18-Geom-B2 Satellite Navigation · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2014 — 3 hours, closed book (approved Casio/Sharp non-programmable calculators only). NINE questions: questions 1–7 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 two short symbolic derivations (Q2 DOP, Q4 double differencing). 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); 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) 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.
GPS positioning methods are best organized along two independent axes: how many receivers are used (single-point/absolute versus relative/differential), and whether the receiver moves during the observation (static versus kinematic). Any real technique is a combination of one choice on each axis, and the choice of observable (code pseudorange versus carrier phase) sets the achievable accuracy.
Single point (absolute / autonomous) positioning. One receiver determines its own position in the global reference frame from code pseudoranges to four or more satellites. It is simple and needs no reference station, but the position carries the full budget of satellite, atmospheric and receiver errors, giving metre-level accuracy (a few metres with modern GPS). Precise Point Positioning (PPP) is the high-accuracy form of single-point positioning, using precise orbit/clock products and carrier phase to reach centimetre level.
Relative (differential) positioning. Two or more receivers observe the same satellites simultaneously and the baseline vector between them is determined by differencing (see Q4). Errors common to both receivers — satellite clock, orbit, and spatially-correlated atmosphere — cancel or reduce, so relative positioning is far more accurate than absolute. With code it gives sub-metre DGPS; with carrier phase and resolved ambiguities it gives centimetre-to-millimetre baselines. This is the workhorse of geodetic surveying.
Static positioning. The receiver(s) remain stationary throughout the observation session. A long occupation (tens of minutes to hours) accumulates a strong, changing satellite geometry that allows reliable carrier-phase ambiguity resolution and averages down random errors, giving the highest precision. Rapid-static is a shortened variant (a few minutes) for shorter baselines with good geometry.
Kinematic positioning. The receiver moves, and a position is produced at every epoch along the trajectory. It requires the carrier-phase ambiguities to be fixed and then kept (or continuously re-fixed) while tracking is maintained. Real-Time Kinematic (RTK) resolves ambiguities on-the-fly and delivers centimetre positions in real time via a data link; post-processed kinematic (PPK) does the same after the fact. Stop-and-go is a hybrid: kinematic between points, with brief static dwells on points of interest.
In practice these combine: absolute + kinematic = navigation and PPP trajectories; relative + static = geodetic control (Q6); relative + kinematic = RTK topographic and construction survey. The Canadian surveyor typically uses relative static or network RTK for control and detail work, and CSRS-PPP for absolute work where no base is available.
