A reference station at a known point measures a pseudorange of 20 000 012.50 m to a satellite whose range computed from the known coordinates is 20 000 000.00 m. The pseudorange correction it broadcasts is

0, because the base station is fixed

A surveyor must stake out building corners to about 2 cm and see the result immediately in the field. The most suitable GNSS method is

Long-session static survey post-processed next day

Which of the following statements about GNSS error sources are correct?

The ionosphere is dispersive, so its delay differs between L1 and L2

The troposphere is non-dispersive, so a dual-frequency combination cannot remove its delay

Satellites spread widely across the sky give a lower DOP than satellites bunched together

The ionosphere is dispersive, so its delay differs between L1 and L2

The troposphere is non-dispersive, so a dual-frequency combination cannot remove its delay

Satellites spread widely across the sky give a lower DOP than satellites bunched together

VDOP is normally smaller than HDOP

Which of the following are correctly matched?

GAGAN — a satellite-based augmentation system over India

NavIC — India's regional navigation satellite system

Galileo — the European Union's global navigation satellite system

GAGAN — a satellite-based augmentation system over India

NavIC — India's regional navigation satellite system

Galileo — the European Union's global navigation satellite system

GLONASS — China's global navigation satellite system

GNSS: Principle, Components, Data Collection Methods, DGPS and Errors

This is a section of Part A, the Common Section, of the Geomatics Engineering (GE) paper. Part A's GNSS heading reads “Principle used, Components of GNSS, Data collection methods, DGPS, Errors in observations and corrections”, and this chapter covers exactly that. A receiver measures its range to several satellites from the travel time of their signals and solves for four unknowns — three coordinates and its own clock error — so it needs at least four satellites. The chapter builds the pseudorange and carrier-phase observations; sets out the space, control and user segments and the constellations, including India's NavIC and the GAGAN augmentation; compares static, rapid-static, kinematic, RTK and PPP surveying; explains differential GNSS; and lists every error source with its correction, from the ionosphere (removed with two frequencies) to multipath (removed only by siting), ending with dilution of precision. The numericals are ranges from travel time, clock errors in metres, the ionospheric frequency ratio and DOP × UERE.

1. The principle: ranging from satellites

Each satellite broadcasts its position (the ephemeris) and a time-tagged signal. The receiver measures the signal's travel time Δt and forms the pseudorange P = cΔt. It is “pseudo” because the receiver's cheap clock is offset from satellite time by δt: P = ρ + c·δt_r − c·δt_s + I + T + ε, where ρ is the true geometric range, δt_s the satellite clock error, I and T the ionospheric and tropospheric delays and ε noise and multipath. With (x, y, z) and δt_r unknown, four satellites give four equations — which is why GNSS positioning is trilateration with a clock unknown, not triangulation. A receiver clock error of just 1 µs is c × 10⁻⁶ ≈ 300 m of range.

Code measurements use the pseudo-random code: the GPS C/A code has a chipping rate of 1.023 MHz, a chip about 293 m long, and the P code 10.23 MHz, about 29.3 m, so code ranging is good to decimetres–metres. Carrier-phase measurements track the carrier itself — GPS L1 at 1575.42 MHz (λ ≈ 19.0 cm), L2 at 1227.60 MHz (λ ≈ 24.4 cm), L5 at 1176.45 MHz — and measure the fractional cycle to millimetres, but the whole number of cycles N (the integer ambiguity) is unknown and must be resolved; a loss of lock that changes N is a cycle slip.

⚠️ Three satellites are not enough

Three ranges would fix a point only if the receiver clock were perfect. Because the clock bias is a fourth unknown, a 3D fix needs four satellites; with a known height, three suffice for a 2D fix. Every extra satellite adds redundancy for least squares.

2. Components of GNSS and the constellations

The three segments
Segment	What it is	What it does
Space	the satellites; for GPS a nominal 24 in six orbital planes at about 20 200 km altitude, 55° inclination, period about 11 h 58 min (half a sidereal day)	transmit codes, carriers and the navigation message; carry atomic clocks
Control	monitor stations, a master control station and ground antennas	track the satellites, compute orbits and clock corrections, upload them
User	receivers and antennas, from phones to geodetic receivers	compute position, velocity and time

Global systems: GPS (United States), GLONASS (Russia), Galileo (European Union), BeiDou (China). Multi-constellation receivers see many more satellites, which improves geometry and availability in cities and valleys.
Regional: India's NavIC (IRNSS), with satellites in geostationary and inclined geosynchronous orbits covering India and its surroundings; Japan's QZSS.
Satellite-based augmentation (SBAS) broadcasts corrections and integrity data from geostationary satellites: GAGAN (India), WAAS (United States), EGNOS (Europe).

3. Data collection methods and differential GNSS

Methods, from least to most precise (typical figures)
Method	How	Typical precision
Single-point (absolute, autonomous)	one receiver, code pseudoranges, broadcast orbits	a few metres
Code DGPS	corrections from a reference station applied to code ranges	sub-metre to about a metre
Static (relative, post-processed)	two or more receivers observing carrier phase together for a long session (an hour or more)	millimetres to a centimetre; control networks
Rapid static	shorter sessions (minutes), dual-frequency, short baselines	about a centimetre
Kinematic / stop-and-go	rover moves after the ambiguities are fixed, keeping lock	centimetres
RTK (real-time kinematic), including network RTK from CORS	base sends carrier-phase corrections by radio or internet; rover fixes ambiguities in real time	1–3 cm, instantly; stakeout and topographic survey
PPP (precise point positioning)	one dual-frequency receiver with precise orbits and clocks from a service	centimetres after a long convergence

Differential GNSS (DGPS) exploits the fact that the satellite clock, orbit and atmospheric errors are nearly the same at two nearby receivers. A reference (base) station on a known point computes the true range to each satellite from the coordinates, subtracts it from its measured pseudorange, and broadcasts the difference as a pseudorange correction; the rover applies it. If the base measures 20 000 012.50 m to a satellite whose computed range is 20 000 000.00 m, the correction is −12.50 m. Corrections decorrelate with distance and age, so accuracy falls with baseline length; receiver noise and multipath are local and are not removed.

4. Errors in observations and their corrections; dilution of precision

Error budget
Error	Cause	Correction
Satellite clock	drift of the onboard atomic clock	broadcast clock coefficients; differencing; precise clocks
Orbit (ephemeris)	broadcast position differs from the true one	precise ephemerides; differencing over short baselines
Ionospheric delay	free electrons; dispersive, delay ∝ TEC/f²; largest by day and at solar maximum	dual-frequency ionosphere-free combination removes it (to first order); broadcast model for single-frequency users
Tropospheric delay	neutral atmosphere, dry and wet parts; non-dispersive	models plus mapping functions; the wet part estimated; cannot be removed by two frequencies
Multipath	reflected signals from buildings, water, vehicles	site selection, choke-ring or ground-plane antennas, elevation mask; not removed by differencing
Receiver noise, antenna phase-centre offset, cycle slips	the receiver and antenna	better hardware, antenna calibration, slip detection

Because the ionospheric delay is ∝ 1/f², the delay on L2 is (f₁/f₂)² = (1575.42/1227.60)² = 1.647 times that on L1; a 5.00 m delay on L1 is 8.23 m on L2. The ionosphere-free combination P_IF = (f₁²P₁ − f₂²P₂)/(f₁² − f₂²) cancels it. (Selective Availability, the deliberate degradation of civil GPS accuracy, was switched off in May 2000.)

Dilution of precision (DOP) converts range error into position error: σ_position ≈ DOP × σ_UERE (user equivalent range error). Satellites spread widely across the sky give low DOP; satellites bunched together give high DOP. GDOP (geometry, all four unknowns), PDOP (3D position), HDOP (horizontal), VDOP (vertical) and TDOP (time); PDOP² = HDOP² + VDOP². VDOP is normally larger than HDOP because all satellites are above the horizon. With PDOP = 2.5 and UERE = 4 m, the 3D position error is about 10 m.

🧠 Which errors does differencing remove?

Anything common to both receivers: satellite clock and orbit (fully, for short baselines), ionosphere and troposphere (largely, over short baselines). Anything local to one receiver — its multipath, its noise, its antenna — survives. That one sentence answers most DGPS questions.

Key takeaways

Pseudorange = cΔt; four unknowns (x, y, z, receiver clock) need four satellites; 1 µs of clock error ≈ 300 m.
Space, control and user segments; GPS, GLONASS, Galileo, BeiDou; NavIC regional; GAGAN, WAAS, EGNOS augmentation.
Code ranging gives metres; carrier phase gives millimetres once the integer ambiguity is fixed; static, RTK and PPP are carrier methods.
DGPS cancels errors common to base and rover; multipath and receiver noise remain.
Ionospheric delay ∝ 1/f² and is removed by two frequencies; tropospheric delay is not; position error ≈ DOP × UERE.

Practice questions (14)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

The minimum number of satellites a GNSS receiver needs for a three-dimensional position fix is
1. 4
2. 3
3. 2
4. 6
Show answer
Answer: A — 4
The unknowns are x, y, z and the receiver clock offset, so four pseudoranges are needed. Three would suffice only with a perfect receiver clock, which inexpensive receivers do not have.
A GNSS signal takes 0.07 s to reach the receiver. Taking c = 299 792 458 m/s, the corresponding range, in kilometres (to the nearest kilometre), is ____.
Numerical answer — type the value.
Show answer
Answer: 20985
Range = cΔt = 299 792 458 × 0.07 = 20,985,472 m ≈ 20,985 km, which is consistent with a GPS satellite at about 20 200 km altitude seen away from the zenith.
A receiver clock is in error by 1 microsecond. Taking c = 3 × 10⁸ m/s, the resulting error in a pseudorange, in metres, is ____.
Numerical answer — type the value.
Show answer
Answer: 300
Range error = c·δt = 3 × 10⁸ × 1 × 10⁻⁶ = 300 m. This is why the clock offset cannot be ignored and is solved as the fourth unknown.
Taking c = 299 792 458 m/s, the wavelength of the GPS L1 carrier (1575.42 MHz), in centimetres (to one decimal place), is ____.
Numerical answer — type the value.
Show answer
Answer: 19
λ = c/f = 299 792 458/1 575 420 000 = 0.19029 m = 19.0 cm. The L2 carrier at 1227.60 MHz has λ = 24.4 cm; carrier-phase precision is a small fraction of these wavelengths.
In carrier-phase GNSS positioning, the unknown whole number of wavelengths between satellite and receiver at the start of tracking is called the
1. integer ambiguity
2. cycle slip
3. pseudorange
4. dilution of precision
Show answer
Answer: A — integer ambiguity
The receiver measures only the fractional phase and counts cycles thereafter; the initial integer N is the ambiguity that must be resolved for centimetre results. A cycle slip is a sudden change in that integer when lock is lost.
Which segment of a GNSS computes satellite orbits and clock corrections and uploads them to the satellites?
1. The control segment
2. The space segment
3. The user segment
4. The augmentation segment
Show answer
Answer: A — The control segment
Monitor stations track the satellites and the master control station computes their ephemerides and clock corrections, which ground antennas upload. The space segment only transmits them, and the user segment receives them.
A reference station at a known point measures a pseudorange of 20 000 012.50 m to a satellite whose range computed from the known coordinates is 20 000 000.00 m. The pseudorange correction it broadcasts is
1. −12.50 m
2. +12.50 m
3. −25.00 m
4. 0, because the base station is fixed
Show answer
Answer: A — −12.50 m
Correction = computed range − measured pseudorange = 20 000 000.00 − 20 000 012.50 = −12.50 m. The rover adds it to its own pseudorange from the same satellite, removing the error common to both. The positive sign would double the error instead.
A surveyor must stake out building corners to about 2 cm and see the result immediately in the field. The most suitable GNSS method is
1. RTK
2. Single-point code positioning
3. Code DGPS
4. Long-session static survey post-processed next day
Show answer
Answer: A — RTK
Real-time kinematic uses carrier-phase corrections from a base or network to fix ambiguities on the fly and gives centimetre positions immediately, which stakeout requires. Code methods give decimetres to metres; static is precise but only after post-processing.
The first-order ionospheric delay on the GPS L1 signal (1575.42 MHz) is 5.00 m. The delay on L2 (1227.60 MHz), in metres (to two decimal places), is ____.
Numerical answer — type the value.
Show answer
Answer: 8.23
Delay ∝ 1/f², so I₂ = I₁(f₁/f₂)² = 5.00 × (1575.42/1227.60)² = 5.00 × 1.2833² = 5.00 × 1.6469 = 8.23 m. Using the plain frequency ratio gives 6.42 m. The lower frequency is always delayed more.
A receiver reports PDOP = 2.5, and the user equivalent range error is 4 m. The expected three-dimensional position error, in metres, is ____.
Numerical answer — type the value.
Show answer
Answer: 10
σ_position ≈ PDOP × σ_UERE = 2.5 × 4 = 10 m. DOP is a pure geometry multiplier: the same range errors give a worse position when the satellites are bunched.
For a GNSS fix, HDOP = 1.2 and VDOP = 1.6. The PDOP is ____.
Numerical answer — type the value.
Show answer
Answer: 2
PDOP² = HDOP² + VDOP² = 1.44 + 2.56 = 4.00, so PDOP = 2.0. Adding them directly (2.8) is wrong because the horizontal and vertical components are orthogonal.
Which of the following errors are largely removed by differencing observations between a base and a rover a few kilometres apart?
1. Satellite clock error
2. Orbit (ephemeris) error
3. Ionospheric delay
4. Multipath at the rover
Show answer
Answer: A — Satellite clock error; B — Orbit (ephemeris) error; C — Ionospheric delay
The satellite clock error is identical at both receivers, the orbit error nearly so over a short baseline, and the signals pass through nearly the same ionosphere, so all three largely cancel. Multipath depends on the reflecting surfaces around one antenna and does not cancel.
Which of the following statements about GNSS error sources are correct?
1. The ionosphere is dispersive, so its delay differs between L1 and L2
2. The troposphere is non-dispersive, so a dual-frequency combination cannot remove its delay
3. Satellites spread widely across the sky give a lower DOP than satellites bunched together
4. VDOP is normally smaller than HDOP
Show answer
Answer: A — The ionosphere is dispersive, so its delay differs between L1 and L2; B — The troposphere is non-dispersive, so a dual-frequency combination cannot remove its delay; C — Satellites spread widely across the sky give a lower DOP than satellites bunched together
Ionospheric delay scales as 1/f², which is what the ionosphere-free combination exploits; tropospheric delay is the same at both frequencies and must be modelled; and wide geometry means well-conditioned equations and low DOP. VDOP is normally larger than HDOP, because all visible satellites lie above the receiver and none below.
Which of the following are correctly matched?
1. GAGAN — a satellite-based augmentation system over India
2. NavIC — India's regional navigation satellite system
3. Galileo — the European Union's global navigation satellite system
4. GLONASS — China's global navigation satellite system
Show answer
Answer: A — GAGAN — a satellite-based augmentation system over India; B — NavIC — India's regional navigation satellite system; C — Galileo — the European Union's global navigation satellite system
GAGAN is India's SBAS, broadcasting corrections and integrity information; NavIC (IRNSS) is India's regional system; Galileo is the European Union's. GLONASS is Russia's; China's global system is BeiDou.