of the obliquity factor, which is determined by the time evolution of the sat- ellite's elevation angle. Note that the ionospheric delay rates also depend on the rate of change of the total electron content (TEC) at zenith, denoted by TECV. However, TECV varies much slower than the satellite's elevation angle; hence, its eff ect may be ignored. e eff ect of ionospheric propagation is sig- nifi cant on LEO satellite signals since (i) the high speed of LEO satellites translates into very fast changing elevation angles, as shown in Figure 8 and (ii) some of the existing LEO satellites transmit in the VHF band where the signals experience very large delay rates. e aforementioned factors result in large ionospheric delay rates, as shown in Figure 9 for 7 Orbcomm satellites over a 100-minute period. In order to visualize the eff ect of (i) the satellite position and velocity errors, (ii) the clock dri error, and (iii) the ionospheric delay rates, the residual error between the measured pseudor- ange rate and the pseudorange rate estimated from the satellite position and velocity obtained from TLE fi les and SGP4 are plot- ted in Figure 10 for 2 Orbcomm satellites (FM 108 and FM 116). STAN Framework To exploit LEO satellite signals for navigation, their states must be known. Unlike GNSS satellites that periodically transmit accurate information about their positions and clock errors, such information about LEO satellites may be unavailable. e STAN framework addresses this by extracting pseudorange and Doppler measurements from LEO satellite to aid the vehi- cle's INS, while simultaneously tracking the LEO satellites. e STAN framework employs an extended Kalman fi lter (EKF) to simultaneously estimate the vehicle's states with the LEO satel- lites' states. Figure 11 depicts the STAN framework. Simulation Results is section presents simulation results obtained with a real- istic simulation environment demonstrating UAVs navigating via the LEO-aided INS STAN framework without GNSS sig- nals. e fi rst subsection evaluates the achieved performance from current LEO constellations (Globalstar, Orbcomm, and Iridium), while the second subsection evaluates the achieved performance with an upcoming LEO constellation: Starlink. A. UAV SIMULATION WITH THE GLOBALSTAR, ORBCOMM, AND IRIDIUM LEO CONSTELLATIONS A UAV was equipped with (i) a tactical-grade IMU, (ii) GPS and LEO satellite receivers, and (iii) a pressure altimeter. e UAV FIGURE 9 Ionospheric delay rates (expressed in m/s) for 7 Orbcomm satellites over a 100-minute period. Each color corresponds to a diff erent Orbcomm LEO satellite. FIGURE 10 Residual errors showing the eff ect of (i) satellite position and velocity errors, (ii) clock errors, and (iii) ionospheric delay rates for 2 Orbcomm LEO satellites. FIGURE 11 LEO-aided INS STAN framework.

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