18-Geom-B3 Networks and Precise Engineering Surveys · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: Closed-book, 3 hours, calculator permitted. TEN questions constitute a complete paper — Part A: all of #1–#8; Part B: one of #9/#10; Part C: one of #11/#12. All twelve questions are solved here for completeness. Most answers are essay-format; Q5, Q6 and Q9 carry short verified numeric illustrations.
Reference texts: Wolf, Ghilani & De Blij, Elementary Surveying: An Introduction to Geomatics (15th ed., Pearson); Mikhail & Gracie, Analysis and Adjustment of Survey Measurements (Van Nostrand, 1981); Kavanagh & Slattery, Surveying with Construction Applications; Hofmann-Wellenhof, Lichtenegger & Wasle, GNSS (Springer, 2008); Kahmen & Faig, Surveying (de Gruyter); Chrzanowski et al. on deformation analysis; USACE Structural Deformation Surveying (EM 1110-2-1009); ISO 17123 field-test procedures. Canadian frame throughout (NAD83(CSRS), CGVD2013).
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.
Conventional (relative) static positioning is the classical, highest-precision GNSS technique for establishing geodetic control. Two or more receivers occupy the endpoints of a baseline simultaneously and stationary for an extended session, recording dual-frequency carrier-phase (and code) data, which are later post-processed to give the vector between the stations to millimetre–centimetre precision.
Field method. One receiver is set on a station of known coordinates (the base); one or more rovers occupy the unknown points. Antennas are centred and levelled over the marks, antenna heights measured carefully (a major error source), and all receivers log data at a common epoch interval (e.g. 15 or 30 s) for a session whose length is chosen from the baseline length and the required precision — typically 20 min to a few hours; long or high-precision baselines need one or more hours so the satellite geometry changes enough to fix ambiguities and average out multipath and residual atmosphere. A minimum of four common satellites (well distributed, low PDOP) must be tracked; more is better.
Processing. Data are combined into double differences, cancelling the satellite and receiver clock errors; the integer carrier-phase ambiguities are resolved (fixed); and the baseline vector $\Delta X,\Delta Y,\Delta Z$ is estimated by least squares. Multiple baselines are then combined in a network adjustment, tied to the national frame (NAD83(CSRS)) through Canadian Active Control System stations or a CSRS-PPP-derived control point, with loop-closure and repeat-baseline checks providing redundancy and reliability.
Characteristics. It delivers the best GNSS precision (a few mm + ~1 ppm relative) and is the standard for control densification, deformation networks and geodetic ties. Its cost is time: sessions are long and results are not real-time. It requires an open sky and benefits from good geometry and long observation to fix ambiguities reliably. Rapid-static is a shortened variant (minutes) for short baselines using fast ambiguity-resolution algorithms, trading some robustness for productivity.
