Position, Navigation, and Timing Technologies in the 21st Century

9 Chapter 43aFigure 43.1 The 1419 operational satellites in orbit in 2016 (Reid [4]).Figure 43.2 Radiation dosage in silicon over a five‐year mission as a functi...Figure 43.3 The Transit “bird cage” constellation. This typically consisted ...Figure 43.4 The 66 satellite Iridium constellation in low Earth orbit (LEO) ...Figure 43.5 The OneWeb constellation of 648 satellites (Reid [4]).Figure 43.6 Slant range to the satellite.Figure 43.7 Slant range and spreading loss as a function of orbital altitude...Figure 43.8 Comparison of signal‐to‐noise ratio for Satelles Satellite Time ...Figure 43.9 Satellite mean motion and orbital period as a function of altitu...Figure 43.10 Comparison of medium and low Earth orbit (LEO) satellite distan...Figure 43.11 Satellite footprint radius as a function of orbital altitude an...Figure 43.12 Number of satellites in view as a function of latitude for the ...Figure 43.13 Iridium‐based STL test locations. These are indoor and deep att...Figure 43.14 Iridium‐based STL timekeeping results based on data from a 30‐d...Figure 43.15 Iridium‐based STL geolocation performance. This shows the conve...Figure 43.16 Roadmap to an LEO navigation system. The user position error is...Figure 43.17 Comparison of 98th percentile geometric dilution of precision (...Figure 43.18 Comparison of user HDOP (95th percentile) as a function of lati...Figure 43.19 Comparison of user vertical dilution of precision (VDOP) (95th ...Figure 43.20 Radiation dosage in silicon over a five‐year mission in LEO and...

10 Chapter 43bFigure 43.21 Existing and future LEO satellite constellations (Kassas et al....Figure 43.22 Residual errors showing the effect of (i) satellite position an...Figure 43.23 SGP4 (a) position and (b) velocity errors. (Kassas et al. [6])....Figure 43.24 Time evolution of 1 − σ bounds of (a) clock bias and...Figure 43.25 (a) Skyplot showing the trajectory of an Orbcomm LEO satellite ...Figure 43.26 Simulated delays in meters due to ionosphere and troposphere pr...Figure 43.27 Ionospheric delay rates (expressed in m/s) for seven Orbcomm sa...Figure 43.28 Orbcomm LEO satellite constellation (Morales et al. [4]).Figure 43.29 Navigation receiver: (a) Each channel is first extracted then f...Figure 43.30 Snapshot of the Orbcomm spectrum (Kassas et al. [6]).Figure 43.31 Outputs of Orbcomm receiver: (a) estimated Doppler, (b) carrier...Figure 43.32 Visualization of proposed LEO Starlink satellites (Ardito et al...Figure 43.33 Base/rover CD–LEO framework. The base, which can be a stationar...Figure 43.34 LEO‐aided INS STAN framework (Morales et al. [4]).Figure 43.35 Logarithm of the PDOP as a function of time at two positions on...Figure 43.36 Heat map of log 10[PDOP] for Orbcomm constellation and an 8 min ...Figure 43.37 Heat map of log 10[PDOP] for the Orbcomm constellation and an 8 ...Figure 43.38 Snapshot of the Starlink LEO constellation (Kassas et al. [6])....Figure 43.39 Heat map showing a snapshot of the number of visible Starlink L...Figure 43.40 Heat map showing PDOP for the Starlink LEO constellation above ...Figure 43.41 Heat map showing log 10[DPDOP] for the Starlink LEO constellatio...Figure 43.42 UAV simulation environment with the Globalstar, Orbcomm, and Ir...Figure 43.43 UAV simulation results with the Globalstar, Orbcomm, and Iridiu...Figure 43.44 UAV simulation environment with the Starlink LEO constellation....Figure 43.45 UAV simulation results with the Starlink LEO constellation. (a)...Figure 43.46 Experimental results showing (a) the expected and measured Dopp...Figure 43.47 Base/rover experimental setup of the CD–LEO framework (Khalife ...Figure 43.48 (a) Sky plot showing the geometry of the two Orbcomm satellites...Figure 43.49 Trajectory of the two Orbcomm satellites during the experiment,...Figure 43.50 Hardware and software setup for the ground vehicle experiment (A...Figure 43.51 (a) Skyplot of the Orbcomm satellite trajectories. (b) Doppler ...Figure 43.52 Results of the ground vehicle experiment. (a) Orbcomm satellite...Figure 43.53 Hardware and software setup for the UAV experiment (Morales et ...Figure 43.54 (a) Skyplot of the Orbcomm satellite trajectories. (b) Doppler ...Figure 43.55 Results of the UAV experiment. (a) Orbcomm satellite trajectori...

11 Chapter 44Figure 44.1 Simplified schematic of a strapdown inertial navigation system (...Figure 44.2 A simple navigation problem to illustrate the effects of errors ...Figure 44.3 Effect of initial condition errors on the navigation error versu...Figure 44.4 Outputs of an ideal sensor and a practical sensor are plotted ve...Figure 44.5 Effect of bias and noise for accelerometers and gyroscopes on th...Figure 44.6 Rotations around the north or east axes, or leveling errors, cau...Figure 44.7 Family tree for accelerometer mechanizations. All types require ...Figure 44.8 As an atom absorbs a photon, the momentum of the photon slows th...Figure 44.9 Three pairs of counterpropagating optical beams combined with a ...Figure 44.10 Schematic diagram of an accelerometer using the displacement of...Figure 44.11 Schematic diagram of an open‐loop pendulous accelerometer using...Figure 44.12 Schematic diagram of a pendulous accelerometer using the change...Figure 44.13 Schematic diagram of a pendulous accelerometer with a servo tha...Figure 44.14 Schematic diagram of a PIGA. The PIGA uses the torque of a gyro...Figure 44.15 A family tree for rotation sensing mechanizations commonly used...Figure 44.16 Schematic diagram of a single‐degree‐of‐freedom gyroscope. Cons...Figure 44.17 Schematic diagram of a two‐degree‐of‐freedom gyroscope. At oper...Figure 44.18 Larmor precession of an atom in an external magnetic field. The...Figure 44.19 Schematic diagram of an NMR gyroscope. A mixture of noble gas a...Figure 44.20 Schematic view of a vibrating string gyroscope that uses the de...Figure 44.21 Schematic view of a vibrating shell gyroscope. The position of ...Figure 44.22 Schematic view of light propagating in opposite directions arou...Figure 44.23 Schematic view of an IFOG. Light from the source, S, is coupled...Figure 44.24 Schematic view of a high‐performance IFOG using an integrated o...Figure 44.25 Schematic view of a RLG, where the frequency difference between...Figure 44.26 Schematic view of a passive ring resonator gyroscope that locks...Figure 44.27 Schematic diagram of an atomic interferometer. A cloud of atoms...Figure 44.28 Schematic diagram of a light pulse atom interferometer. The ato...Figure 44.29 Schematic diagram of a light pulse atom interferometer using du...

12 Chapter 45Figure 45.1 Left: Plan view of a 3‐axis capacitive LIS3DH accelerometer made...Figure 45.2 Optical plan view of the MEMSIC 2‐axis thermal accelerometer. Th...Figure 45.3 Scanning electron microscope (SEM) tilt‐view image of an STMicro...Figure 45.4 Example of a vibratory ring MEMS silicon gyroscope with inductiv...Figure 45.5 Left: Finite element model showing the gyroscope operating conce...Figure 45.6 Examples of commercially available MEMS IMUs. Left: Consumer‐gra...

13 Chapter 46aFigure 46.1 Position drift of inertial navigation that is caused by bias in ...Figure 46.2 Position performance of a naïve GNSS/INS integrated mechanizatio...Figure 46.3 Complementary estimation for GNSS/INS integration. Differences b...Figure 46.4 Main principle of inertial navigation. Acceleration is integrate...Figure 46.5 High‐level block diagram of strapdown INS mechanization. System ...Figure 46.6 Coning motion: the angular rate vector precesses around a certai...Figure 46.7 Example implementation of inertial navigation algorithm in MATLA...Figure 46.8 Example realization of the first‐order Gauss–Markov process. Its...Figure 46.9 Due to errors in gyro measurements, the body‐frame is computatio...Figure 46.10 Loosely coupled GNSS/INS mechanization. GNSS navigation solutio...Figure 46.11 Estimate of relative position between two GNSS antennas can be ...Figure 46.12 Test trajectory applied for the 2D simulation of a loosely coup...Figure 46.13 INS error estimation performance for the 2D simulation scenario...Figure 46.14 Two GNSS outage scenarios are implemented to illustrate the inf...Figure 46.15 GNSS/INS position performance for two outage scenarios. INS dri...Figure 46.16 Tightly coupled GNSS/INS implementation. GNSS measurements (suc...Figure 46.17 Satellite and receiver geometry involved in formulation of rang...Figure 46.18 Deeply integrated GNSS/INS implementation. Deep integration ext...Figure 46.19 Example implementation of deeply integrated GPS/INS system for ...Figure 46.20 Example implementation of deep GPS/INS integration that is cons...Figure 46.21 GNSS/inertial synchronization approach: GNSS and IMU measuremen...Figure 46.22 Example implementation of synchronization module for time stamp...Figure 46.23 Time‐synchronized processing of GNSS and inertial measurements....Figure 46.24 Measurement quality monitoring for detection and exclusion of o...Figure 46.25 Example test environments in San Francisco, California. Typical...Figure 46.26 Typical performance of GNSS position solution in downtown envir...Figure 46.27 Performance of loosely coupled GNSS/INS mechanization in urban ...Figure 46.28 Performance of tightly coupled GNSS/INS mechanization in urban ...Figure 46.29 Performance of tightly coupled GNSS/INS mechanization; consumer...Figure 46.30 Performance of tightly coupled GNSS/INS mechanization with cons...Figure 46.31 Position solution of multi‐sensor fusion mechanization that com...Figure 46.32 Second test example of multi‐sensor solution that fuses consume...Figure 46.33 Example test environment for demonstrating the capabilities of ...Figure 46.34 GPS‐only solution in dense forestry areas: very sparse position...Figure 46.35 Position solution of the deeply integrated GPS/INS implementati...Figure 46.36 Trajectory reconstruction results without measurement quality m...Figure 46.37 Performance of the tightly coupled GPS/INS implementation. Cont...