Global Navigation Satellite Systems (GNSS) and Geodetic Datums

The central engineering problem

GNSS positioning estimates receiver position and clock state from satellite measurements. Multipath, obstruction, ionosphere, troposphere and satellite geometry all affect results.

DOP is a geometry amplification factor, not an absolute accuracy guarantee. A precise-looking number of decimal places does not establish coordinate quality.

RTK and network correction techniques can be valuable but require ambiguity validation, initialization checks, reference-frame alignment and independent control observations.

Four lesson sequence

Lesson 5.1: GNSS observables and positioning modes

Learning target and core concept

GNSS code observations measure a modulated ranging signal, while carrier-phase measurements enable much finer relative positioning after ambiguity estimation. A receiver solves for clock bias as well as position. Single-point, differential, RTK and static processing offer different capabilities and failure modes. Network corrections depend on reference station consistency and communication quality. Never copy a precision figure from one solution mode to another without conditions.

Worked numerical or method example. A satellite-range residual of 3 m cannot be called a 3 m horizontal coordinate uncertainty; the geometry matrix projects pseudorange uncertainty into multiple position and clock components. The distinction is why DOP is important, though still incomplete.

Field context: Rural GNSS reconnaissance

A GNSS receiver produces a fixed-looking position beneath trees with unstable carrier observations. A second session at a different time changes satellite geometry and multipath. Compare solution status, residuals, corrections and control checks instead of trusting displayed precision.

Required engineering artifact. A GNSS log capturing observation interval, mode, constellation, obstruction sketch, correction source and a repeated-check acceptance criterion.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. Explain why an RTK fixed solution near a reflective building may still need two independent occupations.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Lesson 5.2: Satellite geometry and uncertainty budgets

Learning target and core concept

Dilution of precision describes geometry-driven amplification of ranging noise. Other contributors—multipath, unmodeled atmosphere, antenna phase center, reference coordinates, obstructions—are not contained in a single DOP value. A simple illustrative uncertainty model multiplies UERE by HDOP, not as a substitute for formal covariance or field validation but as a teaching bound. Vertical quality often differs from horizontal quality because satellite geometry is asymmetric.

Worked numerical or method example. For UERE=0.7 m and HDOP=1.6, a simplified horizontal standard-error scale is 1.12 m. Reducing HDOP to 1.2 changes this scale to 0.84 m if the other terms remain unchanged.

Field context: High-rise corridor geometry

Tight satellite visibility produces large HDOP at a narrow street while the receiver dashboard still displays many decimal places. Explain the geometry effect with an illustrative UERE, then note why multipath and model mismatch require separate error terms.

Required engineering artifact. A two-scenario uncertainty budget with HDOP sensitivity and an independent terrestrial control comparison.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. Two days have identical HDOP but significantly different multipath. Explain why error can differ without any contradiction.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Lesson 5.3: Ellipsoid, geoid and orthometric heights

Learning target and core concept

Ellipsoid height h is measured with respect to a mathematical reference ellipsoid; orthometric height H refers to the gravity-related vertical datum. In the standard simplified convention h=H+N, with geoid undulation N. This relation is only meaningful when heights and model come from compatible frames, epochs and adopted datums. An incorrect geoid model can shift an entire construction site elevation.

Worked numerical or method example. If h=58.240 m and N=−17.650 m then H=h−N=75.890 m. The negative geoid undulation leads to a larger orthometric height. Rounding N too early can lose centimetres.

Field context: Coastal flood-wall height

The GNSS ellipsoid height and an orthometric flood datum differ substantially. Record the geoid model, benchmark datum, coordinate realization and measurement epoch before converting. A sign error in N can reverse a design elevation decision.

Required engineering artifact. A signed height equation, a sample conversion, and a check against independently leveled benchmark heights with uncertainty.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. A crew imports GNSS heights labeled “MSL” without a named geoid or vertical datum. Define the minimum evidence before using them.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Lesson 5.4: Reference frames, epochs and field GNSS QA

Learning target and core concept

A national datum may be plate-fixed while satellite orbits are represented in a time-dependent global frame. Coordinates can change with epoch, tectonic velocity or deformation, even for the same physical monument. Datum transformations require correct source and destination realization as well as transformation method. Store coordinate frame and observation epoch in every product where centimetre-level comparisons matter.

Worked numerical or method example. At an illustrative 25 mm/year tectonic displacement rate, ten years of neglected epoch difference corresponds to 0.25 m in the moving direction. This multiplication is hypothetical and must not be applied as a real site velocity without geodetic observations.

Field context: Post-earthquake site control

A government benchmark list predates earthquake-related displacement. Do not merge old and new epoch coordinates without assessing frame realization and physical motion. Survey multiple stable references and record transformation or re-establishment strategy with appropriate authority.

Required engineering artifact. A frame/epoch compatibility matrix and a field memo specifying what evidence is missing before issuing final control.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. Design a checklist for combining old design-control points with new GNSS solutions after a major regional earthquake.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Unit synthesis and reflection

The four lessons in satellite positioning connect observation, reduction, uncertainty, and decision. To demonstrate mastery, identify the single weakest piece of evidence in your worked case and propose a new observation that could change the recommendation. Report a sensitivity estimate, a separate independent validation check and an ethical or project safety constraint. End with a statement of what you would refuse to certify based on the available data.

For a fully documented result, preserve a table of raw values, correction quantities, accepted values, units and date. Use a table rather than only prose when comparing field sessions; in the accompanying experiment, try an extreme but physically meaningful input and explain the model breakdown.

Extended field note: GNSS accuracy is conditional, not a display setting

Satellite positioning combines ranging observations with a clock solution and a geometric model. A receiver may observe several constellations, but useful geometry and correction validity matter more than the raw number of satellites. Pseudorange observations yield a position whose quality is affected by satellite geometry, clock and orbit models, atmosphere, antenna characteristics and local reflection. Carrier-phase techniques support much finer positioning once ambiguities are properly resolved; a fixed status indicator does not remove the need for independent control checks.

Dilution of precision is a geometry measure. With an illustrative UERE of 0.7 m and HDOP of 1.6, a simple horizontal error scale is 1.12 m. This number is not a surveyed standard deviation for every possible receiver configuration or environment. The simplified product omits explicit non-Gaussian multipath, cycle slips, differential corrections and other factors. Two sites can have the same HDOP yet different quality because their local reflecting surfaces or obstruction patterns differ. The number of decimal places on the controller is largely a formatting choice, not a measured reliability claim.

Reference frames complicate apparent consistency. A plate-fixed national datum can have a different physical evolution from a global dynamic frame. Coordinates at separate epochs may differ even for a monument that has not moved relative to the ground. Earthquakes, local subsidence and structural deformation can create further site motion. Combining a 2012 control coordinate list with a 2026 receiver solution may require epoch-specific transformations or new control validation. The correct operation depends on the local authority's adopted reference realization and observed motion, not an arbitrary offset chosen until map layers appear aligned.

Vertical GNSS results deserve special scrutiny. Ellipsoid height is a geometric quantity, while orthometric height is related to a gravity-based vertical reference. The relation H=h−N involves geoid undulation N, usually delivered through a named geoid model. For example, h=58.240 m and N=−17.650 m gives H=75.890 m. The sign matters. A height labelled merely “MSL” or “elevation” without a named vertical datum and model is insufficient for a high-consequence floodwall, bridge or sewer invert.

A prudent field plan records receiver and antenna model, antenna height method, occupation durations, correction source, solution type, base coordinates, observation epochs and rejection reasons. Use observations separated in time or changed satellite geometry, compare against independent trusted control and flag poor site visibility. Treat the GNSS receiver as an instrument in a broader quality system, not a machine that automatically knows the legally or physically correct coordinate.

Capstone analysis: GNSS control in a coastal, time-dependent landscape

A planned river embankment relies on existing survey benchmarks and recent GNSS points acquired during separate field campaigns. The coastal location may be affected by subsidence and local ground movement. A responsible geodetic workflow begins with the adopted official horizontal and vertical datums and any time-dependent reference frame specifications. Do not merge coordinates from different years based on a shared place name or an apparently similar numerical range. List each observation epoch, monument condition and source realization.

Compare an open-sky GNSS session against one carried out near an elevated road with multipath. Both might display favorable satellite count, yet the restricted site has reflections that distort range observations. Illustrate the geometry effect using UERE × HDOP, then state what the model leaves out. For a given HDOP, alternative multipath conditions can still yield different positions. Record solution status, antenna-height method, correction network, base-station frame, session length and independent occupation interval. A second field visit with changed satellite geometry is often stronger evidence than an extra decimal digit.

Next, convert heights only with compatible reference data. Suppose a site ellipsoid height is 58.240 m and geoid undulation is −17.650 m; the simplified orthometric result is 75.890 m. Show the signed arithmetic, then request the actual geoid model name and vertical datum before using that result. In a flood risk project, confusion between tidal reference levels, orthometric datum and ellipsoid heights can materially change the apparent freeboard. An independent benchmark-leveling comparison is a meaningful control on the conversion.

The deliverable should flag three different uncertainties: relative repeatability within an occupation, reference/frame consistency across campaigns, and site movement over time. A good answer should not claim a fixed position is invariant over years simply because the point label did not change. Include a conditional statement identifying the evidence needed before comparing a recent embankment top with a historical design elevation.

Unit 5: Satellite positioning

Unit objective. GNSS modes, geometry and height systems.

The central engineering problem

GNSS positioning estimates receiver position and clock state from satellite measurements. Multipath, obstruction, ionosphere, troposphere and satellite geometry all affect results.

DOP is a geometry amplification factor, not an absolute accuracy guarantee. A precise-looking number of decimal places does not establish coordinate quality.

RTK and network correction techniques can be valuable but require ambiguity validation, initialization checks, reference-frame alignment and independent control observations.

Four lesson sequence

Lesson 5.1: GNSS observables and positioning modes

Learning target and core concept

GNSS code observations measure a modulated ranging signal, while carrier-phase measurements enable much finer relative positioning after ambiguity estimation. A receiver solves for clock bias as well as position. Single-point, differential, RTK and static processing offer different capabilities and failure modes. Network corrections depend on reference station consistency and communication quality. Never copy a precision figure from one solution mode to another without conditions.

Worked numerical or method example. A satellite-range residual of 3 m cannot be called a 3 m horizontal coordinate uncertainty; the geometry matrix projects pseudorange uncertainty into multiple position and clock components. The distinction is why DOP is important, though still incomplete.

Field context: Rural GNSS reconnaissance

A GNSS receiver produces a fixed-looking position beneath trees with unstable carrier observations. A second session at a different time changes satellite geometry and multipath. Compare solution status, residuals, corrections and control checks instead of trusting displayed precision.

Required engineering artifact. A GNSS log capturing observation interval, mode, constellation, obstruction sketch, correction source and a repeated-check acceptance criterion.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. Explain why an RTK fixed solution near a reflective building may still need two independent occupations.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Lesson 5.2: Satellite geometry and uncertainty budgets

Learning target and core concept

Dilution of precision describes geometry-driven amplification of ranging noise. Other contributors—multipath, unmodeled atmosphere, antenna phase center, reference coordinates, obstructions—are not contained in a single DOP value. A simple illustrative uncertainty model multiplies UERE by HDOP, not as a substitute for formal covariance or field validation but as a teaching bound. Vertical quality often differs from horizontal quality because satellite geometry is asymmetric.

Worked numerical or method example. For UERE=0.7 m and HDOP=1.6, a simplified horizontal standard-error scale is 1.12 m. Reducing HDOP to 1.2 changes this scale to 0.84 m if the other terms remain unchanged.

Field context: High-rise corridor geometry

Tight satellite visibility produces large HDOP at a narrow street while the receiver dashboard still displays many decimal places. Explain the geometry effect with an illustrative UERE, then note why multipath and model mismatch require separate error terms.

Required engineering artifact. A two-scenario uncertainty budget with HDOP sensitivity and an independent terrestrial control comparison.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. Two days have identical HDOP but significantly different multipath. Explain why error can differ without any contradiction.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Lesson 5.3: Ellipsoid, geoid and orthometric heights

Learning target and core concept

Ellipsoid height h is measured with respect to a mathematical reference ellipsoid; orthometric height H refers to the gravity-related vertical datum. In the standard simplified convention h=H+N, with geoid undulation N. This relation is only meaningful when heights and model come from compatible frames, epochs and adopted datums. An incorrect geoid model can shift an entire construction site elevation.

Worked numerical or method example. If h=58.240 m and N=−17.650 m then H=h−N=75.890 m. The negative geoid undulation leads to a larger orthometric height. Rounding N too early can lose centimetres.

Field context: Coastal flood-wall height

The GNSS ellipsoid height and an orthometric flood datum differ substantially. Record the geoid model, benchmark datum, coordinate realization and measurement epoch before converting. A sign error in N can reverse a design elevation decision.

Required engineering artifact. A signed height equation, a sample conversion, and a check against independently leveled benchmark heights with uncertainty.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. A crew imports GNSS heights labeled “MSL” without a named geoid or vertical datum. Define the minimum evidence before using them.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Lesson 5.4: Reference frames, epochs and field GNSS QA

Learning target and core concept

A national datum may be plate-fixed while satellite orbits are represented in a time-dependent global frame. Coordinates can change with epoch, tectonic velocity or deformation, even for the same physical monument. Datum transformations require correct source and destination realization as well as transformation method. Store coordinate frame and observation epoch in every product where centimetre-level comparisons matter.

Worked numerical or method example. At an illustrative 25 mm/year tectonic displacement rate, ten years of neglected epoch difference corresponds to 0.25 m in the moving direction. This multiplication is hypothetical and must not be applied as a real site velocity without geodetic observations.

Field context: Post-earthquake site control

A government benchmark list predates earthquake-related displacement. Do not merge old and new epoch coordinates without assessing frame realization and physical motion. Survey multiple stable references and record transformation or re-establishment strategy with appropriate authority.

Required engineering artifact. A frame/epoch compatibility matrix and a field memo specifying what evidence is missing before issuing final control.

Independent verification

Before relying on an answer, list the input quantities with units and reference frame, state the equation and its domain of validity, and perform one check independent of the same assumption. An independent check may be a reverse-coordinate calculation, separate control occupation, duplicate observation with altered geometry, laboratory calibration or comparison with a higher-quality benchmark. A check that reuses the same erroneous reference is not independent.

A useful investigation changes one named variable while holding the others fixed, reports the resulting output and explains whether the result reflects real physics or merely the assumptions of the idealized formula. Show the original reading and the corrected or adjusted quantity separately. For field quantities, record whether each standard deviation describes repeatability, control accuracy, calibration or estimated environmental variability; these cannot always be collapsed into one convenient error figure.

Think, calculate, decide

1. Apply the worked method to changed input data and show each unit conversion. How sensitive is the result to a 10% change in the most influential input?
2. Design a checklist for combining old design-control points with new GNSS solutions after a major regional earthquake.
3. Name one error source capable of producing a believable but wrong result, and describe a check that does not repeat that source.
4. Prepare an acceptance statement distinguishing a numerical result from an approved survey or construction deliverable. Identify what professional, statutory or project-specific verification remains required.

Research and technical limitations

Use project-specific adopted standards and instrument manuals for tolerances. The formula in the worked example is an intentionally restricted model. Complex real-world measurements may require covariance propagation, adjusted network solutions, calibration corrections, frame transformations, sophisticated software or formal licensed surveying practice. The model does not establish legal boundary positions or certify construction set-out. When field evidence conflicts with a simplified calculation, investigate the discrepancy instead of changing a control coordinate until the picture appears aligned.

Unit synthesis and reflection

The four lessons in satellite positioning connect observation, reduction, uncertainty, and decision. To demonstrate mastery, identify the single weakest piece of evidence in your worked case and propose a new observation that could change the recommendation. Report a sensitivity estimate, a separate independent validation check and an ethical or project safety constraint. End with a statement of what you would refuse to certify based on the available data.

For a fully documented result, preserve a table of raw values, correction quantities, accepted values, units and date. Use a table rather than only prose when comparing field sessions; in the accompanying experiment, try an extreme but physically meaningful input and explain the model breakdown.