Satellite Geodesy and GNSS - Cheat Sheet
Your last-minute revision companion for Satellite Geodesy and GNSS. Covers positioning principles, observables, error sources, DOP, differential methods, RTK, reference frames, and all exam-critical formulas. Master this in 30 minutes before your exam.
GNSS Positioning Principle & Fundamentals
Formulas
ρ = c × Δt
Meaning
ρ = pseudorange (m); c = speed of light (299,792,458 m/s); Δt = signal travel time (s)
Watch out
Δt is in SECONDS, not milliseconds. Common error: forgetting c is ~3×10⁸ m/s exactly (use 299,792,458 m/s for precision)
When to use
Calculate pseudorange from satellite signal travel time; fundamental to all GNSS positioning
X = X_sat + c × (Δt_sat - Δt_receiver)
Meaning
Solve receiver position (X, Y, Z) and clock bias using satellite ephemeris and pseudorange measurements
Watch out
Four unknowns (X, Y, Z, Δt_receiver) require MINIMUM 4 satellites; three satellites cannot solve a 3-D fix
When to use
Conceptual formulation of trilateration with clock bias correction
n_min = 4
Meaning
Minimum number of satellites for 3-D positioning with clock bias correction
Watch out
Three satellites give only 2-D fix (height constrained). The fourth unknown is RECEIVER CLOCK BIAS, not a satellite
When to use
Any exam question asking 'how many satellites do you need for a 3-D fix?'
Common values
Value
299,792,458 m/s (≈ 3×10⁸ m/s)
Symbol
c
Quantity
Speed of light
Value
~20,200 km (semi-major axis a ≈ 26,560 km)
Symbol
h_GPS
Quantity
GPS orbital altitude
Value
~0.067 s (to ground from geosynchronous altitude)
Symbol
Δt_GPS
Quantity
Signal travel time (GPS)
Value
4
Symbol
n_min
Quantity
Minimum satellites for 3-D fix
Important facts
- GNSS is based on TRILATERATION: measure ranges to satellites of KNOWN POSITION to solve receiver position
- Speed of light c = 299,792,458 m/s (exact, by definition)
- A 3-D fix requires MINIMUM 4 satellites (3 for position, 1 for clock bias)
- Pseudorange accuracy is typically METRES (coarse); achieved in seconds to minutes
- GPS satellites orbit at ~20,200 km altitude; signal travel time ~0.067 s
- GNSS equations are NONLINEAR; usually solved by least-squares adjustment when using >4 satellites
- Dilution of Precision (DOP) is a dimensionless geometry-only factor; accuracy = DOP × measurement error
Key definitions
Pseudorange
Example
If signal takes 0.067 s, pseudorange ≈ 20,086 km (consistent with GPS orbital altitude ~20,200 km)
Range measured by multiplying receiver clock time difference by the speed of light; called 'pseudo' because receiver clock is not synchronized with satellite atomic clock.
Trilateration
Example
In 2-D: three circles intersect at a point; in 3-D with clock bias: four spheres intersect at a unique point
Geometric method of determining position by measuring distances from three or more known reference points (satellites).
Receiver Clock Bias (Δt_receiver)
Example
Even with inexpensive quartz clocks, this bias (typically microseconds) translates to hundreds of metres of range error without correction
The systematic error in the receiver's internal clock relative to satellite atomic time; solved as a fourth unknown in GNSS positioning.
Ephemeris
Example
GPS satellites broadcast their own ephemeris data every 2 hours; used to compute X_sat, Y_sat, Z_sat
Precise 3-D position and velocity of each satellite at a given time; broadcast by the satellite and must be known for positioning calculations.
Diagrams to know
- Receiver and four satellites in 3-D space showing sphere intersection
- Pseudorange vs travel time relationship (ρ vs Δt graph)
- Receiver clock bias effect on position solution
GNSS Observables: Pseudorange & Carrier Phase
Formulas
ρ_pseudorange = c × Δt
Meaning
Pseudorange (m); speed of light c; signal travel time Δt (s)
Watch out
Pseudorange is COARSE (~1 m noise) because it depends on receiver clock accuracy; not suitable for precise work alone
When to use
Single-frequency pseudorange positioning; DGPS and standard GPS receivers
Φ_carrier = (f/c) × ρ + N × λ + errors
Meaning
Φ = carrier phase (cycles); f = frequency; ρ = true range; N = integer ambiguity (cycles); λ = wavelength (m)
Watch out
Ambiguity N is UNKNOWN integer; must be resolved (fixed) to use carrier phase. This is the bottleneck of precise GNSS
When to use
Precise GNSS positioning (geodetic surveys, RTK); carrier-phase observables
λ = c / f
Meaning
Wavelength (m); c = speed of light; f = frequency (Hz)
Watch out
GPS L1 = 1575.42 MHz → λ_L1 ≈ 0.19 m; L2 = 1227.60 MHz → λ_L2 ≈ 0.24 m
When to use
Relate frequency to wavelength for L-band GNSS frequencies
Precision = λ / N_observable
Meaning
Carrier phase precision (m); wavelength λ; cycling ambiguity N
Watch out
Carrier phase is PRECISE but AMBIGUOUS; pseudorange is COARSE but UNAMBIGUOUS
When to use
Compare pseudorange (~1 m) vs carrier phase (~mm) accuracy
Common values
Value
1575.42 MHz
Symbol
f_L1
Quantity
GPS L1 frequency
Value
0.1905 m ≈ 19.05 cm
Symbol
λ_L1
Quantity
GPS L1 wavelength
Value
1227.60 MHz
Symbol
f_L2
Quantity
GPS L2 frequency
Value
0.2442 m ≈ 24.42 cm
Symbol
λ_L2
Quantity
GPS L2 wavelength
Value
1–5 m (1-σ)
Symbol
σ_pseudorange
Quantity
Pseudorange noise (typical)
Value
2–5 mm (1-σ)
Symbol
σ_phase
Quantity
Carrier phase noise (typical)
Important facts
- PSEUDORANGE: coarse observable (~1 m precision), unambiguous, from travel time measurement
- CARRIER PHASE: precise observable (~mm precision), ambiguous (integer ambiguity must be resolved)
- GPS L1 frequency = 1575.42 MHz (wavelength ≈ 0.19 m)
- GPS L2 frequency = 1227.60 MHz (wavelength ≈ 0.24 m)
- Dual-frequency receivers can form ionosphere-free combinations to remove first-order iono delay
- Ambiguity resolution is the key to cm-level positioning; without it, carrier phase is useless
- Cycle slips (loss of lock) cause ambiguity jumps; must be detected and repaired
Key definitions
Carrier Phase Observable
Example
GPS L1 carrier phase at 1575.42 MHz (λ ≈ 0.19 m); one cycle = 0.19 m of range
Count of whole wavelengths plus fractional phase from satellite to receiver; precision ~mm but requires integer ambiguity resolution.
Integer Ambiguity (N)
Example
With 4 satellites × 2 frequencies, solve 8 ambiguities; fixing these reduces error from metres to centimetres
Unknown number of complete wavelengths between satellite and receiver at the start of tracking; resolved in post-processing or real-time via RTK.
Dual-Frequency GNSS
Example
Single-frequency: ambiguity fixing takes minutes; dual-frequency: seconds to minutes
Receiver tracking two frequencies (e.g., GPS L1 and L2) to remove ionospheric delay and resolve ambiguities faster.
Diagrams to know
- Pseudorange vs Carrier Phase observable accuracy vs time
- Integer ambiguity effect on solution convergence
- L1 and L2 frequency spectrum diagram
Error Sources in GNSS
Formulas
Total Error = Clock Error + Orbit Error + Iono Delay + Tropo Delay + Multipath + Receiver Noise
Meaning
All systematic and random errors contribute to pseudorange/phase bias
Watch out
Errors are NOT always additive; correlations (especially between iono and tropo) exist
When to use
Understand error budget and why differential GNSS removes common errors
Iono Delay = 40.3 × (TEC / f²)
Meaning
TEC = Total Electron Content (electrons/m²); f = frequency (Hz); delay in metres
Watch out
Single-frequency receivers see ~5–50 m error on L1 alone; dual-frequency reduces this to ~0.1 m
When to use
Explain why dual-frequency receivers form ionosphere-free combinations
Tropo Delay ≈ 2.5 m at zenith (dry component)
Meaning
Depends on temperature, pressure, humidity; increases with lower elevation angle
Watch out
Tropo is FREQUENCY-INDEPENDENT (same for L1 and L2); cannot remove by dual-frequency like iono
When to use
Estimate systematic delay for low-elevation satellites; corrected using models (Hopfield, Saastamoinen)
Common values
Value
~1 m
Symbol
δt_sat
Quantity
Satellite clock error (uncorrected)
Value
2–5 m
Symbol
δr_orbit
Quantity
Orbit error (broadcast ephemeris)
Value
5–50 m (varies by time of day, solar activity)
Symbol
δ_iono
Quantity
Ionospheric delay (L1, zenith)
Value
2.5 m (dry) + 0.1–0.5 m (wet)
Symbol
δ_tropo
Quantity
Tropospheric delay (zenith)
Value
1–3 m
Symbol
δ_MP_code
Quantity
Multipath (pseudorange)
Value
5–50 mm
Symbol
δ_MP_phase
Quantity
Multipath (carrier phase)
Important facts
- SATELLITE CLOCK ERROR: ~1 m (corrected by broadcast ephemeris); residual ~0.1 m after correction
- ORBIT ERROR: ~2–5 m; reduced by precise ephemeris (IGS products ~0.05 m)
- IONOSPHERIC DELAY: 5–50 m single-frequency; removed by dual-frequency (~0.1 m residual)
- TROPOSPHERIC DELAY: 2–20 m depending on elevation; modelled, ~0.1 m residual after correction
- MULTIPATH: 1–3 m for pseudorange; 5–50 mm for carrier phase; mitigated by antenna design and environment
- RECEIVER NOISE: 1–5 m pseudorange; 2–5 mm carrier phase
- DOP multiplies measurement error: accuracy ≈ DOP × σ_measurement
- Typical DOP values: PDOP = 2–10 (PDOP < 4 is excellent; > 10 is poor)
Key definitions
Ionospheric Delay
Example
L1 (1575 MHz) sees more delay than L2 (1227 MHz); difference used to estimate and remove iono effects
Propagation delay caused by free electrons in the ionosphere; frequency-dependent, causing code/phase distortion on different frequencies.
Tropospheric Delay
Example
~2.5 m at zenith; increases to ~20 m for 5° elevation angle
Propagation delay in the neutral atmosphere (troposphere); frequency-independent, caused by dry gases and water vapor.
Multipath
Example
GPS receiver near building or water surface sees multipath; solution: use choke-ring antenna or move away from reflectors
Signal reflected off nearby objects before reaching antenna; creates phase distortion and range bias.
Cycle Slip
Example
Typical during low elevation, obstructed sky, or receiver motion; must be detected and repaired
Loss of phase lock on satellite signal, causing discontinuity in carrier-phase count (integer ambiguity jumps by N cycles).
Satellite Geometry (DOP)
Example
Satellites spread across sky → low DOP → high accuracy; satellites clustered overhead → high DOP → poor accuracy
Quality of spatial distribution of satellites; quantified by Dilution of Precision (DOP); lower DOP = better geometry.
Diagrams to know
- Error budget pie chart (relative contributions of each error source)
- Satellite elevation vs tropospheric delay curve
- Ionospheric delay vs frequency relationship
- Multipath geometry (direct + reflected signals)
Dilution of Precision (DOP) & Positioning Accuracy
Formulas
Accuracy ≈ DOP × σ_measurement
Meaning
Accuracy (m); DOP = dimensionless geometry factor; σ = user-equivalent range error (UERE) or noise (m)
Watch out
DOP is GEOMETRIC ONLY; does not include systematic errors (iono, tropo, orbit); this formula gives PRECISION, not ACCURACY
When to use
Estimate positioning uncertainty from satellite geometry and receiver noise
PDOP = √(σ_X² + σ_Y² + σ_Z²)
Meaning
Position DOP; combines 3-D position uncertainty
Watch out
PDOP includes clock uncertainty; cannot isolate horizontal/vertical separately
When to use
Overall accuracy estimate including all coordinates
HDOP = √(σ_X² + σ_Y²)
Meaning
Horizontal DOP; includes only X and Y (horizontal plane)
Watch out
HDOP alone does NOT tell you Z error; use VDOP for vertical or PDOP for total
When to use
Estimate horizontal accuracy (useful for navigation, surveying horizontal control)
VDOP = σ_Z
Meaning
Vertical DOP; includes only Z (height)
Watch out
VDOP is typically 1.5–3 times larger than HDOP due to poor vertical satellite geometry
When to use
Estimate vertical (height) accuracy
UERE ≈ 5 m (typical single-frequency GPS, standard code)
Meaning
User Equivalent Range Error; combined pseudorange noise including all unmodelled errors
Watch out
Can increase to 10+ m in poor conditions (low elevation, high humidity, solar activity)
When to use
Default estimate if no other information given; scales with elevation mask and atmospheric conditions
Common values
Value
< 4
Symbol
PDOP_excellent
Quantity
Excellent PDOP
Value
4–8
Symbol
PDOP_good
Quantity
Good PDOP
Value
8–16
Symbol
PDOP_moderate
Quantity
Moderate PDOP
Value
16
Symbol
PDOP_poor
Quantity
Poor PDOP
Value
1–2
Symbol
HDOP_typical
Quantity
Typical HDOP (open sky)
Value
2–4
Symbol
VDOP_typical
Quantity
Typical VDOP (open sky)
Value
5 m (1-σ)
Symbol
UERE
Quantity
Standard UERE (GPS code)
Important facts
- DOP is a PURE GEOMETRY FACTOR; does not include atmospheric errors, multipath, or clock bias
- Lower DOP = better (multiplies measurement error); higher DOP = worse (amplifies error)
- PDOP < 4 is EXCELLENT; PDOP 4–8 is GOOD; PDOP > 16 is POOR and should be avoided for surveys
- VDOP is always LARGER than HDOP (satellites rarely come from horizon in one direction like elevation)
- Satellites at LOW ELEVATION angles have HIGHER DOP contribution (weight less in solution)
- Elevation mask (e.g., 10°) removes low-elevation satellites but improves PDOP by excluding poor-geometry solutions
- Real-time DOP prediction via almanac allows pre-mission planning (choose time/location with good DOP)
- DOP calculations available in all survey-grade GNSS receivers; monitor during field work
Key definitions
Dilution of Precision (DOP)
Example
PDOP = 2.5 with σ = 3 m gives ~7.5 m accuracy; same σ with PDOP = 5 gives ~15 m accuracy
Dimensionless factor describing how satellite geometry affects positioning accuracy; lower DOP = better accuracy for same measurement precision.
PDOP (Position DOP)
Example
Excellent: PDOP < 4; Good: PDOP 4–8; Moderate: PDOP 8–16; Poor: PDOP > 16
3-D position dilution of precision; affects accuracy of X, Y, Z, and clock bias simultaneously.
HDOP (Horizontal DOP)
Example
Typically 0.8–2.5 for open sky; HDOP < 2 is considered good for surveying
Horizontal dilution of precision; affects accuracy of X and Y only (latitude and longitude).
VDOP (Vertical DOP)
Example
Typically 1.5–3× larger than HDOP due to poor satellite elevation distribution (satellites overhead, not at horizon)
Vertical dilution of precision; affects accuracy of Z (height/ellipsoid height) only.
UERE (User Equivalent Range Error)
Example
UERE = 5 m typical; UERE = 3 m with dual-frequency and correction models
Pseudo-range noise equivalent, combining all unmodelled systematic and random errors; typical 3–10 m for standard GPS.
Diagrams to know
- DOP vs satellite count curve
- DOP vs elevation angle for a single satellite
- PDOP contour map over time of day
- Satellite skyplot showing good vs poor geometry
Differential GNSS (DGPS) & Static Differential
Formulas
Correction = ρ_true_reference - ρ_observed_reference
Meaning
ρ_true = known pseudorange to reference station; ρ_observed = measured pseudorange at reference; difference = error to broadcast
Watch out
Assumes errors are CORRELATED between base and rover (true for iono/tropo/orbit within ~20–30 km); multipath is NOT correlated
When to use
Compute correction at a base station on known point; apply to rover to remove common errors
Accuracy_rover ≈ 0.5–1 m (DGPS, static differential)
Meaning
Horizontal accuracy after differential correction; depends on baseline length and correction model
Watch out
Accuracy DEGRADES with longer baselines (>50 km); iono/tropo decorrelation; use precise ephemeris for longer lines
When to use
Planning survey accuracy with DGPS (Code-based differential)
Common values
Value
5–10 m
Symbol
σ_standalone
Quantity
Standalone GPS accuracy
Value
0.5–1 m
Symbol
σ_DGPS_5km
Quantity
DGPS accuracy (5 km baseline)
Value
1–2 m
Symbol
σ_DGPS_50km
Quantity
DGPS accuracy (50 km baseline)
Value
~100 km (accuracy degrades beyond)
Symbol
L_DGPS_max
Quantity
Max practical DGPS baseline
Value
1–10 Hz
Symbol
f_corr
Quantity
Correction update rate (typical)
Important facts
- DGPS requires REAL-TIME or POST-PROCESSED corrections from a base station on a known point
- Error sources removed by differential: satellite clock, orbit, ionosphere, troposphere (partial)
- Error sources NOT removed: multipath (site-specific), receiver noise, baseline-dependent decorrelation
- Accuracy typically 0.5–1 m horizontal (compared to 5–10 m for standalone GPS)
- Accuracy degrades with baseline length (~5 cm/km for baseline > 50 km)
- Communication link needed for real-time DGPS (radio, cellular, internet); post-processing doesn't need real-time link
- Static differential: base and rover both stationary; corrections computed and applied in post-processing
- Kinematic differential: rover moving; corrections applied in real-time (less common than RTK now)
Key definitions
Differential GNSS (DGPS)
Example
Reference on monument broadcasts corrections; rover 20 km away applies them → accuracy improves from ~5 m to ~0.5–1 m
Technique where corrections computed at a known-position reference station are transmitted to rover receiver to remove common systematic errors.
Base Station (Reference Station)
Example
Coast Guard DGPS network uses fixed reference stations to broadcast 50 Hz corrections over radio
Receiver on a point of known coordinates (from prior survey or high-order control); computes and broadcasts corrections to rovers.
Rover
Example
Survey crew with rover receiver receives DGPS corrections from base on monument; position improves in real-time
Mobile receiver that applies corrections from base station to improve its own position estimate.
Baseline
Example
5 km baseline: 90% error correlation; 50 km: ~70%; 100 km: ~50%
Vector distance between base and rover; errors decorrelate at longer baselines (typically >50 km for DGPS)
Diagrams to know
- Base–rover geometry with error correlation decay vs distance
- DGPS workflow: base computes corrections → rover applies corrections → improved position
- Correction broadcast architecture (radio/cellular/internet link)
Real-Time Kinematic (RTK) & Precise GNSS Methods
Formulas
RTK Accuracy ≈ 2–5 cm horizontal + 3–10 cm vertical (fixed integers)
Meaning
Centimetre-level accuracy for real-time positioning with carrier-phase differential and resolved ambiguities
Watch out
Accuracy valid ONLY after ambiguity fixing (status = FIXED); before fix (FLOAT), accuracy is similar to DGPS (0.5–1 m)
When to use
Machine guidance, stake-out, rapid control densification; only when fix status is FIXED
Ambiguity Search Space = N_sat × N_freq × (2 × max_cycle_slip + 1)
Meaning
Total integer combinations to test; N_sat = satellites, N_freq = frequencies; cycle slip ≈ 1–3 cycles typical
Watch out
Fixing is PROBABILISTIC; low PDOP, weak signals, or multipath cause false fix (wrong integer); always validate before use
When to use
Understand why RTK initialization takes seconds (with dual-frequency) vs minutes (single-frequency)
Time-to-Fix (s) ≈ N_ambiguities / (f_update × SNR)
Meaning
Rough estimate of convergence time; depends on receiver update rate, signal strength, and geometry
Watch out
Poor geometry (high PDOP) or obstructed sky significantly increases time-to-fix; can exceed 5 minutes in bad conditions
When to use
Field planning: how long to wait after initializing RTK?
Common values
Value
2–5 cm
Symbol
σ_RTK_H
Quantity
RTK horizontal accuracy (FIXED)
Value
3–10 cm
Symbol
σ_RTK_V
Quantity
RTK vertical accuracy (FIXED)
Value
0.5–1 m
Symbol
σ_RTK_float
Quantity
RTK accuracy (FLOAT, before fix)
Value
10–30 s
Symbol
t_fix_dual
Quantity
Typical time-to-fix (dual-freq)
Value
1–5 minutes
Symbol
t_fix_single
Quantity
Typical time-to-fix (single-freq)
Value
20–50 km (standard); ~100 km with network
Symbol
L_RTK
Quantity
RTK baseline limit
Value
1–2 s
Symbol
Δt_link
Quantity
Correction link latency (max)
Important facts
- RTK achieves 2–5 cm accuracy through CARRIER-PHASE DIFFERENTIAL + INTEGER AMBIGUITY RESOLUTION (not pseudorange alone)
- Time-to-fix varies: dual-frequency 10–30 s; single-frequency 1–5+ minutes; depends on baseline, geometry, and code/phase noise
- RTK baseline typically limited to 20–50 km (network RTK extends this via regional base stations)
- Ambiguity fixing is PROBABILISTIC; false fixes possible if PDOP poor or multipath severe; validate with redundant observations
- Loss of lock (cycle slip) reverts status to FLOAT; automatic re-initialization usually 5–30 s; must monitor skyplot during dynamic survey
- Dual-frequency receivers fix ambiguities ~10× faster than single-frequency (iono elimination reduces noise)
- Real-time requirement: correction link latency must be < 1–2 s; satellite geometry must remain stable during fix hold
- RTK is now dominant method for control densification and stake-out in Philippines; replaces classical surveying
Key definitions
Real-Time Kinematic (RTK)
Example
Construction equipment or survey drone uses RTK for autonomous stake-out; position updates 1–20 Hz at cm accuracy
Real-time carrier-phase differential GNSS with integer ambiguity resolution, providing cm-level positioning without post-processing.
Fixed Solution (Fix)
Example
After initialization, receiver enters FIXED mode; accuracy typically 2–5 cm if geometry and signal strength remain good
Integer ambiguities are resolved to integers with high confidence; solution has cm-level accuracy.
Float Solution (Float)
Example
During RTK initialization, receiver shows FLOAT status with ~0.5 m accuracy; once fixed, jumps to 2–5 cm
Ambiguities solved as real numbers (not integers) via least-squares; accuracy similar to DGPS (0.5–1 m); lower than FIXED.
Ambiguity Initialization / Time-to-Fix
Example
Dual-frequency: 10–30 s typical; single-frequency: 1–5 minutes or longer
Time required to resolve integer ambiguities from FLOAT to FIXED status; depends on geometry, satellite count, and baseline.
RTK Network (RTN)
Example
Philippines: PRISM (PRS-based RTN) provides coverage; single rover connects to nearest base instead of owning base station
Regional network of fixed base stations (e.g., CORS) that compute and transmit real-time corrections via wireless link.
NTRIP (Network Transport of RTCM via Internet Protocol)
Example
Receiver connects via cellular/WiFi to NTRIP server; receives RTK corrections and achieves cm accuracy
Standard protocol for distributing GNSS correction data (RTCM) over internet to mobile receivers; enables internet-based RTK.
Diagrams to know
- RTK workflow: base tracks satellites → computes ambiguities and corrections → rover initializes and fixes → cm-level positioning
- Fix/Float transition during RTK survey
- Time-to-fix vs baseline length curve
- NTRIP architecture and mobile RTK network diagram
Post-Processing & Static Surveys
Formulas
Accuracy ≈ 5 mm + 1 ppm × baseline
Meaning
Typical accuracy after post-processing static survey with dual-frequency carrier phase; 5 mm fixed error + 1 ppm of baseline length
Watch out
Assumes good geometry, minimal multipath, and convergence; poor conditions can degrade to 1–2 cm
When to use
Estimate precision of baseline after post-processing (e.g., survey network, control densification)
Session Duration ≥ (10 + baseline_km) minutes
Meaning
Rough rule-of-thumb for static observation duration to achieve ambiguity resolution and stable solution
Watch out
Modern dual-freq receivers with good sky view can fix faster (5–10 min for 20 km); poor geometry requires longer
When to use
Plan field sessions: 5 km line needs ~15 min; 50 km needs ~60 min
Common values
Value
5 mm + 1 ppm baseline
Symbol
σ_static
Quantity
Static survey accuracy (dual-freq)
Value
1–2 cm + 1 ppm
Symbol
σ_rapidstatic
Quantity
Rapid-static accuracy
Value
30 min (10 km baseline); 2–4 h (100 km)
Symbol
t_session
Quantity
Typical static session duration
Value
5–10 min (dual-freq, good sky)
Symbol
t_min_fix
Quantity
Minimum session for ambiguity fix
Important facts
- Post-processing can achieve 5 mm + 1 ppm accuracy (much better than real-time RTK) due to precise ephemeris use
- Static survey minimum 30 minutes typical; longer sessions (2–4 hours) improve reliability and reduce systematic errors
- Rapid-static (5–10 min) with dual-frequency sufficient for many surveys; single-frequency may need 30+ min for reliable fix
- Kinematic processing requires good initialization (5 min + static at start, or fixed ambiguities from prior baseline)
- Cycle slips in kinematic must be detected and repaired; modern software handles this automatically
- Multi-system (GPS + GLONASS + Galileo + BeiDou) significantly improves convergence speed and reliability
- Processing software (Leica Infinity, Trimble Business Centre, RTKLIB, Bernese) all use least-squares adjustment
- Control network adjustment ties multiple baselines together; distributes errors; improves closure
Key definitions
Static Survey
Example
Survey crew occupies point A for 30 minutes (carrier phase), then point B for 30 minutes; baseline A–B computed with 5–10 mm accuracy
Both receiver and surveyor remain stationary during session; processed in post-processing mode; highest accuracy (~5 mm + 1 ppm).
Rapid-Static
Example
Quick control densification: occupy each point 10 min with modern receiver → 1–2 cm accuracy, much faster than traditional static
Shortened static session (5–10 min) with dual-frequency receiver and resolved ambiguities; accuracy ~1–2 cm.
Kinematic Survey
Example
Drone surveys: fly trajectory while tracking; post-process to get cm-level orthophoto/DTM
Rover moves along trajectory while tracking satellites; processed in post-processing; intermediate accuracy (few cm) if well-initialized.
Post-Processing
Example
Collect 2-hour static session on 100 km baseline; download precise ephemeris; post-process offline; achieve 5–10 mm accuracy
GNSS data processing done after field session complete; uses stored raw observations and precise ephemeris; no real-time correction link needed.
Diagrams to know
- Static survey session plan (two points, observation times)
- Baseline processing workflow: raw data → ambiguity fixing → least-squares → coordinates
- Convergence curve: RMS error vs observation duration
- Network adjustment diagram (multiple baselines, control points)
Reference Frames: WGS84, PRS92, ITRF
Formulas
WGS84 (World Geodetic System 1984)
Meaning
Geocentric reference frame fixed to Earth's center of mass; origin at Earth's centre; Z-axis toward North Pole; X-axis toward 0° meridian/equator
Watch out
WGS84 ≠ PRS92; difference up to ~1 m in Philippines; must apply transformation to comply with RA 8560
When to use
All GPS/GNSS measurements are computed in WGS84; must transform to local datum (PRS92) for Philippine surveys
PRS92 (Philippine Reference System 1992) based on Clarke 1866 ellipsoid
Meaning
Local datum for Philippines; uses Clarke 1866 ellipsoid (a = 6378206.4 m, e² ≈ 0.00674); fixed to monument constellation
Watch out
Never use WGS84 directly for Philippine property or engineering surveys; VIOLATION of RA 8560 and RA 4374
When to use
All Philippine land surveys, property deeds, engineering projects must use PRS92 coordinates and monuments
WGS84 to PRS92 transformation: Δ E ≈ −127.5 m, Δ N ≈ −116 m (rough, Luzon region)
Meaning
Approximate shift between WGS84 and PRS92 in Philippines; varies by region (Visayas, Mindanao differ)
Watch out
Official PRS92–WGS84 transformation uses 7-parameter Helmert or region-specific grids (BX files); do NOT use simple shift
When to use
Quick sanity check: if WGS84 and PRS92 differ by >2 m, check transformation parameters
Common values
Value
6378137 m
Symbol
a_WGS84
Quantity
WGS84 semi-major axis
Value
1/298.257
Symbol
f_WGS84
Quantity
WGS84 flattening
Value
6378206.4 m
Symbol
a_Clarke
Quantity
Clarke 1866 (PRS92) semi-major axis
Value
ΔE ≈ −127.5 m, ΔN ≈ −116 m
Symbol
δ_LuzonShift
Quantity
WGS84–PRS92 shift (Luzon, approx)
Value
1992 (frozen; no plate motion updates)
Symbol
t_PRS92
Quantity
PRS92 epoch
Value
5–10 cm/year
Symbol
v_plate
Quantity
Typical plate motion (Philippines)
Important facts
- All GNSS results are computed in WGS84 or ITRF (geocentric frame); LOCAL DATUM (PRS92) required for Philippine land surveys by law
- WGS84 ≠ PRS92: difference typically 1–2 m in Philippines; use PROPER TRANSFORMATION, not informal shift
- RA 8560 and RA 4374 mandate PRS92 for all surveys, cadastral records, property transactions in Philippines
- PRS92 monuments (NAMRIA benchmarks) define the local datum; all surveys tied to these monuments
- ITRF is more accurate than WGS84 but also constantly updates (ITRF2000 → 2005 → 2008 → 2014 → 2020); modern use ITRF2014/2020
- Transformation methods: 7-parameter Helmert (precise, rigorous); 3-parameter (faster, less precise); grid shift files (NAMRIA BX files)
- PPCS (Philippine Plane Coordinate System) uses PRS92 and UTM projection; coordinates in metres on local plane
- DO NOT mix frames: WGS84 + PRS92 data in same project invalidates results; always transform to common frame
Key definitions
WGS84 (World Geodetic System 1984)
Example
GPS satellite ephemeris in WGS84; raw receiver coordinates in WGS84; must transform to PRS92 for Philippine use
Geocentric reference frame (origin at Earth's centre); global standard for GNSS. Uses WGS84 ellipsoid (a = 6378137 m; f = 1/298.257).
PRS92 (Philippine Reference System 1992)
Example
Property deed coordinates in PRS92; survey monuments in PRS92; engineering design in PRS92
Local datum for Philippines; fixed to monuments (NAMRIA control points); uses Clarke 1866 ellipsoid; required by law (RA 8560, RA 4374).
ITRF (International Terrestrial Reference Frame)
Example
IGS precise ephemeris and station coordinates in ITRF; permanent monitoring stations track plate tectonics
Global, high-precision geocentric frame; multiple realizations (ITRF2000, 2005, 2008, 2014, 2020); supercedes WGS84 for geodetic work.
Datum Transformation / Shift
Example
WGS84 → PRS92: apply 7-param transform or NAMRIA grid; PRS92 → WGS84: inverse transform
Mathematical conversion between two reference frames; 7-parameter (Helmert) transform or region-specific grid shift (BX file).
Plate Tectonics & Frame Realization
Example
PRS92 coordinates valid for 1992 epoch; Philippine monument at 0° has drifted ~1 m by 2024; modern surveys use dynamic WGS84 or PRS92/2015 variant
Earth's crust moves ~5–10 cm/year; ITRF realizations updated every ~3–5 years; PRS92 fixed to historical epoch (1992) → accumulates ~1 m drift.
Diagrams to know
- WGS84 vs PRS92 vs ITRF sphere/ellipsoid visual comparison
- 3-D transformation flow: WGS84 (raw GNSS) → ITRF → PRS92 → PPCS (plane coordinates)
- Map showing WGS84–PRS92 shift vectors across Philippines regions (Luzon, Visayas, Mindanao)
- PRS92 monument network distribution across Philippines
GNSS Constellations: GPS, GLONASS, Galileo, BeiDou
Common values
Value
24–30 (typically 31–33 active)
Symbol
n_GPS
Quantity
GPS satellites
Value
24 (3 orbital planes × 8 satellites)
Symbol
n_GLONASS
Quantity
GLONASS satellites
Value
30 (24 active + 6 backup)
Symbol
n_Galileo
Quantity
Galileo satellites
Value
30+ (MEO + GEO + IGSO)
Symbol
n_BeiDou
Quantity
BeiDou satellites
Value
20,200 km
Symbol
h_GPS
Quantity
GPS orbital altitude
Value
19,100 km
Symbol
h_GLONASS
Quantity
GLONASS orbital altitude
Value
23,200 km
Symbol
h_Galileo
Quantity
Galileo orbital altitude
Important facts
- GPS: 24–30 active satellites; oldest GNSS; global coverage; frequencies L1 = 1575.42 MHz, L2 = 1227.60 MHz
- GLONASS: 24 satellites; Russian system; similar frequencies to GPS; useful redundancy, especially high latitudes
- Galileo: 30 satellites; European system; full constellation operational 2024; civilian codes on multiple frequencies
- BeiDou: 30+ satellites; Chinese system; strong Asia-Pacific coverage; best for Philippines in combination with GPS
- Multi-GNSS improves availability in urban/forest/canyon environments (satellite count increases, PDOP improves)
- Each constellation has different orbit geometry; combining them significantly speeds ambiguity fixing (10–100× faster)
- Code modulation varies by constellation (GPS C/A on L1, GLONASS C/A, Galileo E5b, BeiDou B1); receivers must support all
- Frequency diversity: Galileo and BeiDou have additional frequencies (E5a/E5b, B2a) → potential better iono correction
Key definitions
GPS (Global Positioning System / NAVSTAR)
Example
GPS alone provides 4–12 satellite visibility at any time; minimum 4 for 3-D fix
U.S. space-based GNSS constellation; 24–30 satellites in 6 orbital planes at ~20,200 km altitude; all-in-view within 5 min typical.
GLONASS (Globalnaya Navigazionnaya Sputnikovaya Sistema)
Example
Combined GPS + GLONASS improves satellite availability in obstructed areas (urban canyons, forests)
Russian GNSS constellation; 24 satellites in 3 orbital planes at ~19,100 km; same dual-frequency architecture as GPS.
Galileo (Galileo System)
Example
Full operational constellation as of 2024; improving accuracy and redundancy
European GNSS constellation; 30 satellites (24 active + 6 backup) at ~23,200 km; newer frequencies (E1, E5a, E5b, E6) with civilian access.
BeiDou (BDS / Compass)
Example
Strongest coverage in Asia-Pacific region (Philippines included); improving rapid growth
Chinese GNSS constellation; 30+ satellites (MEO + GEO + IGSO orbits) at various altitudes; dual-frequency for civilians.
Multi-GNSS / Multi-Constellation Receiver
Example
Modern survey receivers track all 4 constellations; fixes ambiguities 2–3× faster than GPS-only
Receiver tracking GPS + GLONASS + Galileo + BeiDou simultaneously; improves satellite count, geometry, and convergence speed.
Diagrams to know
- Constellation orbital planes and satellite distribution (GPS, GLONASS, Galileo, BeiDou)
- Frequency bands comparison (GPS L1/L2 vs Galileo E1/E5 vs BeiDou B1/B2/B3)
- Global coverage map showing GPS vs multi-constellation satellite availability
Philippine Legal & Regulatory Framework for GNSS
Common values
Value
1998
Symbol
yr_RA8560
Quantity
RA 8560 enactment year
Value
1965 (RA 4374)
Symbol
yr_PRS92
Quantity
PRS92 adoption year
Value
4 zones (Luzon, Visayas, Mindanao, Palawan with PCS)
Symbol
n_zones
Quantity
PPCS standard zones
Important facts
- All Philippine surveys must use PRS92 datum (not WGS84 directly); non-compliance violates RA 8560 and RA 4374
- GNSS raw results in WGS84 must be TRANSFORMED to PRS92 before legal/property use; document transformation method
- Licensed Geodetic Engineers required for cadastral surveys, boundary disputes, property deeds under RA 8560
- NAMRIA control monuments define PRS92 frame; all surveys must tie to nearest NAMRIA benchmark
- PRISM (Philippine Reference System CORS Network) provides real-time RTK corrections tied to PRS92; operational since ~2010
- PRS92 coordinates mandatory on all legal documents, property deeds, engineering designs, government maps
- Datum transformation validation: NAMRIA publishes official transformation grids (BX files) and 7-param Helmert constants
- Surveyors must document survey standards (RA 8560 compliance), datum used, transformation applied, and monument ties
Key definitions
RA 8560 (Geodetic Engineer License Law, 1998)
Example
Only licensed Geodetic Engineers (PRC certified) can conduct surveys for property deeds, cadastral records in Philippines
Philippine law defining professional qualification and scope of geodetic engineers; mandates PRS92 for all surveys; governs cadastral/property surveys.
RA 4374 (PRS92 Adoption & Standardization, 1965)
Example
All Philippine government maps, coordinates, property records must use PRS92; non-compliance invalidates legal documents
Philippine law adopting Clarke 1866 ellipsoid and PRS92 datum as official reference system; established NAMRIA as official mapping agency.
PD 1529 (Surveyors License Decree, 1978; repealed by RA 8560 but principles remain)
Example
Historical context for evolution of surveying profession in Philippines; RA 8560 supersedes
Historical decree on surveyor licensing; modern surveying (GNSS-based) regulated under RA 8560 instead.
CA 141 (Commonwealth Act 141 / Public Land Act, 1936)
Example
Surveys under CA 141 must follow RA 8560 standards; GNSS surveys tied to PRS92 monuments
Philippine land ownership and cadastral survey law; defines free patents, homesteads, and survey requirements for public lands.
NAMRIA (National Mapping and Resource Information Authority)
Example
NAMRIA publishes transformation parameters (PRS92 ↔ WGS84); maintains PRISM (PRS92-based RTN) for real-time GNSS
Philippine government agency maintaining official geodetic control network (PRS92 monuments), maps, and reference systems.
PPCS (Philippine Plane Coordinate System)
Example
Survey blueprints, engineering designs, cadastral maps use PPCS coordinates (Easting, Northing in metres)
Projected (plane) coordinate system based on PRS92 and UTM projection (Transverse Mercator); coordinates in metres.
Diagrams to know
- Philippine survey regulatory hierarchy: RA 8560 → RA 4374 → CA 141 → NAMRIA implementation
- NAMRIA control monument network map (Luzon, Visayas, Mindanao)
- PRISM RTK coverage map across Philippines
Must remember
4 SATELLITES MINIMUM for 3-D fix: 3 unknowns (X, Y, Z) + 1 unknown (receiver clock bias Δt_receiver) = 4 pseudorange equations required. Three satellites alone cannot solve a 3-D position.
Pseudorange ρ = c × Δt where c = 299,792,458 m/s (exact). Always use correct value; off-by-one order of magnitude is a common exam trap.
Carrier phase is PRECISE (~mm) but AMBIGUOUS; pseudorange is COARSE (~m) but UNAMBIGUOUS. RTK success depends on rapid ambiguity resolution (FIXED status).
DOP multiplies measurement error: Accuracy ≈ DOP × σ_measurement. Lower DOP is BETTER. PDOP < 4 is excellent; > 16 is poor. DOP is geometric only (does not include atmospheric errors).
DGPS (pseudorange differential) gives 0.5–1 m accuracy; RTK (carrier-phase differential with ambiguity fix) gives 2–5 cm. RTK requires FIXED integer status; FLOAT is similar to DGPS.
WGS84 ≠ PRS92. All GNSS results from WGS84 MUST be transformed to PRS92 for Philippine legal use (RA 8560, RA 4374). Difference ~1 m; do NOT use informal shift.
Multi-constellation (GPS + GLONASS + Galileo + BeiDou) improves satellite availability and speeds ambiguity fixing 2–10×. Modern receivers exploit this; single-constellation slower.
Ionospheric delay is FREQUENCY-DEPENDENT (~40.3 × TEC / f²); Tropospheric delay is FREQUENCY-INDEPENDENT (~2.5 m zenith). Dual-frequency removes iono; both remain in single-frequency.
Static survey post-processing accuracy: 5 mm + 1 ppm of baseline (dual-frequency, good conditions). Faster than RTK for long baselines but requires offline processing and waiting for precise ephemeris.
Time-to-fix (RTK ambiguity initialization) depends on baseline, geometry (DOP), satellite count, signal strength. Typical: 10–30 s dual-frequency; 1–5+ min single-frequency. Plan field sessions accordingly.
Last minute tips
Always write the 4 SATELLITES = 4 UNKNOWNS fact when asked 'why do you need 4 satellites?' Examiners test this fundamental concept constantly. Missing this loses easy marks.
When calculating pseudorange, remember c = 299,792,458 m/s (not 3×10⁸). Travel time Δt in SECONDS, not milliseconds. Check units: m/s × s = m. A 0.1 s error = ~30 million metres wrong; catch it.
DOP formula trap: Accuracy ≈ DOP × σ means if you double DOP, accuracy doubles (gets WORSE, not better). Low DOP = good. High DOP = bad. Invert in your head: smaller number = better precision.
On WGS84 vs PRS92 questions: ALWAYS state 'GNSS is WGS84, must transform to PRS92 for Philippines (RA 8560)' to show legal knowledge. Bonus marks for citing transformation method (7-param or grid).
RTK FIXED vs FLOAT distinction: if you see 'FIXED' you have cm accuracy; 'FLOAT' is still ~0.5–1 m (same as DGPS). Exam often asks 'why wait for FIXED if FLOAT is instant?' Answer: accuracy difference.
Comparison tables
GNSS Observables: Pseudorange vs Carrier Phase
| Characteristic | Pseudorange (Code) | Carrier Phase |
|---|---|---|
| Precision | ~1 m (coarse) | ~2–5 mm (precise) |
| Ambiguity | UNAMBIGUOUS (direct range) | AMBIGUOUS (integer N unknown) |
| Speed of measurement | Fast (~1 s) | Slow (minutes+ for fixing N) |
| Multipath sensitivity | High (1–3 m error) | Low (5–50 mm error) |
| Typical use | Navigation, DGPS, rapid positioning | Precise geodetic surveys, RTK, control |
| Integer ambiguity resolution needed? | NO (inherently unambiguous) | YES (critical; time-consuming) |
| Cycle slip problem | None | YES; must detect & repair |
DGPS vs RTK vs Static Post-Processing
| Method | Mode | Accuracy | Time-to-Result | Best Use |
|---|---|---|---|---|
| DGPS (Pseudorange Diff) | Real-time or post | 0.5–1 m | 1–2 min | Navigation, rapid surveys, <50 km baseline |
| RTK (Carrier Phase Diff) | Real-time (FIXED) | 2–5 cm (FIXED); 0.5–1 m (FLOAT) | 10 s–5 min | Stake-out, machine guidance, 20–50 km baseline |
| RTK (FLOAT, not fixed) | Real-time (unfixed) | 0.5–1 m | Immediate | Same as DGPS; no benefit until fixed |
| Static Post-Processing | Post-processing (offline) | 5 mm + 1 ppm baseline | Hours–days | Precise control surveys, long baselines 50+ km |
| Rapid-Static | Post-processing | 1–2 cm + 1 ppm | 10 min + post-proc | Quick control densification, 5–20 km |
GNSS Constellations: GPS vs GLONASS vs Galileo vs BeiDou
| Constellation | Country | Satellites | Altitude (km) | Orbital Planes | Key Frequencies | Coverage |
|---|---|---|---|---|---|---|
| GPS | USA | 24–30 | 20,200 | 6 | L1 (1575.42 MHz), L2 (1227.60 MHz) | Global |
| GLONASS | Russia | 24 | 19,100 | 3 | L1 (1602+N×562.5 kHz), L2 | Global |
| Galileo | Europe | 30 | 23,200 | 3 | E1, E5a, E5b, E6 | Global (full 2024) |
| BeiDou | China | 30+ | Various (MEO/GEO/IGSO) | Mixed | B1, B2, B3 | Strong Asia-Pacific |
DOP Quality Ratings & Positioning Accuracy Impact
| PDOP Range | Rating | Horizontal Accuracy (σ = 5 m) | Vertical Accuracy (σ = 5 m) | Survey Suitability |
|---|---|---|---|---|
| < 2 | Excellent | ~5–10 m | ~7–15 m | Ideal (rare without augmentation) |
| 2–4 | Good | ~10–20 m | ~15–30 m | Recommended for surveys; good geometry |
| 4–8 | Moderate | ~20–40 m | ~30–60 m | Acceptable; caution on critical work |
| 8–16 | Poor | ~40–80 m | ~60–120 m | Avoid if possible; degraded solution |
| > 16 | Very Poor | > 80 m | > 120 m | REJECT; do not use for surveys |
WGS84 vs PRS92 vs ITRF Reference Frames
| Frame | Origin | Ellipsoid | Datum Type | Use Region | Philippine Legal Status |
|---|---|---|---|---|---|
| WGS84 | Earth's centre | WGS84 (a=6378137 m) | Geocentric, global | Global (GPS) | NOT acceptable for final legal/property surveys |
| PRS92 | Earth's centre (fixed 1992) | Clarke 1866 (a=6378206.4 m) | Local Philippine datum, frozen epoch | Philippines | MANDATORY for all Philippine surveys by law (RA 8560) |
| ITRF | Earth's centre (continuously updated) | GRS80 (nearly WGS84) | Geocentric, high-precision global | Global (geodetic community) | Optional; more accurate than WGS84 but requires transformation to PRS92 |
Diagrams
GNSS Positioning Principle & Fundamentals
Mind map showing how GNSS positioning works through trilateration: 4 satellites provide ranges (pseudoranges) to solve 4 unknowns (X, Y, Z, receiver clock bias) by finding the intersection of 4 spheres. Speed of light is the key constant converting travel time to distance.
GNSS Error Sources & Mitigation Strategy
Flowchart mapping GNSS error sources (satellite clock/orbit, ionosphere, troposphere, multipath, receiver noise) to typical magnitudes and mitigation strategies (broadcast ephemeris, models, antenna design, filtering). Shows how DGPS (pseudorange differential) or RTK (carrier-phase differential) removes common errors.
RTK Workflow: From GNSS Observation to cm-Level Fix
Flowchart showing RTK workflow from base station reference and rover receiver through ambiguity resolution to final FIXED or FLOAT status. FIXED (integer ambiguities resolved) gives cm accuracy; FLOAT (ambiguities unsolved) gives m-level accuracy similar to DGPS. Time-to-fix 10s–5min depends on geometry and satellite count.
Pseudorange vs Carrier Phase Observable Decision Tree
Decision tree comparing pseudorange (coarse ~1 m, unambiguous, fast) vs carrier phase (precise ~mm, ambiguous, slow). Shows when to use each: pseudorange for rapid DGPS navigation, carrier phase for precise RTK surveys after integer ambiguity resolution.
GNSS Datum Transformation: WGS84 → PRS92 for Philippines
Flowchart showing mandatory transformation from WGS84 (raw GNSS) to PRS92 (Philippine datum) required by law (RA 8560, RA 4374). Three methods: 7-parameter Helmert (rigorous), 3-parameter (fast), or NAMRIA grid shift (official). Final output: PRS92 coordinates → PPCS plane coordinates for legal/engineering use.
Typical GNSS Error Budget (Standalone GPS, Pseudorange)
Pie chart showing typical contributions to GNSS pseudorange error budget: ionospheric delay (35%, frequency-dependent), satellite clock/orbit (25%, corrected by ephemeris), tropospheric delay (15%, frequency-independent model), multipath (15%, site-specific), receiver noise (10%, hardware-limited). Differential GNSS removes first 3 components, improving accuracy.
GNSS Constellation Selection: Single vs Multi-Constellation
Flowchart comparing single-constellation (GPS, slow ambiguity fix) vs multi-constellation receivers (GPS+GLONASS+Galileo+BeiDou, rapid fix). Multi-constellation improves satellite availability in obstructed areas and speeds convergence 2–10×. Modern production surveys use multi-constellation.