Question 4 of 8: Establishing a Control Network by Static GNSS Baseline Observations

Question 4: Establishing a Control Network by Static GNSS Baseline Observations (15 marks)

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.

Establishing engineering control by static GNSS proceeds through four stages that mirror the four aspects the question names: design the network on paper, observe the baselines in the field with simultaneous static occupations, process each baseline into a vector with its covariance, and adjust the whole set of vectors by least squares onto the existing datum. The technique is conventional (relative) static positioning — two or more receivers occupy stations at the same time and the precise inter-station baseline vectors are recovered from carrier-phase double differences.

1 — Network design. Before any fieldwork, lay out the geometry: fix the project’s coordinate/datum requirements, select and monument the new station marks at sites with a clear sky view and low multipath, and connect them to at least two (preferably more) existing higher-order control marks so the network is tied to the datum and orientation. Design the baselines so that every new station is determined by redundant, independent baselines (closed loops rather than open spurs), because redundancy is what lets the later adjustment detect blunders and give realistic uncertainties. Plan the observing sessions from a satellite-visibility (almanac) prediction so each occupation falls in a window with enough satellites and low PDOP, and specify session length appropriate to baseline length and required accuracy.

2 — Baseline observations. In the field, set geodetic (e.g. choke-ring) antennas over the marks, centre and level them, and measure the antenna height carefully (this maps directly into the height component). Receivers observe the same satellites simultaneously for the planned session (commonly 30 minutes to several hours, increasing with baseline length) at a common sampling interval and a fixed elevation mask. Multiple receivers form several baselines per session; stations are re-occupied in different sessions so that the network accumulates independent, redundant observations rather than a single measurement of each line.

3 — Baseline processing. Each occupied pair is processed into a baseline vector \((\Delta X,\Delta Y,\Delta Z)\) by forming between-receiver and between-satellite (double) differences, which cancel the satellite and receiver clock errors and greatly reduce the orbit and spatially-correlated atmospheric errors (Q6). The carrier-phase integer ambiguities are then resolved to obtain a fixed, centimetre-or-better vector together with its covariance matrix. Solution quality is checked (fixed vs float, RMS, ratio test) and loop closures are examined before the vectors are accepted.

4 — Baseline network adjustment. The full set of accepted baseline vectors, each with its covariance, is combined in a least-squares network adjustment. A minimally-constrained (free) adjustment first tests the internal consistency of the observations and detects blunders through the residuals and loop misclosures; a fully-constrained adjustment then holds the known control coordinates fixed and produces the adjusted coordinates of the new stations with a rigorous statistical assessment — standard deviations, relative and absolute error ellipses, and a variance-factor check. In Canada the network is tied to NAD83(CSRS) through the Canadian Active Control System / Canadian Base Network, and data may be submitted to NRCan for processing.