Conventional (Relative Static) GPS Control Surveying: 18-Geom-B2 Satellite Navigation, May 2015, Q6

Question 6: Conventional (Relative Static) GPS Control Surveying (10 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.

Conventional (relative) static positioning is the classical high-accuracy GNSS technique used to establish and densify geodetic control. Two or more receivers occupy stations simultaneously for an extended session, and the precise baseline vectors between them are computed from carrier-phase double differences and adjusted into a network tied to known control.

Field procedure. Receivers with geodetic (e.g. choke-ring) antennas are set on the stations to be connected and levelled/centred over the marks, with antenna heights carefully measured. They observe the same satellites simultaneously for a session long enough (commonly 30 minutes to several hours, increasing with baseline length) to accumulate strong, changing geometry. Sessions are planned in advance using an almanac so observations fall in windows with adequate satellites and low PDOP. Multiple receivers form several baselines per session, and stations are re-occupied in different sessions so the network contains redundant, independently-observed baselines.

Processing. Each baseline is processed by forming between-receiver and between-satellite (double) differences, which cancel the satellite and receiver clock errors and reduce the atmospheric and orbit errors (Q4); the carrier-phase integer ambiguities are then resolved to yield a fixed, centimetre-or-better baseline vector with its covariance. The full set of baseline vectors is combined in a least-squares network adjustment, constrained to the coordinates of the known control stations, producing adjusted coordinates and a rigorous statistical assessment (error ellipses, residuals).

Accuracy and use. Relative static routinely achieves a few millimetres plus roughly 0.1–1 ppm of baseline length — the highest accuracy available from field GNSS — which is why it is used for first-order geodetic control, densification of the national framework, and any project demanding the best coordinates. In Canada the network is tied to NAD83(CSRS) through the Canadian Active Control System and Canadian Base Network stations, and observations can be submitted to NRCan for processing.

Concept & Theory

Topic. Static carrier-phase relative positioning and network adjustment for control.

Key relations. Double-differenced carrier phase \(\nabla\!\Delta\phi\) with resolved integer ambiguity \(\nabla\!\Delta N\); baseline accuracy \(\approx a\;\text{mm}+b\;\text{ppm}\times L\); least-squares adjustment \(\hat{\mathbf{x}}=(\mathbf{A}^{\mathsf T}\mathbf{P}\mathbf{A})^{-1}\mathbf{A}^{\mathsf T}\mathbf{P}\mathbf{l}\).

Why this works. Long, simultaneous occupation gives the geometry change and redundancy needed to fix integer ambiguities reliably; once fixed, the carrier phase is a millimetre-level ranging observable. Redundant baselines and constrained adjustment detect blunders and distribute residuals rigorously, delivering coordinates with defensible uncertainties.

Common pitfall. Under-observing (too-short sessions or too-weak geometry) so ambiguities fix to the wrong integers, giving a precise but wrong baseline; and mis-measuring the antenna height, which maps directly into the height component.

Source. Leick, GPS Satellite Surveying, ch. 9; NRCan Canadian Geodetic Survey guidelines for GNSS control surveys.

Question 6 of 9: Conventional (Relative Static) GPS Control Surveying

Question 6: Conventional (Relative Static) GPS Control Surveying (10 marks)