TODO(instructor): retitle — the deck teaches trilateration, not triangulation. GPS solves for position from measured *distances* (ranges), not from measured angles. The title is kept as the source deck has it; suggested replacement is "GPS and Trilateration". Every body reference to the ranging concept has already been corrected.

TODO(instructor): the subtitle reads "CCE 214 Geomatics" in the source deck. That course number is out of date for this course and was NOT guessed at or replaced. Confirm the correct course line before class.

Week 12 concepts lecture. This hour is a review of how satellite positioning actually works, and why the position a receiver reports is never exactly where you are. It runs as a refresher: most students met GPS in the introductory geomatics course, so move quickly through the signal material and spend the time on error sources and differential correction.

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Read these out loud, then come back to them at the end. The last two are the ones students most often get wrong on the quiz: geometry is not the same as signal quality, and differential correction only removes *common* error.

TODO(graphic): a five-icon strip matching the five outcomes would work better here than the stock satellite render.

Answer: Prague. Multiply each time difference by the speed of light: about 711 km from Amsterdam, 885 km from Paris, and 1035 km from London. Three distances, three circles, one intersection. This is the whole lecture in one slide — do it before any of the theory.

Fix (2026-09-03): the source speaker note read "711 miles from Prague to Amsterdam" while giving the other two distances in kilometers. 2.37e-3 s x c = 711 km, so "miles" was a unit typo; corrected to kilometers here.

This slide and its companion Prague photo were HIDDEN in the source deck (slides 2 and 3). They are kept as a usable warm-up because they teach exactly the concept the deck is about. If the instructor prefers the Air Force One version that follows, delete this slide.

Second version of the same warm-up, and the one that is not hidden in the source. Hide the object somewhere in the room beforehand.

Instructor note from the source deck, calibrated for room Clyde 254: Satellite 1 is the light on the zoom camera, Satellite 2 is the light above row 2 left, Satellite 3 is the BYU sticker on the front control panel. The source also lists an alternate set for the same room: 221 inches from the projector lens on the ceiling, 260 inches from the screw on the bottom of the front left speaker, 149 inches from the angled smoke detector on the ceiling. Re-measure if the class is in a different room.

VERIFY: the room measurements above are copied from the source deck's speaker notes and are specific to one classroom. Confirm the room and re-measure before running the activity.

Recall from the introductory course these three ways of acquiring vector data. Today is the third one. Ask which of the three the students used in their labs this semester — almost all of it has been downloaded, which is exactly why the metadata question matters.

TODO(graphic): a three-panel figure — a data portal, a digitizing session in ArcGIS Pro, and a field receiver — would carry this slide. The source slide had only a text callout box.

The four-part structure of the rest of the hour. Each concept answers one question, and each question depends on the one before it: you cannot get a range without a travel time, and you cannot get a position without ranges.

Fix (2026-09-03): the source deck labeled item C "Triangulation". Changed to "Trilateration" — GPS solves for position from measured distances, not measured angles.

Frame the design problem before giving the answer. Students who see why the problem is hard remember the solution. The answer to the third question is the whole of parts A and B: you cannot measure distance directly, so you measure time and multiply.

Amplitude, frequency, and phase modulation. A carrier signal at a fixed frequency is altered to carry a message signal. GPS uses phase modulation of the carrier by the code sequence, which is what makes the next slide's comparison possible. Play about a minute of the linked video if the class has not seen modulation before.

This is the key mechanism. The satellite and the receiver each generate the *same* pseudorandom code, started at the same time by synchronized clocks. The receiver slides its own copy of the code along in time until it lines up with the code it received. The amount of the shift is the travel time. That is what makes a pseudorandom sequence, rather than a plain tone, the right thing to transmit: it lines up in exactly one place.

The whole of part B in one line. Note that this gives a *pseudorange*, not a true range, until the receiver clock error is solved for — which is why a fourth satellite is needed. That point is made on the trilateration slides.

Work the multiplication live. The arithmetic on this slide is self-consistent: 0.674 s x 299,792,458 m/s does equal 202,060,116 m.

VERIFY: the travel time on this slide is almost certainly off by one decimal place. GPS satellites orbit at roughly 20,200 km, which gives a travel time near 0.0674 s and a range near 20,200 km — the slide's 0.674 s puts the satellite about ten times too far away. The correction was NOT applied, because nothing on this slide fixes the intended value: the distance is derived *from* the time, so both numbers move together and the right answer depends on the orbital altitude, which the slide never states. Instructor: set the intended travel time and let the distance follow.

Fix (2026-09-03): the source slide title read "3. Triangulation (Where am I?)". Retitled, and the distances-not-angles bullet added, because the mechanism the figure shows is trilateration. Triangulation — fixing a position from measured angles to known points — is the classical surveying method, and it is worth naming the difference out loud since students will meet both terms.

Fix (2026-09-03): source title read "3. Triangulation (where am I?)". Retitled to trilateration. The body text is the source deck's own paragraph, broken into steps.

The last bullet is the reason a receiver needs four satellites in view rather than three: the fourth solves for the receiver's own clock error, which is far too large to ignore at the speed of light. A one-microsecond clock error is a 300-meter range error.

The pivot point of the lecture. Everything so far has assumed the ranges are exact. They are not, and the next block of slides is a catalog of why.

The signal does not travel through a vacuum for its whole path, and it does not always arrive by the direct route. Both effects make the measured travel time longer than the true one, so both make the computed range too long.

TODO(instructor): the plan calls for a decision on how much depth to give atmospheric delay here — dual-frequency ionospheric correction and modeled tropospheric delay are the modern answers, and neither is in this deck. Content not written.

A reflected signal takes a longer path than the direct one, so the receiver computes a range that is too long. This is why a fix taken against the side of a building is worse than one taken in the open, and why the same receiver can be accurate in a field and useless downtown.

TODO(instructor): the plan lists multipath mitigation as an instructor decision — choke-ring and multipath-resistant antennas, signal-quality masks, and simply re-occupying the point. Content not written.

Coverage is about sky view, not about the receiver. The satellites are there; the terrain and the canopy are in the way. Tie this forward to dilution of precision: losing the satellites low on the horizon is worse than losing the same number overhead, because it collapses the geometry.

TODO(graphic): a photograph or diagram contrasting an open-sky fix with a fix under canopy or in an urban canyon. The source slide carried no visual at all.

The chart is the actual transition, 2 May 2000, recorded at Colorado Springs: horizontal and vertical error collapse partway through the record. It is a nice piece of history and it makes the size of the effect concrete.

TODO(instructor): the plan flags this framing for revision. The last bullet is the source deck's, and how to characterize the current policy — including the newer satellites' capability, and regional denial as the modern approach — is an instructor call. Content not written.

Read down the column and note that the largest number by far is the last one. The system is better than its users. Selective availability is listed as "see notes" in the source deck because it has been off since May 2000.

VERIFY: these per-source error magnitudes are the source deck's own figures and were not independently checked against a current reference. They are the right order of magnitude for uncorrected single-frequency SPS, but the instructor may want to update the table.

TODO(graphic): an error-budget bar chart would read far better than the table, and would make the "user error dominates" point without narration.

The small purple circle is everything the system does wrong — under about 9 meters. The large blue circle is user error, plus or minus a kilometer: standing in the wrong place, mistyping a point ID, recording the wrong feature. The visual point is the ratio between the two circles.

"Positional dilution of precision" — PDOP. With the satellites bunched together, the range spheres cross at a shallow angle and a small range error becomes a large position error. Spread them out and the same range error produces a much tighter fix. Geometry, not signal strength.

TODO(instructor): the plan lists satellite geometry as an area to expand — the DOP family (PDOP, HDOP, VDOP, GDOP), and what a receiver's reported DOP value should tell a field crew about whether to keep collecting. Content not written.

Start here before the two DOP figures that follow. A measured range is not a line, it is a band: the true position lies somewhere inside the range uncertainty. Everything about dilution of precision follows from how those bands cross.

Three uncertainty bands crossing. The shaded lozenge in the middle is the area the receiver cannot distinguish between — that area is the position uncertainty, and its size depends entirely on the angles at which the bands cross.

Side by side: satellites close together give a large area of uncertainty; satellites widely spaced give a small one. Same receiver, same signal, same ranges — only the geometry changed. Ask the class which of the two situations they would get under a canopy or in a canyon, which ties this back to the coverage slide.

Section break into part D. The idea in one sentence: two receivers standing near each other see almost the same errors, so if one of them already knows where it is, it can tell the other one how far off the satellites are right now.

The correction can be applied after the fact — post-processing, as drawn here — or streamed to the rover in real time. Post-processing is what a student with a mapping-grade receiver and a nearby CORS station will actually do.

The assumption that makes this work is that the base and the rover see the *same* errors — same satellites, same atmosphere. That holds while the two are close together, and degrades as the baseline grows. Errors that are not shared, like the rover's own multipath, are not removed by differential correction at all.

Walk the numbers. The base station's true coordinates are (Bx, By), but the satellites report it at (Bx+5, By-3). The measured position is therefore 5 too high in x and 3 too low in y, so the correction to apply is (-5, +3). Apply the same correction to the rover: Rx = x - 5, Ry = y + 3.

VERIFY: inside this figure the label reading "Correction = Bx-5, By+3" is written as a coordinate rather than as an offset; the offset is the (-5, +3) shown on the arrow. The wording is the source deck's and was left as drawn — flagged so it can be relabeled when the graphic is redrawn.

TODO(instructor): the plan lists real-time and network methods — SBAS/WAAS, RTK, network RTK, and PPP — as topics to add after this slide. Content not written.

TODO(instructor): the plan also lists coordinate reference frames — what datum a receiver reports in, and what that means for data collected against a project's own coordinate system. Content not written.

Four or five minutes, individually, then a show of hands on the last two items. The one that reliably splits the room is the differential-correction question: most of the class expects the base station to fix everything, and the point worth saying out loud is that it only removes what the two receivers share - the rover's own multipath off the building beside it is its own, and so is the operator standing in the wrong place. The canyon item is the other one to argue: "enough satellites for a fix" is not the same as a good fix, which is the whole of dilution of precision. If the room has no signal, put the URL on the board; the items read aloud just as well, and the canyon and differential items are worth working through together anyway.

Conversion notes (2026-09-03): Source deck "CE 414 Week 12 - Review - GPS and Triangulation.pptx", 30 slides (3 hidden, so the PDF renders 27 pages), extracted 2026-09-03. SLIDE COUNT: 30 source slides -> 30 slides in this deck. One source slide was dropped and two were merged into one, giving 28 source-derived slides; two slides were added (Today's Goals and Before Next Class), per the conversion guide. One previously untitled figure slide was given a title ("Every Range Carries Uncertainty"). DROPPED: source slide 13 (HIDDEN, "d1 / d2 / d3") — three stray shape labels with no figure and no media attached to them; genuinely empty. Nothing else was dropped. RESTORED FROM HIDDEN: source slides 2 and 3 (the Prague "Where am I?" activity and its photo) were hidden in the source and are kept here as one activity slide. They teach the deck's central idea directly and work as an alternative to the Air Force One activity. Delete the slide if the instructor wants only one warm-up. TRILATERATION CORRECTIONS (the deck's substantive fix). GPS solves for position from measured distances, not measured angles, so the ranging concept is trilateration. Four changes: 1. Source slide 7, list item "C. Triangulation" -> "C. Trilateration". 2. Source slide 14, title "3. Triangulation (Where am I?)" -> "C. Trilateration (Where Am I?)", plus one added bullet stating "distances, not angles". 3. Source slide 15, title "3. Triangulation (where am I?)" -> "C. Trilateration: Fixing Your Position". 4. Today's Goals uses "trilateration". The DECK TITLE is unchanged — "GPS and Triangulation", as the source has it — with a TODO(instructor) on the title slide proposing the retitle. Note that the two rendered figures on the trilateration slides came from the source and carry no "triangulation" text, so no image needed changing. TRAVEL-TIME DECIMAL: NOT changed. Source slide 12 gives travel time 0.674 s, c = 299,792,458 m/s, distance 202,060,116 m = 202,060.116 km. That arithmetic is internally correct (0.674 x 299,792,458 = 202,060,116.7). What is wrong is the physics: a GPS satellite at roughly 20,200 km gives about 0.0674 s, so the time appears to be off by one decimal place and the distance is about ten times too large. The correct value does NOT follow unambiguously from the numbers on the slide — the distance is derived from the time, so both move together, and the intended answer depends on an orbital altitude the slide never states. Left as written and flagged VERIFY in place. OTHER FIXES: the source speaker note on the hidden Prague slide read "711 miles from Prague to Amsterdam" while giving the other two distances in kilometers; 2.37e-3 s x c = 711 km, so this was a unit typo and is corrected to kilometers. Ampersand-free plain-text punctuation, curly quotes, and the source's inconsistent "aka" subtitles were normalized. No ArcGIS 9 / ArcMap / ArcCatalog / ArcToolbox wording appears anywhere in this deck — it has no GIS software UI in it at all. COURSE NUMBER: the title slide's subtitle reads "CCE 214 Geomatics" in the source. That number is out of date for this course. It was NOT guessed at or replaced; it is left visible with a TODO(instructor) beside it so the error is not silently hidden. STALE / SOURCED IMAGES kept as-is and flagged: images/gps-selective-availability-2000.jpg is a 2 May 2000 SA-transition chart, historical by nature and fine as history, but it is the deck's only evidence slide and its provenance is not stated on the slide. images/gps-dgps-base-rover-diagram.png, gps-errors-cumulative.png, gps-prn-travel-time.png, gps-signal-interference.png, gps-multipath-building.png, gps-pdop-good-vs-poor.png, gps-radio-modulation-methods.png and gps-radio-range-illustration.png are 200 dpi renders of PowerPoint-shape slides from the source PDF rather than rebuilt figures — they carry the source deck's clip art and typography and would benefit from being redrawn. gps-dop-range-intersection.jpg, gps-pdop-high-vs-low.jpg and gps-range-uncertainty.jpg are scanned line drawings of unstated origin; check the source before publishing widely. TODO(graphic) — no images were generated in this pass, per instruction. Content slides with no visual: Today's Goals (has a stock satellite, wants an outcomes strip), The 3 D's of Map Data, Error Sources: Bad Coverage, Error Sources: Summary, Before Next Class. TODO(instructor) — topics the plan lists as instructor decisions, recorded in place and deliberately NOT written: selective-availability framing and current policy; current GNSS constellations (the deck is GPS-only and never mentions GLONASS, Galileo, BeiDou or QZSS); atmospheric-delay depth and dual-frequency correction; multipath mitigation; the DOP family and what a field crew should do with a reported DOP; SBAS/WAAS, RTK, network RTK and PPP; coordinate reference frames and datums. Also: the deck title retitle, the course number, and the reading chapter. VERIFY items: the travel-time decimal (slide "B. Range (How Far Away?)"); the error-magnitude table, which is the source deck's own figures and was not independently checked; the classroom measurements in the Air Force One activity, which are specific to one room; the "Correction = Bx-5, By+3" label inside the DGPS worked-example figure, which is written as a coordinate rather than an offset; and the Before Next Class schedule, which was reconstructed from the repository's assignment order because the source deck has no wrap-up slide.

TODO(graphic): a "what's due this week" visual, or a screenshot of the Final Project proposal template.