GELE Geodesy — Satellite Geodesy and GNSSRevision Notes
Final-week revision notes for Satellite Geodesy and GNSS. If you have already studied the full chapter, this page is your go-to refresher before sitting the GELE. Compact, high-yield, and aligned with what Professional Regulation Commission (PRC) — Board of Geodetic Engineering tests in the Geodesy subtest.
Exam context
On the GELE 2026, the Geodesy subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Geodetic Engineering's pattern. Satellite Geodesy and GNSS lands at position 6th out of 6 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Geodesy on a typical GELE paper.
Satellite Geodesy and GNSS - Revision Notes
Satellite Geodesy and GNSS (Global Navigation Satellite Systems) form the backbone of modern geodetic practice in the Philippines and worldwide. For the PRC Geodetic Engineer Licensure Examination, you must master the positioning principle (trilateration with four unknowns), the two primary observables (pseudorange and carrier phase), error sources quantified by DOP, and the practical methods of DGPS and RTK. Critically, all GNSS results are in WGS84/ITRF and must be transformed to PRS92 before tying to Philippine control monuments. This chapter is consistently tested in the board exam — expect 3–6 items mixing conceptual questions with numerical computations.
Sections
Formulas
Example
If ρ₁ = 20,200 km, ρ₂ = 21,500 km, ρ₃ = 22,100 km, ρ₄ = 23,000 km, the four equations are solved to yield receiver geocentric coordinates and clock bias.
Formula
ρᵢ = √[(X - Xᵢ)² + (Y - Yᵢ)² + (Z - Zᵢ)²] + c·Δt
Variables
ρᵢ = pseudorange to satellite i (m); X,Y,Z = receiver coordinates (m); Xᵢ,Yᵢ,Zᵢ = satellite coordinates (m); c = speed of light = 299,792,458 m/s; Δt = receiver clock bias (s)
Application
This is the fundamental observation equation for GNSS pseudorange positioning. Four such equations (i = 1 to 4) are solved simultaneously for the four unknowns X, Y, Z, Δt.
Exam Tips
- Memorize: 4 satellites minimum for 3-D fix (3 position unknowns + 1 clock bias = 4 unknowns).
- If the question asks 'why 4 satellites?', the answer is always the receiver clock bias as the 4th unknown.
- GNSS geometry: satellites spread across the sky = good (low DOP); all in one quadrant = poor (high DOP).
Key Points
- GNSS positions a receiver by measuring its distance (range) to multiple satellites whose orbital positions (ephemerides) are precisely known — this is TRILATERATION, not triangulation.
- Each satellite–receiver range defines a sphere; the receiver lies at the intersection of all spheres.
- Three unknowns exist for 3-D position: X, Y, Z in a geocentric Cartesian frame (WGS84).
- A fourth unknown — receiver clock bias Δt — is always present because receiver oscillators are imperfect. This requires a MINIMUM OF 4 SATELLITES for a full 3-D fix.
- With more than 4 satellites, the system is over-determined; a least-squares solution improves accuracy.
- 2-D positioning (on a known ellipsoidal height) requires only 3 satellites.
- Each satellite transmits on two frequencies: L1 (1575.42 MHz) and L2 (1227.60 MHz) for GPS — dual-frequency use allows ionospheric delay modelling.
Definitions
Term
Trilateration
Definition
A positioning method that determines location by measuring distances (ranges) to known reference points — in GNSS, these are the satellites. Distinct from triangulation which uses angles.
Importance
Board exam frequently tests the distinction between trilateration (ranges) and triangulation (angles). GNSS uses trilateration.
Term
Receiver Clock Bias (Δt)
Definition
The difference between the receiver's internal clock time and true GPS system time. It introduces a systematic error into all range measurements, making them 'pseudo' ranges.
Importance
This is THE reason why 4 satellites are needed, not 3 — the most commonly tested conceptual fact in board exams.
Term
Ephemeris
Definition
The precise orbital parameters broadcast by each satellite, allowing the receiver to compute the satellite's position (Xᵢ, Yᵢ, Zᵢ) at any given epoch.
Importance
Ephemeris errors are a significant error source; precise ephemerides from IGS improve accuracy.
Section Title
1. Positioning Principle — Trilateration and the Four-Unknown Problem
Common Mistakes
- Saying GNSS uses triangulation — it uses TRILATERATION (distance-based, not angle-based).
- Stating only 3 satellites are needed for 3-D positioning — the clock bias adds a 4th unknown requiring a 4th satellite.
- Confusing 2-D fix (3 satellites, known height) with 3-D fix (4 satellites).
- Forgetting that satellite coordinates are in WGS84 geocentric frame — receiver solution is also in WGS84, not PRS92.
Formulas
Example
Signal travel time Δt = 0.067 s → ρ = 299,792,458 × 0.067 = 20,086,095 m ≈ 20,086 km (consistent with GPS orbit altitude ~20,200 km).
Formula
ρ = c · Δt
Variables
ρ = pseudorange (m); c = 299,792,458 m/s; Δt = signal travel time measured by receiver (s)
Application
Converts the measured signal travel time to a distance. Called 'pseudo' because Δt includes receiver clock bias, so ρ ≠ true geometric range.
Example
For L1 (λ = 0.1903 m): if ρ = 20,200,000 m and N = 106,200,000, then Φ = 20,200,000/0.1903 + 106,200,000 ≈ 212,190,752 cycles.
Formula
Φ = ρ/λ + N
Variables
Φ = carrier phase observable (cycles); ρ = geometric range (m); λ = carrier wavelength (m); N = integer ambiguity (cycles, unknown integer)
Application
The full carrier phase observation equation. Once N is resolved (by techniques such as LAMBDA method, wide-laning), the phase gives sub-centimetre range precision.
Exam Tips
- ρ = c·Δt is the most direct formula tested — practice unit checking: m/s × s = m.
- Remember the accuracy hierarchy: carrier phase (mm) > pseudorange (m).
- L1 wavelength ≈ 19 cm, L2 ≈ 24 cm — sometimes used in numerical items.
- If a question mentions 'ambiguity resolution', it is referring to carrier-phase GNSS.
Key Points
- Two primary observables are used in GNSS: pseudorange (code-based) and carrier phase.
- PSEUDORANGE: Measured by correlating the satellite's broadcast PRN code with a replica generated by the receiver. Accuracy is metre-level (1–10 m for standard GPS).
- CARRIER PHASE: Counts the number of complete and fractional wavelengths of the carrier signal between satellite and receiver. Accuracy is millimetre-level (1–10 mm) but requires resolution of the INTEGER AMBIGUITY (N).
- The L1 carrier wavelength is approximately 19 cm; L2 is approximately 24 cm.
- Integer ambiguity N is the unknown number of complete cycles at the start of tracking — once resolved, the phase observable becomes very precise.
- Carrier phase is the observable for all high-precision geodetic GNSS work: control surveys, RTK, CORS networks.
- Loss of lock (cycle slip) interrupts phase tracking and requires re-initialization of ambiguity resolution.
Definitions
Term
Pseudorange
Definition
The apparent range from receiver to satellite computed as ρ = c·Δt, where Δt is the measured signal travel time. It is 'pseudo' because it is contaminated by receiver clock bias, ionospheric delay, tropospheric delay, and multipath.
Importance
The fundamental observable for standard GPS positioning. Board exams often give a travel time and ask for the pseudorange — apply ρ = c·Δt directly.
Term
Carrier Phase
Definition
The measurement of the phase of the satellite carrier wave at the receiver, expressed in cycles or metres. Provides millimetre-level precision once the integer ambiguity is resolved.
Importance
The basis for all geodetic-quality GNSS surveys (static, RTK). The integer ambiguity is the key challenge.
Term
Integer Ambiguity (N)
Definition
The unknown whole number of complete carrier wavelengths in the initial range between satellite and receiver at the start of tracking. It must be resolved to unlock the full precision of carrier-phase positioning.
Importance
Understanding why carrier phase needs ambiguity resolution — and pseudorange does not — is a common exam distinction.
Term
Cycle Slip
Definition
A sudden jump in the carrier phase count caused by momentary loss of signal lock (e.g., due to obstruction, ionospheric scintillation). Requires detection and repair before using the data.
Importance
Cycle slips must be detected and repaired in post-processing; they are a quality-control concern in geodetic surveys.
Section Title
2. GNSS Observables — Pseudorange and Carrier Phase
Common Mistakes
- Applying ρ = c·Δt and forgetting the units: c must be in m/s and Δt in seconds to get ρ in metres.
- Thinking pseudorange gives millimetre accuracy — it is METRE-level; carrier phase gives millimetre-level.
- Confusing 'integer ambiguity' with a random error — it is a systematic, fixed integer offset per satellite per continuous arc.
- Using the wavelength of light (c = 3×10⁸ m/s) without the precise value: c = 299,792,458 m/s; use the precise value in numerical problems.
Formulas
Example
PDOP = 2.5, σ = 3 m → Accuracy ≈ 2.5 × 3 = 7.5 m. If HDOP = 1.8 and σ = 2.5 m → Horizontal accuracy ≈ 1.8 × 2.5 = 4.5 m.
Formula
Accuracy ≈ DOP × σ
Variables
DOP = relevant dilution of precision (dimensionless); σ = user equivalent range error, UERE (m); Accuracy = estimated position error (m)
Application
Estimates the expected position accuracy given the satellite geometry and measurement precision. Used to plan surveys (choose times with low PDOP/HDOP).
Example
If HDOP = 1.2 and VDOP = 2.1, then PDOP = √(1.2² + 2.1²) = √(1.44 + 4.41) = √5.85 ≈ 2.42.
Formula
GDOP² = PDOP² + TDOP² = HDOP² + VDOP² + TDOP²
Variables
GDOP = Geometric DOP; PDOP = Position DOP (3-D); HDOP = Horizontal DOP; VDOP = Vertical DOP; TDOP = Time DOP
Application
Decomposition of the overall geometric dilution. For most surveying applications, PDOP and HDOP are the most relevant.
Exam Tips
- PDOP < 2 = excellent; 2–5 = good; 5–10 = moderate; > 10 = poor — memorise these thresholds.
- DOP is purely geometric — it does not depend on signal strength or measurement noise, only satellite configuration.
- For horizontal surveys (cadastral, topographic), HDOP is the relevant DOP; for 3-D control, use PDOP.
- PDOP = √(HDOP² + VDOP²) — useful for partial DOP computations in exam problems.
Key Points
- GNSS range errors arise from: (1) satellite clock errors, (2) satellite orbit (ephemeris) errors, (3) ionospheric delay, (4) tropospheric delay, (5) multipath, and (6) receiver noise.
- IONOSPHERIC DELAY is the largest environmental error — the ionosphere slows the code and advances the phase. Dual-frequency receivers model and remove ~99% of ionospheric delay.
- TROPOSPHERIC DELAY affects both code and phase equally; modelled using standard atmosphere models (Saastamoinen, Hopfield).
- MULTIPATH: signal reflections from nearby surfaces (buildings, water) — minimised by antenna design and site selection.
- SELECTIVE AVAILABILITY (SA): intentional GPS signal degradation by the US DoD — officially discontinued in May 2000; no longer a concern.
- DOP (Dilution of Precision) quantifies how satellite geometry amplifies range errors into position errors.
- PDOP (Position DOP, 3-D), HDOP (Horizontal), VDOP (Vertical), TDOP (Time), GDOP (Geometric, 3-D + time). PDOP < 2 is excellent; PDOP > 6 is poor.
- Accuracy ≈ DOP × σ_UERE, where σ_UERE is the User Equivalent Range Error (a combined single-satellite range error budget).
- Lower DOP = better satellite geometry = better accuracy. High DOP when satellites are clustered in one part of the sky.
Definitions
Term
Ionospheric Delay
Definition
A range error caused by the dispersive effect of free electrons in the ionosphere (50–1000 km altitude) on the GNSS signal. Ranges from < 1 m (high elevation, solar minimum) to > 50 m (low elevation, solar maximum). Modelled using Klobuchar model (single-frequency) or removed with dual-frequency observation.
Importance
Largest environmental range error source; dual-frequency operation is the standard solution in geodetic work.
Term
Dilution of Precision (DOP)
Definition
A dimensionless scalar that reflects how satellite geometry magnifies range measurement errors into position/time errors. It is derived from the trace of the variance–covariance matrix of the position solution. DOP = 1 (ideal, perfect geometry); higher DOP = worse geometry.
Importance
Directly used in accuracy estimation formula: Accuracy ≈ DOP × σ. Board exams test both the formula and the concept (lower DOP = better).
Term
UERE (User Equivalent Range Error)
Definition
The combined root-sum-square of all individual range error contributions for a single satellite: σ_UERE = √(σ_clock² + σ_orbit² + σ_iono² + σ_tropo² + σ_multipath² + σ_receiver²).
Importance
The σ in the accuracy formula. Typical values: ~2–3 m for standard GPS, ~1–2 m with SBAS, ~0.01–0.02 m for carrier-phase RTK.
Term
Multipath
Definition
Signal reception error caused by the satellite signal arriving at the antenna via one or more reflections from surfaces (buildings, terrain, vehicles) in addition to the direct path. Causes range errors of centimetres to metres.
Importance
Mitigated by careful site selection, choke-ring antennas, and signal processing. A persistent error that cannot be modelled away.
Section Title
3. Error Sources and Dilution of Precision (DOP)
Common Mistakes
- Confusing low DOP (GOOD) with high DOP (BAD) — examinees sometimes reverse this relationship.
- Forgetting that VDOP > HDOP almost always because satellites are always above the horizon (no satellites directly below) — vertical accuracy is typically worse than horizontal.
- Thinking ionospheric delay is removed automatically by single-frequency receivers — it is only partially corrected using the broadcast Klobuchar model (~50–60% correction).
- Using DOP × σ and forgetting that σ must be in metres (not cm or mm) to get the accuracy in metres.
Formulas
Example
Base at known position computes geometric range to SAT-1 = 20,186,000 m; observes pseudorange = 20,186,025 m → correction = 20,186,000 − 20,186,025 = −25 m broadcast to rover.
Formula
Δρᵢ = ρᵢ_known - ρᵢ_measured
Variables
Δρᵢ = differential range correction for satellite i (m); ρᵢ_known = geometric range computed from known base position and satellite ephemeris (m); ρᵢ_measured = pseudorange observed at base (m)
Application
The base station computes this correction for each visible satellite and broadcasts it to the rover. The rover applies Δρᵢ to its own pseudorange observations to reduce common-mode errors.
Example
For a 50 km baseline with 1 ppm accuracy: 50,000 m × 10⁻⁶ = 0.05 m = 5 cm. Longer baselines need longer occupation or dual-frequency receivers.
Formula
Accuracy (static geodetic) ≈ 1 ppm × baseline length
Variables
1 ppm = 1 part per million (relative accuracy); baseline length in km; accuracy in mm
Application
Rule of thumb for static carrier-phase baseline accuracy. For a 10 km baseline: accuracy ≈ 10 × 1 mm = 10 mm = 1 cm.
Exam Tips
- Accuracy hierarchy: Static geodetic (mm) > RTK (cm) > DGPS code (dm–m) > Single-point (m).
- RTK = real-time + carrier phase + cm accuracy. DGPS = pseudorange corrections + dm-m accuracy.
- NAMRIA administers the Philippine CORS network under RA 8560 (PRC Act for Geodetic Engineers) context — institutional governance questions.
- For cadastral surveys under PD 1529 and CA 141 regulations, RTK with transformation to PRS92 is now the standard technology.
Key Points
- DIFFERENTIAL GNSS (DGNSS/DGPS): A BASE RECEIVER on a known point continuously computes range corrections by comparing measured pseudoranges with the known ranges to each satellite. These corrections (or position corrections) are transmitted to ROVER receivers, cancelling common-mode errors (satellite clock, orbit, ionosphere, troposphere).
- STATIC DIFFERENTIAL GPS: Long occupation times (30 min to several hours); both base and rover record simultaneously; processed in post-processing. Achieves cm-to-mm accuracy using carrier phase. Used for primary and secondary geodetic control.
- RTK (Real-Time Kinematic): Carrier-phase differential GNSS processed in REAL TIME. Base transmits raw phase data (via radio link or cellular) to rover; rover resolves integer ambiguity on-the-fly (OTF) and outputs cm-accuracy coordinates in real time.
- RTK is the standard method for: cadastral surveys, stake-out, road/construction surveys, and densification of the Philippine Reference Network.
- CORS (Continuously Operating Reference Stations): Networks of permanent GNSS base stations (e.g., NAMRIA CORS network in the Philippines) providing corrections to rover receivers via internet (NTRIP protocol).
- Network RTK (e.g., VRS — Virtual Reference Station): Models spatial variation of errors across a network of CORS, providing corrections as if a base were located next to the rover.
- Baseline length limitation: ionospheric error becomes spatially decorrelated over long baselines, degrading DGPS corrections. Typical RTK range: < 10–20 km from base for reliable cm accuracy.
- SBAS (Satellite-Based Augmentation System): Wide-area differential corrections broadcast by geostationary satellites (e.g., MSAS for Japan/Asia-Pacific) — sub-metre accuracy, no additional ground base required.
Definitions
Term
Base Station (Reference Receiver)
Definition
A GNSS receiver placed at a precisely known control point. It computes differential corrections by comparing observed ranges with computed ranges from its known position. In RTK, it also transmits raw phase data to the rover.
Importance
The quality of the base station coordinates directly affects all rover results — errors at the base propagate to all derived rover positions.
Term
RTK (Real-Time Kinematic)
Definition
A carrier-phase differential GNSS technique that resolves integer ambiguities in real time (on-the-fly, OTF), delivering centimetre-accuracy positions to a moving or stationary rover in the field without post-processing.
Importance
The dominant method for cadastral and engineering surveys in the Philippines today. Board exams test accuracy claims (cm-level), requirements (base on known point, data link), and limitations (baseline distance, PDOP).
Term
CORS (Continuously Operating Reference Station)
Definition
A permanently installed GNSS reference receiver that continuously records observations and/or broadcasts real-time corrections. The NAMRIA CORS network supports geodetic control maintenance in the Philippines.
Importance
NAMRIA's CORS network underpins the maintenance of PRS92 and supports RTK surveying in the Philippines — expect legal/institutional context questions.
Term
On-the-Fly (OTF) Ambiguity Resolution
Definition
An algorithm that resolves the carrier-phase integer ambiguities dynamically while the rover is in motion or within a short initialization period (typically < 1 minute with good geometry), enabling real-time cm accuracy.
Importance
OTF distinguishes RTK from conventional static differential — no lengthy initialization needed.
Section Title
4. Differential GNSS and RTK Methods
Common Mistakes
- Thinking DGPS uses carrier phase — standard DGPS uses pseudorange corrections; carrier-phase differential is RTK or static geodetic.
- Confusing the roles: the BASE is on the KNOWN point; the ROVER is the unknown point being surveyed.
- Applying RTK over very long baselines (> 30 km) without network corrections and expecting cm accuracy — ionospheric decorrelation degrades results.
- Forgetting that RTK results are in WGS84 and must be TRANSFORMED to PRS92 before tying to Philippine BM network.
Formulas
Example
A rover RTK fix: WGS84 X = 4,847,301.234 m, Y = 1,259,802.456 m, Z = 1,284,901.789 m → apply NAMRIA Helmert parameters → PRS92 X, Y, Z → compute φ, λ → project to PPCS N, E.
Formula
[X_PRS92] [1 -Rz Ry] [X_WGS84] [ΔX] [Y_PRS92] = [Rz 1 -Rx] [Y_WGS84] + [ΔY] [Z_PRS92] [-Ry Rx 1 ] [Z_WGS84] [ΔZ]
Variables
ΔX, ΔY, ΔZ = translation parameters (m); Rx, Ry, Rz = rotation parameters (radians or arc-seconds); scale factor s (ppm) is applied as (1+s) multiplier on the rotation matrix; all parameters published by NAMRIA
Application
The 7-parameter Helmert similarity transformation converts WGS84 geocentric coordinates to PRS92 geocentric coordinates. After transformation, convert to geographic coordinates (φ, λ, h) and then to PPCS grid coordinates using TM projection.
Example
GPS epoch 1,392,249,618 s → UTC = GPS Time − 18 s → PST = UTC + 8 h.
Formula
GPS Time = UTC + leap seconds (currently +18 s as of 2024)
Variables
GPS Time: continuous atomic time; UTC: Coordinated Universal Time with leap seconds; PST = UTC + 8 h
Application
Convert between GNSS epoch times and civil time for survey records, tidal analysis, and legal instrument timestamps.
Exam Tips
- WGS84 → (datum transform) → PRS92 → (TM projection) → PPCS: memorise this workflow.
- PRS92 replaced Luzon Datum 1911 — know both datums for historical context questions.
- The five PPCS zones I–V are analogous to UTM zones but with Philippine-specific central meridians: I=117°, II=119°, III=121°, IV=123°, V=125° E.
- Ellipsoidal height (GNSS) ≠ mean sea level height — subtract geoid undulation N (Philippine geoid model from NAMRIA) to get orthometric height.
- RA 8560 = the Geodetic Engineering Law; know it references PRS92 as the mandatory datum.
Key Points
- GNSS satellites broadcast positions in the WGS84 (World Geodetic System 1984) reference frame — a geocentric, Earth-centred, Earth-fixed (ECEF) system.
- WGS84 ellipsoid parameters: semi-major axis a = 6,378,137.0 m; flattening f = 1/298.257223563.
- ITRF (International Terrestrial Reference Frame): the most precise global geocentric frame, maintained by the IERS. Current realization: ITRF2020. WGS84 and ITRF are aligned at the centimetre level.
- PRS92 (Philippine Reference System of 1992): the national horizontal datum for the Philippines, defined by the Luzon Datum origin at NAMRIA, Taguig. Tied to the ITRF at the epoch of its establishment.
- PPCS (Philippine Plane Coordinate System): the grid coordinate system (using Transverse Mercator projection) overlaid on PRS92 — analogous to UTM but using Philippine-specific zones.
- GNSS output in WGS84 must be transformed to PRS92/PPCS for use in Philippine cadastral and engineering surveys. The transformation involves a 3-D Helmert (7-parameter) datum transformation.
- RA 8560 (Philippine Geodetic Engineering Law) mandates that all geodetic surveys use the national reference system (PRS92) — GNSS practitioners must apply the datum transformation.
- NAMRIA publishes the official transformation parameters between WGS84 and PRS92 for use in the Philippines.
- Time in GNSS: GPS Time (GPST) is an atomic time scale; it does not follow leap seconds. As of 2024, GPST is 18 seconds ahead of UTC. Philippine Standard Time (PST) = UTC + 8 hours.
Definitions
Term
WGS84 (World Geodetic System 1984)
Definition
The global geocentric reference system used by GPS. Defines the Earth's shape (ellipsoid), gravity model, and the coordinate frame in which GPS satellite orbits are computed and broadcast. Practically coincident with ITRF at the centimetre level.
Importance
All GNSS coordinates are initially in WGS84 — understanding its relationship to PRS92 is critical for Philippine practice and board exams.
Term
PRS92 (Philippine Reference System of 1992)
Definition
The current official horizontal geodetic datum of the Philippines, replacing the Luzon Datum of 1911. Realised through a network of BLLM (Bureau of Lands Lot Monuments) and geodetic control points adjusted in a geocentric frame tied to ITRF.
Importance
All surveys in the Philippines must reference PRS92 per NAMRIA and DENR/LMB regulations. GNSS output in WGS84 must be transformed to PRS92.
Term
PPCS (Philippine Plane Coordinate System)
Definition
The official grid coordinate system of the Philippines, based on five Transverse Mercator zones (Zones I–V) covering the archipelago, with each zone having a central meridian and a scale factor of 0.99995. Used for cadastral and engineering plane coordinates.
Importance
GNSS geographic coordinates (PRS92 φ, λ) must be projected to PPCS (N, E in metres) for cadastral plans, subdivision surveys, and engineering layout — tested in coordinate transformation problems.
Term
Helmert (7-Parameter) Transformation
Definition
A 3-D similarity transformation between two datum frames using 7 parameters: 3 translations (ΔX, ΔY, ΔZ), 3 rotations (Rx, Ry, Rz), and 1 scale factor (s). Used to convert between WGS84 and PRS92.
Importance
The standard datum transformation method; NAMRIA publishes official parameters for WGS84-to-PRS92 conversion in the Philippines.
Section Title
5. Reference Frames — WGS84, ITRF, and PRS92
Common Mistakes
- Using WGS84 coordinates directly in PPCS computations without applying the datum transformation to PRS92 first — results in position errors of tens of metres.
- Confusing PRS92 (datum) with PPCS (grid projection system) — PRS92 is the datum; PPCS is the coordinate projection on top of it.
- Thinking GPS coordinates are directly in PPCS — they are in WGS84 geocentric (X, Y, Z) or geographic (φ, λ, h) coordinates.
- Ignoring the ellipsoidal height component: GNSS gives ELLIPSOIDAL HEIGHT (h), not ORTHOMETRIC HEIGHT (H). H = h − N, where N is the geoid undulation (from EGM2008 or local geoid model).
Connections
- Chapter: Geodetic Datums and Reference Frames — WGS84 and PRS92 are directly introduced here; GNSS output must always be transformed to PRS92 using the Helmert transformation covered in the datums chapter.
- Chapter: Map Projections (PPCS/UTM) — After datum transformation to PRS92, geographic coordinates are projected to PPCS using the Transverse Mercator projection; the full coordinate pipeline (GNSS → WGS84 → PRS92 → PPCS) spans both chapters.
- Chapter: Geodetic Control Surveys — RTK and static GNSS are the primary instruments for establishing and densifying geodetic control networks in the Philippines (BLLM monuments, BM network under NAMRIA).
- Chapter: Traverse and Triangulation — GNSS has largely replaced classical triangulation for control; GNSS baselines serve as the modern equivalent of measured traverse legs for control densification.
- Chapter: Hydrographic Surveying — GNSS is the standard positioning tool for bathymetric surveys; ellipsoidal-to-orthometric height reduction (using tidal benchmarks) connects GNSS heights to chart datum.
- Philippine Law: RA 8560 (Geodetic Engineering Act) — Mandates use of PRS92 as the national datum; defines the professional scope of geodetic engineers, including GNSS survey practice.
- Philippine Law: PD 1529 (Property Registration Decree) and CA 141 (Public Land Act) — Cadastral surveys that establish lot boundaries for land titling must use PPCS coordinates derived from PRS92-referenced GNSS surveys.
- Chapter: Adjustment Computations — Over-determined GNSS networks (more than 4 satellites, or multiple GNSS baselines) are adjusted by least squares; the covariance matrix of the adjustment yields the DOP values.
- Chapter: Topographic and Cadastral Surveying — RTK GNSS is the standard field method for topographic data collection and cadastral stake-out in Philippine engineering practice.
Exam Strategy
For the GNSS/Satellite Geodesy section of the PRC Geodetic Engineer board exam, allocate your review time as follows: (1) FORMULAE FIRST — master ρ = c·Δt and Accuracy = DOP × σ; these appear in almost every numerical GNSS item. (2) CONCEPTUAL ANCHORS — the four-unknown problem (why 4 satellites), pseudorange vs carrier phase (accuracy levels), and low DOP = good geometry are the most frequent conceptual items. (3) COORDINATE PIPELINE — the sequence WGS84 → (Helmert transform) → PRS92 → (TM projection) → PPCS is tested both as a process question and in numerical problems; never skip the datum transformation step. (4) ACCURACY HIERARCHY — memorise: Static geodetic (mm) > RTK (cm) > Code DGPS (dm–m) > Single-point (m); these thresholds appear in technique-selection questions. (5) LEGAL CONTEXT — RA 8560 mandates PRS92; PD 1529 and CA 141 govern cadastral applications; NAMRIA administers CORS and publishes transformation parameters. (6) COMMON TRAPS — check units in pseudorange calculations (c in m/s × Δt in s = ρ in metres); remember VDOP > HDOP is normal; never use WGS84 coordinates directly for Philippine cadastral work. Practice the eight quick review questions in this set under timed conditions (90 seconds per item) to simulate board exam pace.
Quick Review Questions
A GPS signal is received after a travel time of Δt = 0.072 s. Compute the pseudorange in kilometres.
Apply the pseudorange formula directly: ρ = c·Δt. Use c = 299,792,458 m/s (exact defined value of speed of light). Multiply by travel time in seconds to get metres, then convert to km. This is consistent with GPS orbit altitudes of ~20,200 km.
With a UERE of σ = 2.5 m and HDOP = 1.8, what is the estimated horizontal positioning accuracy?
Use Accuracy ≈ DOP × σ with the appropriate DOP for the dimension in question. For horizontal accuracy, use HDOP. The UERE σ = 2.5 m represents the combined range error budget. Result: 4.5 m horizontal accuracy.
Why does a 3-D GNSS fix require a minimum of 4 satellites?
Even with perfect satellite geometry, 3 satellites only provide 3 equations. The receiver clock is never perfectly synchronised with GPS time, introducing an additional unknown Δt. Adding Δt to X, Y, Z gives 4 unknowns requiring 4 equations (one per satellite).
Two GNSS scenarios: (A) PDOP = 1.5, σ = 3 m; (B) PDOP = 4.0, σ = 3 m. Which is more accurate and by how much?
Lower PDOP indicates better satellite geometry and less amplification of range errors. Both scenarios have the same measurement noise (σ = 3 m), but poor geometry in Scenario B multiplies the error by 4.0 instead of 1.5, resulting in nearly three times worse accuracy.
If HDOP = 1.5 and VDOP = 2.3, what is the PDOP?
PDOP is the 3-D position DOP, combining horizontal and vertical components. Apply Pythagoras: PDOP = √(HDOP² + VDOP²). Note VDOP > HDOP is typical because satellites are all above the horizon.
A geodetic engineer obtains RTK coordinates in WGS84 and wants to tie the survey to existing PPCS monuments. What is the correct transformation sequence?
GNSS delivers WGS84 results; Philippine cadastral monuments use PPCS (projected from PRS92). The mandatory intermediate step is the datum transformation (WGS84 → PRS92) using official NAMRIA parameters, before the TM map projection. Skipping this step introduces systematic errors of tens of metres.
What distinguishes RTK from static differential GNSS in terms of observable used, real-time capability, and expected accuracy?
The key RTK distinctions are: (1) carrier phase observable, (2) real-time processing with OTF ambiguity resolution via radio/cellular data link, and (3) centimetre accuracy. Static carrier-phase is more accurate (mm) because of longer observation and more robust ambiguity resolution, but lacks real-time output.
A GPS receiver's GNSS antenna is located at an ellipsoidal height h = 54.321 m above the WGS84 ellipsoid. The geoid undulation at that location is N = 23.150 m. What is the orthometric (MSL) height H?
GNSS gives ellipsoidal height h measured from the reference ellipsoid surface. Mean sea level approximately follows the geoid. Orthometric height H = h − N, where N is the geoid undulation (positive when geoid is above ellipsoid, as is typical in the Philippines). The Philippine geoid model (from EGM2008 or NAMRIA local model) provides N values.
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