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GELE GeodesySatellite Geodesy and GNSSMemory Anchors

Memory anchors for Satellite Geodesy and GNSS — mnemonic devices, acronyms, and tricks that make the GELE Geodesy syllabus stick. Use these when a concept just will not stay in your head.

Exam context

Professional Regulation Commission (PRC) — Board of Geodetic Engineering runs the Geodetic Engineer Licensure Examination on September 2026. Its Geodesy section sits under a "Core" weighting, and Satellite Geodesy and GNSS is the 6th chapter in the 6-chapter GELE Geodesy rotation. The GELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Geodesy.

Satellite Geodesy and GNSS - Memory Anchors

Memory techniques — mnemonics, analogies, micro-stories, and visual associations — can increase long-term retention by up to 600% compared to rote reading. The human brain is wired for stories, images, and patterns, not isolated facts. By hooking abstract GNSS concepts onto vivid mental images and familiar Filipino experiences, you will recall formulas and principles under board-exam pressure the way you recall a catchy jingle. Work through each anchor, test yourself with the recall triggers, and use the revision games to make review sessions fast and fun.

Anchors

Tags

  • definition
  • sequence
  • formula

Topic

Positioning Principle

Concept

Minimum 4 satellites needed for a 3-D GNSS fix

Anchor Id

A1

Difficulty

easy

Memory Aid

Remember '4 LEGS' — Four signals, Location (X), Elevation (Z), Grid (Y), Seconds (clock bias Δt). Just as a table needs 4 legs to stand without wobbling, your GNSS position needs 4 satellite signals to stand firm in 3-D space. Three legs make the table tip; three satellites leave your clock bias unsolved!

Anchor Type

acronym

Why It Works

The '4 LEGS' image physically anchors the number 4, and the table analogy makes the structural necessity intuitive — remove one leg and everything collapses.

Example Usage

Board question: 'Why does a 3-D GNSS fix require at least 4 satellites?' — Think FOUR LEGS → 3 for position + 1 for clock bias (Δt). Answer: The receiver clock bias is a 4th unknown, requiring 4 pseudorange equations.

Recall Trigger

Picture a 4-legged table in the sky made of satellite beams.

Tags

  • formula
  • definition

Topic

Observables

Concept

Pseudorange formula: ρ = c·Δt

Anchor Id

A2

Difficulty

easy

Memory Aid

Rhyme it: 'Rho equals c times t, that's the range from you to me — pseudo means the clock's not free, so four sats give the key!' Here 'rho' (ρ) is the pseudorange, 'c' is the speed of light, and 'Δt' is the measured travel time. The word 'pseudo' reminds you the range is not true because of the receiver clock error.

Anchor Type

rhyme

Why It Works

Rhymes exploit phonological memory loops; the word 'pseudo' embedded in the rhyme automatically triggers the concept of clock bias error.

Example Usage

Given Δt = 0.067 s, recall ρ = c·Δt. Plug in: ρ = 299,792,458 × 0.067 ≈ 20,086,095 m ≈ 20,086 km. This matches GPS orbit altitude — sanity check passed!

Recall Trigger

Hum the rhyme whenever you see 'pseudorange' on the board exam.

Tags

  • formula
  • definition

Topic

Observables

Concept

Speed of light c = 299,792,458 m/s

Anchor Id

A3

Difficulty

easy

Memory Aid

Chunk it as: '3 — 00 — 7.9 — 2 — 458'. Better yet, use the Filipino street-number trick: imagine your house address is No. 299, street 792, barangay 458. Every time you think of the 'barangay address of light', you recall 299,792,458 m/s. Alternatively: nearly 300 million m/s (3×10⁸) is the fast approximation; the exact board value is 299,792,458.

Anchor Type

chunking

Why It Works

Chunking reduces cognitive load from 9 digits to 3 groups. The familiar Filipino 'address' structure embeds the numbers in an autobiographical memory structure.

Example Usage

When computing pseudorange, use c = 299,792,458 m/s. For board exams, 3×10⁸ m/s is acceptable for estimates; use exact value when precision is specified.

Recall Trigger

Think: 'What is the barangay address of light?'

Tags

  • definition
  • formula
  • classification

Topic

Errors and DOP

Concept

DOP (Dilution of Precision): lower DOP = better geometry = better accuracy

Anchor Id

A4

Difficulty

medium

Memory Aid

Think of DOP like traffic in EDSA at rush hour. When satellites are spread all around the sky (like a nearly empty EDSA), signals flow freely, geometry is excellent, and DOP is LOW — you arrive (at your position) accurately. When all satellites cluster at one part of the sky (like everyone cramming into one lane), the geometry is poor, DOP is HIGH, and your position error inflates. 'Low DOP = Open EDSA = Good day for surveying!'

Anchor Type

analogy

Why It Works

EDSA traffic is universally relatable to Filipino students. The analogy maps a non-intuitive mathematical concept (DOP magnitude) onto a lived, visceral experience.

Example Usage

Board question: 'PDOP = 2.5, σ = 3 m. What is the positioning accuracy?' Think low EDSA → multiply: accuracy ≈ PDOP × σ = 2.5 × 3 = 7.5 m.

Recall Trigger

Picture EDSA traffic: light traffic (low DOP, good) vs gridlock (high DOP, bad).

Tags

  • formula
  • process

Topic

Errors and DOP

Concept

Accuracy formula: Accuracy ≈ DOP × σ (range error)

Anchor Id

A5

Difficulty

medium

Memory Aid

Visualize a magnifying glass (DOP) held over your measurement error (σ). A DOP of 1.0 is a flat glass — no magnification, perfect geometry. A DOP of 5 is a thick magnifying lens — your 3 m error ballooned to 15 m! Burn this image: the DOP lens always makes your error BIGGER, never smaller. 'DOP is never your friend — only a small DOP is a good DOP.'

Anchor Type

visual_association

Why It Works

The magnifying glass is a universal visual metaphor for amplification. It directly encodes the multiplicative relationship and the directional rule (DOP ≥ 1 always increases error).

Example Usage

HDOP = 1.8, σ = 2.5 m → Horizontal accuracy ≈ 1.8 × 2.5 = 4.5 m. The glass magnified 2.5 m into 4.5 m.

Recall Trigger

See a magnifying glass hovering over your GPS receiver.

Tags

  • classification
  • definition

Topic

Errors and DOP

Concept

Types of DOP: PDOP, HDOP, VDOP, TDOP, GDOP

Anchor Id

A6

Difficulty

medium

Memory Aid

Use the acronym 'P-H-V-T-G' → 'Please Help Very Tired Geodesists!' P = Position (3-D), H = Horizontal, V = Vertical, T = Time (clock), G = Geometric (all combined). Remember: PDOP is the most commonly cited on board exams. 'Please Help Very Tired Geodesists' gives you all five in order.

Anchor Type

acronym

Why It Works

Acronym-based sentence mnemonics exploit the brain's language processing system; the humorous context (tired geodesists) creates an emotional hook that boosts encoding.

Example Usage

Board question asks about the DOP that measures combined horizontal and vertical uncertainty: that is PDOP (Position). If it asks 3-D position accuracy = DOP × σ, use PDOP.

Recall Trigger

Imagine exhausted geodesists begging for help in the field.

Tags

  • classification
  • definition
  • sequence

Topic

Errors and DOP

Concept

GNSS error sources: Satellite clock, Orbit, Ionosphere, Troposphere, Multipath, Receiver noise

Anchor Id

A7

Difficulty

medium

Memory Aid

Use 'SOIMR' — Say: 'Some Old Iguanas Make Ridiculous Noises' → S = Satellite clock/orbit errors, O = Orbit ephemeris errors, I = Ionospheric delay, M = Multipath, R = Receiver noise. Add T for Troposphere: 'Some Old Iguanas Tumble Making Ridiculous Noises' = S, O, I, T, M, R (SITMR). These six error sources are the complete list tested on PRC boards.

Anchor Type

mnemonic

Why It Works

Absurd animal imagery (iguanas tumbling) is highly memorable due to the bizarreness effect — the brain flags unusual images for deeper encoding.

Example Usage

Board question: 'Enumerate the major error sources in GNSS positioning.' Recall the tumbling iguana → list: Satellite clock, Orbit, Ionosphere, Troposphere, Multipath, Receiver noise.

Recall Trigger

Picture an iguana tumbling off a satellite dish.

Tags

  • definition
  • classification

Topic

Observables

Concept

Carrier-phase vs. pseudorange accuracy levels

Anchor Id

A8

Difficulty

medium

Memory Aid

Think of pseudorange as measuring the length of a hallway using your foot (metre-level, rough but easy). Carrier phase is measuring the same hallway using a precision steel ruler with millimetre markings — but you do not know where on the ruler you started (the integer ambiguity). The steel ruler is far more precise once you figure out where you started counting. This is why carrier phase gives mm-level accuracy but needs ambiguity resolution.

Anchor Type

analogy

Why It Works

The physical act of measuring with foot vs. ruler is a tactile, concrete analogy that maps directly onto the precision levels and the concept of an unknown starting point (ambiguity).

Example Usage

Board question: 'Which observable is used in RTK and geodetic control?' Answer: Carrier phase — the precision steel ruler — gives cm/mm accuracy needed for control surveys.

Recall Trigger

Foot = pseudorange (rough); steel ruler = carrier phase (precise, but find your starting notch first).

Tags

  • definition
  • process

Topic

Observables

Concept

Integer ambiguity in carrier-phase GNSS

Anchor Id

A9

Difficulty

hard

Memory Aid

Imagine Engr. Ana starts counting the waves of the ocean from her boat to the shore. She knows each wave is exactly 19 cm apart (like L1 carrier wavelength ≈ 19 cm). She counts 500,000 waves — but she missed the first few waves when she started her stopwatch. Those 'missed waves at the start' are the integer ambiguity (N). Until she knows exactly how many she missed, her distance measurement has an error of N × 19 cm. RTK resolves N in real-time so Engr. Ana knows her exact distance.

Anchor Type

micro_story

Why It Works

Embedding the concept in a character-driven narrative makes it emotionally and sequentially memorable. The wavelength of 19 cm is also encoded concretely into the story.

Example Usage

Board question: 'Why does carrier-phase GNSS require ambiguity resolution?' Recall: Engr. Ana's missed waves (N). The receiver does not know how many full cycles occurred before it started tracking — N must be resolved for mm accuracy.

Recall Trigger

Think of Engr. Ana on her boat counting ocean waves and missing the first few.

Tags

  • process
  • definition

Topic

Differential and RTK

Concept

Differential GNSS / DGPS: base on known point sends corrections

Anchor Id

A10

Difficulty

medium

Memory Aid

DGPS is like a basketball referee (base station) standing at a known spot on the court. The referee can see exactly how far off the players' (rover's) position calls are because he knows the true court markings. He radios corrections to the scoreboard (rover receiver) in real time. Result: the rover's 'called position' is corrected from rough GPS meter-level to decimeter-to-centimeter accuracy. The referee only works if he can SEE the same satellites as the rover.

Anchor Type

analogy

Why It Works

Basketball is culturally popular in the Philippines. The referee metaphor maps perfectly onto the base-rover-common-satellite requirement of DGPS.

Example Usage

Board question: 'How does DGPS improve accuracy?' Recall the referee: base on known point computes corrections → radios to rover → common errors (iono, clock) cancel → cm-dm accuracy.

Recall Trigger

Picture a basketball referee radioing corrections from half-court.

Tags

  • definition
  • classification

Topic

Differential and RTK

Concept

RTK (Real-Time Kinematic) gives centimetre accuracy in real time

Anchor Id

A11

Difficulty

medium

Memory Aid

Visualize RTK as a laser-guided smart missile (the rover) versus a dumb rocket (standalone GPS). The smart missile gets continuous corrections from a ground controller (base station) and hits within centimetres of the target. The dumb rocket drifts metres off. Burn the image: RTK = smart missile = cm accuracy. This is why RTK is used for stake-out, construction, and control densification — you need to hit the mark every time.

Anchor Type

visual_association

Why It Works

High-contrast imagery (smart vs. dumb) plus a dramatic action metaphor (missile vs. rocket) creates a vivid, emotionally charged memory node.

Example Usage

Board question: 'Which GNSS method achieves centimetre accuracy for real-time stake-out?' Answer: RTK — the smart missile approach using real-time carrier-phase differential corrections.

Recall Trigger

Smart missile vs. dumb rocket — RTK vs. standalone GPS.

Tags

  • definition
  • classification

Topic

Reference Frames

Concept

WGS84 is the reference ellipsoid/frame used by GPS

Anchor Id

A12

Difficulty

easy

Memory Aid

Remember: 'GPS Wears WGS84 — it's their uniform.' Just as the PNP wears a specific uniform, GPS satellites operate in WGS84. GLONASS wears PZ-90, Galileo uses GTRF (tied to ITRF), and BeiDou uses CGCS2000. But for the PRC board, the GPS-WGS84 pair is the primary one tested. Philippine work uses PRS92, which must be transformed FROM WGS84.

Anchor Type

mnemonic

Why It Works

The uniform metaphor is simple and nationally familiar. It also implies you cannot 'mix uniforms' — you must transform WGS84 to PRS92 before using Philippine control.

Example Usage

Board question: 'What datum does GPS use?' Answer: WGS84. For Philippine surveys, transform to PRS92 (the local datum based on GRS80 ellipsoid).

Recall Trigger

GPS in its WGS84 uniform; PRS92 is the local barong tagalog you must change into.

Tags

  • definition
  • classification

Topic

Reference Frames

Concept

PRS92 — Philippine Reference System of 1992 — is the local geodetic datum

Anchor Id

A13

Difficulty

medium

Memory Aid

In 1992, after years of using the old Luzon Datum, Philippine geodesists decided to upgrade the nation's coordinate address book. They adopted the GRS80 ellipsoid (same shape as WGS84 for practical purposes) and established PRS92 — the official 'home address system' of the Philippines. Every cadastral plan, PPCS/UTM grid, and land title coordinates in the Philippines uses PRS92. When your GPS gives you WGS84 coordinates, you must 'translate the address' to PRS92 before writing it on a PD 1529 document.

Anchor Type

micro_story

Why It Works

The 'address book upgrade' narrative gives PRS92 a historical context and functional purpose, embedding it alongside PD 1529 (Property Registration Decree) for cross-topic linking.

Example Usage

Board question: 'What is the local geodetic datum of the Philippines?' Answer: PRS92, based on GRS80 ellipsoid, adopted in 1992. RTK results in WGS84 must be transformed to PRS92 for use with existing monuments.

Recall Trigger

Think of PRS92 as the Philippines' official coordinate address book, established in 1992.

Tags

  • definition
  • classification

Topic

Positioning Principle

Concept

GNSS positioning is trilateration, not triangulation

Anchor Id

A14

Difficulty

easy

Memory Aid

Trilateration = measuring DISTANCES (ranges from satellites). Triangulation = measuring ANGLES. Remember: 'GNSS is TRI-late-ration — it LATE(ly) uses distances, not angles.' A surveyor with a theodolite does triangulation (angles only). A GNSS receiver does trilateration (distances only). The word 'lateral' in tri-lateral-tion reminds you of lateral = side = distance, not angle.

Anchor Type

analogy

Why It Works

The embedded word trick ('lateral' in 'trilateration') creates a phonological link. The contrast with triangulation prevents the most common board-exam confusion.

Example Usage

Board question: 'GNSS determines position by ___.' Answer: Trilateration — measuring distances (pseudoranges) from satellites of known position, NOT triangulation.

Recall Trigger

Say 'lateral = side = distance' — GNSS uses distances, so it is trilateration.

Tags

  • definition
  • process
  • classification

Topic

Errors and DOP

Concept

Ionospheric delay is the largest error source in single-frequency GNSS

Anchor Id

A15

Difficulty

hard

Memory Aid

Imagine the ionosphere as a busy wet market (palengke) the GPS signal must pass through. The signal enters as a fast, clean signal — but the charged particles in the ionosphere are like market vendors grabbing at the signal, slowing it down and bending it. A dual-frequency receiver can measure how much each frequency is slowed (since delay depends on frequency), and calculate the true path — like having a VIP pass that lets you through the palengke without delay. Single-frequency receivers cannot do this and suffer the full market delay.

Anchor Type

micro_story

Why It Works

The palengke is a culturally vivid Filipino image. The VIP pass neatly encodes the dual-frequency solution to ionospheric correction.

Example Usage

Board question: 'How is ionospheric delay mitigated in geodetic GNSS?' Answer: Use dual-frequency receivers (L1 + L2) to model and remove ionospheric delay through the ionosphere-free linear combination.

Recall Trigger

The ionosphere is a GPS palengke — dual-frequency is your VIP pass.

Tags

  • definition
  • process

Topic

Errors and DOP

Concept

Multipath error: signal arrives via reflected paths, not direct path

Anchor Id

A16

Difficulty

medium

Memory Aid

Visualize a GPS signal as a tricycle trying to reach you directly, but some tricycles take detours through alleyways (building reflections) and arrive LATE. The receiver confuses the direct tricycle with the detoured ones, mixing real and reflected signals. The detoured tricycles travel extra distance → they falsely inflate the measured range. Solution: use choke-ring antennas or avoid locations near buildings, water, and metal structures.

Anchor Type

visual_association

Why It Works

Tricycles navigating Metro Manila alleys is an instantly relatable Filipino image. The 'late arrival' directly maps onto the timing error caused by multipath.

Example Usage

Board question: 'What is multipath in GNSS, and how is it mitigated?' Recall the detoured tricycles → multipath = reflected signals arriving late → inflate range → mitigate by site selection (avoid reflectors) and choke-ring antennas.

Recall Trigger

Tricycles taking detour alleys = multipath — some signals arrive late via reflection.

Tags

  • classification
  • definition

Topic

Positioning Principle

Concept

GNSS systems: GPS (USA), GLONASS (Russia), Galileo (Europe), BeiDou (China)

Anchor Id

A17

Difficulty

easy

Memory Aid

Use 'GPS Goes Round (the) Globe Beautifully' → G = GPS (USA), G = GLONASS (Russia), G = Galileo (EU), B = BeiDou (China). Or use the Filipino joke: 'Ang GPS ay American, GLONASS ay Russian, Galileo ay Europeo, at BeiDou ay Intsik — lahat sila nagtatrabaho para sa'yo!' (All four work for you!) The initials G-G-G-B can also be remembered as 'Grande Grande Grande Bagets' — three giants plus one rising star.

Anchor Type

mnemonic

Why It Works

The Filipino-language sentence creates a bilingual memory hook, and the informal 'bagets' label for BeiDou adds humor and differentiation.

Example Usage

Board question: 'Enumerate the four major GNSS constellations.' Recall G-G-G-B → GPS (USA), GLONASS (Russia), Galileo (EU), BeiDou (China).

Recall Trigger

G-G-G-B: GPS, GLONASS, Galileo, BeiDou — four systems, one sky.

Tags

  • definition
  • formula

Topic

Observables

Concept

GPS satellite orbital altitude approximately 20,200 km

Anchor Id

A18

Difficulty

easy

Memory Aid

Chunk 20,200 as '20-200': 'Twenty thousand, two hundred' — the '20' is easy (like 20 pesos), and '200' adds the hundreds. Cross-check: the pseudorange from Example 1 (≈ 20,086 km) confirms the orbit altitude is approximately 20,200 km. Memorise: 'GPS satellites orbit at 20,200 km — about 20 times around the Philippines from north to south (the country is about 1,854 km long).'

Anchor Type

chunking

Why It Works

Chunking reduces memory load; the sanity-check relationship between pseudorange magnitude and orbit altitude reinforces the number through reasoning, not just rote.

Example Usage

Board question: 'A GPS signal travel time is 0.067 s. Compute the pseudorange and verify consistency with known orbital altitude.' ρ = c × 0.067 = 20,086 km ≈ 20,200 km orbital altitude — consistent!

Recall Trigger

Think '20-200' — twenty-two-hundred, like a jeepney fare upgrade.

Tags

  • classification
  • definition
  • process

Topic

Differential and RTK

Concept

Static differential GNSS vs. RTK: accuracy comparison

Anchor Id

A19

Difficulty

medium

Memory Aid

Static differential GNSS is like sending a balikbayan box (base corrections) by cargo ship — it arrives later (post-processed), but the contents are well-packed and accurate (cm level after long observation). RTK is like sending by LBC express — corrections arrive in real time, still cm accurate, and you know instantly if it reached. Both use the same carrier-phase technology; the difference is WHEN the corrections arrive: post-processing vs. real-time radio link.

Anchor Type

analogy

Why It Works

Balikbayan boxes and LBC are quintessentially Filipino cultural references. The cargo vs. express metaphor maps exactly onto post-processed vs. real-time correction delivery.

Example Usage

Board question: 'Which GNSS method is better for real-time construction stake-out?' Answer: RTK — LBC express, not the balikbayan box. Corrections arrive in real time via radio link.

Recall Trigger

Balikbayan box = post-processed; LBC express = RTK real-time.

Tags

  • definition
  • classification
  • process

Topic

Errors and DOP

Concept

Tropospheric delay affects both frequencies equally (non-dispersive)

Anchor Id

A20

Difficulty

hard

Memory Aid

The troposphere is like a blanket of humid air (think Cebu in summer) that slows down all GPS signals equally regardless of frequency — it is 'colorblind' to frequency. This is why the dual-frequency trick (used for ionosphere) does NOT work for troposphere. Instead, meteorological models (e.g., Hopfield, Saastamoinen) estimate the tropospheric delay using temperature, pressure, and humidity data. 'Troposphere is the humid blanket — models solve it, not frequency pairs.'

Anchor Type

analogy

Why It Works

The humid blanket is a sensory image familiar to any Filipino student. The contrast with the ionospheric dual-frequency method deepens understanding through comparison.

Example Usage

Board question: 'Why can dual-frequency GNSS not eliminate tropospheric delay?' Recall the colorblind blanket — troposphere is non-dispersive; use meteorological models instead.

Recall Trigger

Troposphere = humid blanket — affects all frequencies equally — use models, not dual-frequency.

Revision Game

Distance (Range / Pseudorange)

Clue

I am what separates 'trilateration' from 'triangulation' in GNSS — I am a type of measurement, not an angle. What am I?

Memory Link

A14 — 'lateral = side = distance; GNSS uses distances, so trilateration.'

Receiver clock bias (Δt)

Clue

I am the fourth unknown that forces you to track one extra satellite beyond the three needed for 3-D position. Remove me and three sats suffice. What am I?

Memory Link

A1 — '4 LEGS: the fourth leg is the clock bias Δt.'

DOP (Dilution of Precision)

Clue

I multiply your measurement error and make it bigger. The smaller I am, the better your surveying day. A value of 1.0 means perfect geometry. What am I?

Memory Link

A4 and A5 — 'EDSA traffic and the magnifying glass — low DOP = open EDSA = clear day.'

ρ = c × Δt = 299,792,458 × 0.072 ≈ 21,585,057 m ≈ 21,585 km

Clue

I am the GPS travel-time formula. I equal the product of the speed of light and the measured signal travel time. If Δt = 0.072 s, what is my value in kilometres?

Memory Link

A2 and A3 — 'Rho = Sea-Tea; c = barangay address 299-792-458.'

PRS92 (Philippine Reference System of 1992)

Clue

I am the Philippine geodetic datum established in 1992, based on the GRS80 ellipsoid. RTK results in WGS84 must be transformed to me before being placed on a PD 1529 land title document. Who am I?

Memory Link

A13 — 'PRS92 is the Philippines' official coordinate address book, established in 1992.'

RTK (Real-Time Kinematic)

Clue

I give centimetre-level accuracy in real time using carrier-phase differential corrections from a base station on a known point. I am the LBC Express of GNSS methods. What am I?

Memory Link

A11 and A19 — 'Smart missile / LBC Express = RTK = cm real-time accuracy.'

Ionospheric delay

Clue

I am the largest error source in single-frequency GNSS. I am caused by charged particles in the upper atmosphere that slow and bend the GPS signal. A dual-frequency receiver can cancel me. What am I?

Memory Link

A15 — 'The palengke of the ionosphere — dual-frequency is your VIP pass.'

Tropospheric delay

Clue

I affect all GNSS frequencies equally (non-dispersive), so dual-frequency cannot remove me. I am modelled using temperature, pressure, and humidity data. I am the humid blanket over the Philippines. What am I?

Memory Link

A20 — 'Troposphere = humid blanket — colorblind to frequency — use meteorological models.'

Formula Mnemonics

Formula

ρ = c · Δt

Mnemonic

Rho = 'c·t' → 'Sea-Tea' — imagine drinking sea-tea (ocean tea) and the cup is your pseudorange! c = speed of light (sea), Δt = travel time (steep tea time).

When To Use

Use whenever a board problem gives you the signal travel time and asks for the pseudorange (or range to satellite). Also used in reverse: Δt = ρ/c if range is known.

What Each Part Means

ρ = pseudorange (metres, the measured but imperfect range to satellite); c = speed of light = 299,792,458 m/s; Δt = signal travel time in seconds measured by the receiver.

Formula

Accuracy ≈ DOP × σ

Mnemonic

DOP × sigma = 'Dirty Old Pants times Sigma (size)' → the dirtier and bigger the DOP, the worse your accuracy. Low DOP = clean small pants = precise position.

When To Use

Use when a problem gives PDOP (or HDOP/VDOP) and a range error (σ) and asks for expected positioning accuracy. This is the primary DOP problem type on PRC boards.

What Each Part Means

Accuracy = estimated position error in metres; DOP = Dilution of Precision (dimensionless, lower is better — ideal < 2, acceptable < 5); σ = User Equivalent Range Error (UERE) in metres.

Formula

Minimum satellites = 4 (for 3-D fix)

Mnemonic

4 unknowns → 4 equations → 4 satellites. Count unknowns: X, Y, Z, Δt = FOUR. 'Four is the floor.'

When To Use

Use when asked why 4 satellites are the minimum, or when a problem specifies available satellites and asks if a fix is possible.

What Each Part Means

Three unknowns are the 3-D position coordinates (X, Y, Z in geocentric Cartesian or φ, λ, h in ellipsoidal). The fourth unknown is the receiver clock bias Δt. Each satellite provides one pseudorange equation, so four satellites give four equations for four unknowns.

Formula

GDOP² = PDOP² + TDOP² ; PDOP² = HDOP² + VDOP²

Mnemonic

Pythagorean DOP tower: VDOP + HDOP stack to form PDOP, then PDOP + TDOP stack to form GDOP. Build it from the ground up like a tower: Horizontal floor + Vertical wall = Position room; Position room + Time ceiling = full Geometric house (GDOP).

When To Use

Use when a board problem gives component DOPs and asks for PDOP or GDOP, or explains the relationship between DOP types.

What Each Part Means

GDOP = Geometric DOP (all sources combined); PDOP = Position DOP (3-D); HDOP = Horizontal DOP; VDOP = Vertical DOP; TDOP = Time DOP (clock contribution). All are root-sum-squares combinations.

Quick Recall Chains

Chain Title

Four Unknowns in GNSS 3-D Fix

Recall Test

Without looking: What are the 4 unknowns solved in a GNSS 3-D fix? Name them in order.

Memory Chain

Story: 'Engineer XYZ fell asleep (Δt, the time delay) on the job — now there are FOUR problems to fix before the boss arrives!' X, Y, Z are three coordinates; Δt is the sleeping engineer (clock bias). Four engineers, four problems, four satellites needed.

Items To Remember

  • X (Easting / geocentric X)
  • Y (Northing / geocentric Y)
  • Z (Height / geocentric Z)
  • Δt (Receiver clock bias)

Chain Title

GNSS Error Sources (Six Types)

Recall Test

Close your eyes and list all 6 GNSS error types from satellite to receiver. Did you get all six?

Memory Chain

Sentence: 'Some Officers In The Military Rest' → S = Satellite clock, O = Orbit, I = Ionosphere, T = Troposphere, M = Multipath, R = Receiver noise. Six officers, six errors — memorise the rank order from space to ground: satellite-level errors (S, O) → atmospheric delays (I, T) → local errors (M, R).

Items To Remember

  • Satellite clock error
  • Orbital (ephemeris) error
  • Ionospheric delay
  • Tropospheric delay
  • Multipath
  • Receiver noise

Chain Title

GNSS Accuracy Hierarchy (Best to Worst)

Recall Test

Rank the 5 GNSS positioning methods from most precise to least precise. State the approximate accuracy of each.

Memory Chain

Story: 'The most precise surveyor uses a Swiss watch (carrier-phase static), then an LBC express rider (RTK), then a balikbayan box correction (DGPS), then a local jeepney estimate (pseudorange), then an educated guess (SPS autonomous).' Each vehicle is slower and less precise than the last.

Items To Remember

  • Carrier-phase static geodetic (mm–cm)
  • RTK carrier-phase (cm)
  • DGPS pseudorange differential (dm–cm)
  • Single-frequency pseudorange (1–5 m)
  • Standard SPS autonomous (5–10 m)

Chain Title

Steps to Convert RTK WGS84 to PRS92 PPCS/UTM

Recall Test

Without looking: List the 5 steps to convert RTK WGS84 results to PRS92 PPCS/UTM coordinates for a Philippine cadastral survey.

Memory Chain

Acronym: 'O-T-C-S-V' → 'Only Trained Chainmen Survey Victoriously.' O = Observe RTK, T = Transform (7-parameter), C = Convert to grid, S = Scale/false origin correct, V = Verify with control. Five steps, five letters.

Items To Remember

  • Observe with RTK rover (WGS84 ellipsoidal coordinates)
  • Apply 7-parameter datum transformation (WGS84 → PRS92)
  • Convert PRS92 geographic coords (φ, λ) to PPCS/UTM grid (N, E)
  • Apply scale factor and false origin corrections
  • Verify against existing PRS92 control monuments

Chain Title

Four Major GNSS Constellations

Recall Test

Name all 4 GNSS constellations and their operating countries. Which one uses WGS84?

Memory Chain

Story: 'Four countries sent their best runners to a space relay race: Uncle Sam (GPS), Ivan (GLONASS), Esteban (Galileo), and Bong (BeiDou) — all running in orbit for you!' The four runners form 'G-G-G-B' — three G's and one B, like scoring in a game.

Items To Remember

  • GPS — United States
  • GLONASS — Russia
  • Galileo — European Union
  • BeiDou — China
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