GPS/GNSS

Global Navigation Satellite Systems (GPS, GLONASS, Galileo, BeiDou, NavIC) give positions anywhere on Earth. Learn how ranging and trilateration work, error sources, DOP, differential and RTK positioning, static surveys, datums, ellipsoidal vs orthometric heights and the geoid.

Satellites broadcasting precise time signals let a receiver compute its distance to each satellite; with four or more, it solves for position and clock error. A phone gets a few metres; survey receivers using carrier phase and corrections get centimetres.

GNSS has transformed control surveys, mapping, machine guidance and monitoring.

An analogy

Like finding your location from how long thunder takes to arrive from several known lightning strikes — each delay gives a distance, and the distances intersect at your position.

How GNSS works

Each satellite transmits its orbit and time. The receiver measures travel time (≈ 0.07 s from 20 000 km), converts it to distance, and solves for 3D position plus its own clock offset — needing at least four satellites.

Errors and DOP

Error sources: satellite clocks/orbits, ionosphere and troposphere delays, multipath (reflections), receiver noise. Satellite geometry multiplies range errors: DOP < 2 is excellent, > 6 poor. Open sky and good mask angles matter.

Differential, RTK and static

A base station at a known point computes corrections for nearby rovers (DGPS: sub-metre; RTK carrier-phase: 1–2 cm in real time). Network RTK/CORS services replace personal bases. Static sessions (30 min–hours) with post-processing give mm-level control.

Datums, projections and heights

GNSS gives coordinates on a global datum (WGS84/ITRF). Surveys transform them to local datums and map projections (UTM). Heights from GNSS are ellipsoidal (h); engineering needs orthometric heights (H, above the geoid) via H = h − N using geoid models — ignoring N causes errors of tens of metres.

Formulas

• Range: ρ = c · Δt
• Position accuracy: σ_pos ≈ PDOP × σ_range (UERE)
• Heights: H = h − N
• Baseline accuracy (typical): ± (5 mm + 1 ppm × baseline)

Worked example: Range from travel time

Given: Signal travel time 0.07 s

Find: Distance to satellite.

• ρ = 3 × 10⁸ × 0.07 = 2.1 × 10⁷ m

Answer: ≈ 21 000 km

Worked example: Orthometric height

Given: GNSS ellipsoidal height h = 150.00 m; Geoid undulation N = −52.30 m

Find: Orthometric height H.

• H = h − N = 150.00 − (−52.30) = 202.30 m

Answer: 202.30 m above MSL (geoid)

Common mistakes

• Wrong: Using ellipsoidal heights as levels. — Right: Convert with a geoid model: H = h − N.
• Wrong: Surveying under trees or near tall buildings. — Right: Multipath and poor DOP degrade results — use total stations there.

Applications

• Control networks: Static GNSS for project control and CORS-based surveys.
• Construction: RTK stake-out and machine guidance on earthworks and paving.
• Monitoring & mapping: Landslide and structure monitoring; mobile mapping and drones.

Key takeaways

• Ranges from timing → trilateration (≥ 4 sats).
• Accuracy ≈ DOP × range error; use differential methods.
• Static for control, RTK for real-time work.
• Convert heights: H = h − N.

Going further

• PPP: Precise Point Positioning uses precise orbits/clocks for cm accuracy without a local base.
• Multi-constellation: Combining GPS, Galileo, BeiDou, GLONASS and NavIC improves availability and DOP.
• Integrity & spoofing: Critical applications need integrity monitoring and anti-spoofing.