18-Geom-B2 Satellite Navigation · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2015 — 3 hours, closed book (approved Casio/Sharp non-programmable calculators only). NINE questions: Q1–Q7 are mandatory (80 marks) and the candidate answers one of Q8/Q9 (20 marks) for a total of 100. This is a theory paper — answers are in essay form, with one short symbolic derivation (Q4 double differencing) and one counting problem (Q5, measurements vs unknowns). All nine questions, including both Q8 and Q9, are solved below for completeness.
Reference texts: Hofmann-Wellenhof, Lichtenegger & Wasle, GNSS — Global Navigation Satellite Systems (Springer, 2008); Leick, Rapoport & Tatarnikov, GPS Satellite Surveying (4th ed., Wiley, 2015); Kaplan & Hegarty, Understanding GPS/GNSS: Principles and Applications (3rd ed., Artech House); Groves, Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems (2nd ed., Artech House, 2013) for Q9; Natural Resources Canada — Canadian Geodetic Survey (CSRS-PPP service, Canadian Active Control System). Canadian frame throughout (NAD83(CSRS), NRCan reference products).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Global Navigation Satellite Systems fall into global constellations (a full complement of satellites, nominally 24 or more in Medium Earth Orbit, giving worldwide coverage) and regional systems plus space-based augmentation systems (SBAS) that serve a limited area. At the time of this examination two global systems are fully operational, two more are in active deployment, and several regional systems are being built.
Fully operational (global). GPS (NAVSTAR), operated by the United States, has been at Full Operational Capability since 1995 with a nominal 24-satellite (currently ~31-satellite) constellation. GLONASS, operated by the Russian Federation, was restored to a full 24-satellite constellation in 2011. These two are, on their own, globally complete and continuously usable.
Under development (global). Galileo (European Union, civil-controlled) has completed In-Orbit Validation and is launching toward its 30-satellite constellation; BeiDou/Compass (China) is operational regionally over Asia-Pacific and is expanding to a global BeiDou-3 constellation. Regional / augmentation. QZSS (Japan, quasi-zenith orbits) and IRNSS/NavIC (India) are regional; the SBAS — WAAS (North America), EGNOS (Europe), MSAS (Japan), GAGAN (India) — broadcast wide-area differential corrections and integrity from geostationary satellites. For Canadian users GPS+GLONASS is the operational multi-constellation backbone, with WAAS augmentation available nationwide.
GPS is organized into three functional segments — space, control and user — each with a distinct task, that together deliver a positioning, velocity and timing (PVT) service.
Space segment. The satellites themselves — nominally 24 (currently ~31) in six orbital planes at about 20 200 km altitude with a ~12-hour period. Their task is to generate and continuously broadcast the ranging signals: the L-band carriers modulated with the C/A and P(Y) ranging codes and the navigation message (satellite ephemeris, clock corrections, almanac and health). Each satellite carries highly stable atomic (rubidium/cesium) clocks that provide the precise time reference on which ranging depends.
Control segment. The ground infrastructure — the Master Control Station (at Schriever AFB), globally distributed monitor stations, and ground antennas. Its task is to monitor and manage the constellation: the monitor stations continuously track every satellite and measure its signal; the Master Control Station uses these observations to compute precise orbit (ephemeris) and clock corrections, predict them forward, and upload the refreshed navigation message to each satellite through the ground antennas. It also commands manoeuvres, manages satellite health and maintains system time (GPS Time).
User segment. The receivers — from survey-grade instruments to navigation and timing devices. Their task is to receive and exploit the broadcast signals: acquire and track the satellites, measure pseudoranges (and carrier phase and Doppler), decode the navigation message, and solve for the user’s position, velocity and time. The user segment is passive — it only listens — which is what allows an unlimited number of simultaneous users.