Читать книгу Global Navigation Satellite Systems, Inertial Navigation, and Integration - Mohinder S. Grewal - Страница 70

Refer to Appendix B for coordinate system definitions and to Section B.3.10 for satellite orbit equations.

1 2.1 Which of the following coordinate systems is not rotating?North–east–down (NED)East–north–up (ENU)Earth‐centered, Earth‐fixed (ECEF)Earth‐centered inertial (ECI)Moon‐centered, moon fixed

2 2.2 Show that the 3 × 3 identity matrix. (Hint: ).

3 2.3 Rank VDOP, HDOP, and PDOP from smallest (best) to largest (worst) under normal conditions:VDOP ≤ HDOP ≤ PDOPVDOP ≤ PDOP ≤ HDOPHDOP ≤ VDOP≤PDOPHDOP ≤ PDOP ≤ VDOPPDOP ≤ HDOP ≤ VDOPPDOP ≤ VDOP ≤ HDOP

4 2.4 UTC time and the GPS time are offset by an integer number of seconds (e.g. 16 seconds as of June 2012) as well as a fraction of a second. The fractional part is approximately.0.1–0.5 s1–2 ms100–200 ns10–20 ns

5 2.5 Derive equations (2.41) and (2.42).

6 2.6 For the following GPS satellites, find the satellite position in ECEF coordinates at t = 3 seconds. (Hint: See Appendix B.) Ω0 and θ0 are given below at time t0 = 0:Ω0 (°)θ0 (°)(a)32668(b)2634

7 2.7 Using the results of the previous problem, find the satellite positions in the local reference frame. Reference should be to the COMSAT facility in Santa Paula, California, located at 32.4° latitude, −119.2° longitude. Use coordinate shift matrix S = 0. (Refer to Section B.3.10.)

8 2.8 Given the following GPS satellite coordinates and pseudoranges:SatelliteΩ0 (°)θ0 (°)ρ (m)1326682.324 × 1072263402.0755 × 10731461982.1103 × 1074862712.3491 × 107Find the user's antenna position in ECEF coordinates.Find the user's antenna position in locally level coordinates referenced to 0° latitude, 0° longitude. Coordinate shift matrix S = 0.Find the various DOPs.

9 2.9 Given two satellites in north and east coordinateswith pseudorangesand starting with an initial guess of xest, yest, find the user's antenna position.

10 2.10 A satellite position at time t = 0 is specified by its orbital parameters as Ω0 = 92.847°, θ0 = 135.226°, α = 55°, R = 26 560 000 m.Find the satellite position at one second, in ECEF coordinates.Convert the satellite position from (a) with user atfrom WGS84 (ECEF) to ENU coordinates with origin at