A jump in carrier phase is not yet a movement of the monument
A position series suddenly steps upward. The timing coincides with an interruption in satellite tracking, so a reviewer suspects a cycle slip. That is a useful hypothesis, not a complete diagnosis. The observed phase, the receiver’s tracking history and the inferred ground displacement belong to different parts of the evidence chain.
Carrier-phase observations are valuable because a wave supplies a fine repeating measurement scale. Their interpretation also depends on maintaining and modelling the count of cycles. This guide explains how an integer change can enter a time difference, why a detector can miss or misclassify a discontinuity, and what should survive a careful handoff.
All wavelengths, phases, thresholds and displacement histories below are fictional teaching fixtures. They are not actual GPS or other GNSS signal parameters, and the examples do not prescribe a field detector setting or repair algorithm. Operational processing requires supported software, suitable observations and documented validation for the intended task.
Geodesy subject guide · Learning that transfers into life · How X Works hub
Choose your reading route
Route 1: Understand phase and ambiguity · Chapters 1–3
Route 2: Read discontinuities carefully · Chapters 4–6
Route 3: Test detector assumptions · Chapters 7–8
Route 4: Preserve and validate arcs · Chapters 9–10
Distinguish a physical displacement from an observation artefact
Route 5: Transfer and report · Chapters 11–12
Full chapter index · Independent worked case · Questions and practical checks
Chapter index
Understand phase and ambiguity · Chapters 1–3
Separate the observable from the estimated position
Understand the ambiguity term and the idea of a continuous arc
Convert cycles into length without inventing real signal parameters
Read discontinuities carefully · Chapters 4–6
Show how an integer jump enters a time difference
Keep a wrapped phase display separate from a lost cycle count
Read loss-of-lock and status indicators as evidence with scope
Test detector assumptions · Chapters 7–8
Understand what a detector actually compares
Expose a combination’s blind spot with a two-signal fixture
Preserve and validate arcs · Chapters 9–10
Distinguish a physical displacement from an observation artefact
Segment or repair only through a justified processing path
Transfer and report · Chapters 11–12
Build an independent continuity workshop
Report continuity and displacement as separate claims
CHAPTER 1 OF 12
1. Separate the observable from the estimated position
A carrier-phase observation is not a direct readout of the monument’s coordinate. Position is estimated through a model involving satellite geometry, clocks, propagation, antenna response and other relevant terms. A discontinuity in one observable therefore needs interpretation before it can be described as a discontinuity of the physical point being positioned.
Think of measuring travel along a repeating floor pattern. The fine position within one pattern unit can be clear while the number of complete units traversed remains uncertain. Counting continuity adds information. Losing that count creates a different problem from a noisy reading of the fraction within the current unit. The analogy illustrates ambiguity, not the full physics of a radio receiver.
The ESA Navipedia description explains that receiver loss of lock can produce integer-cycle discontinuities in phase measurements. That is one important observation pathway. It does not mean every step in a final coordinate series has this cause, or that every tracking interruption produces the same effect across all signals and receivers.
Begin an audit with separate columns for raw observable, tracking or quality information, processing decision and estimated coordinate. This makes it possible to ask which evidence supports each arrow between them. A receiver status label or an attractive displacement plot cannot replace the chain needed to establish what happened to the phase observations.
CHAPTER 2 OF 12
2. Understand the ambiguity term and the idea of a continuous arc
In a deliberately simplified phase model, write L(t)=g(t)+λN+other terms, with L expressed in length units. Here g represents the geometric contribution and N is an integer ambiguity within a correctly modelled continuous tracking arc. The model leaves many real effects inside other terms. It is a teaching account of continuity, not a complete GNSS observation equation.
If the same ambiguity applies at two times, differencing cancels λN. That cancellation is one reason continuity matters. If the ambiguity changes between those times, an additional wavelength-times-integer term remains in the difference. A calculation that assumes the old arc continued can then attribute the unexplained change to another parameter.
A continuous arc is not simply a set of adjacent rows in a spreadsheet. It concerns the observation and tracking history represented by the processing model. Two records can be close in time while belonging to different ambiguity states. Conversely, a missing stored row does not by itself tell you whether a particular receiver maintained the relevant phase tracking internally.
Preserve the actual observation times, signal identities and quality information. Do not infer continuity solely from a regular-looking table index. The relationship being tested belongs to a particular receiver, satellite and signal under the applicable processing. A gap or change needs evidence at that level rather than a blanket statement about the whole campaign.
CHAPTER 3 OF 12
3. Convert cycles into length without inventing real signal parameters
For our fictional signal, stipulate λ=0.200 metres per cycle. An increment of0.10 cycles corresponds to0.020 metres in this simplified conversion. Five extra cycles correspond to1.000 metre. The arithmetic is multiplication by the declared wavelength; it does not determine which component of an estimated position would change by that amount.
A range-related change and a vertical coordinate change are not generally identical. Position estimation combines observations with geometry and other unknowns. A one-metre discontinuity in one phase-derived length cannot be copied directly into a claim of one-metre ground uplift. Its influence depends on the actual model, available observations and processing decisions.
Keep observable units explicit during export. A column of phase cycles and a column of phase expressed as a length can contain different numerical values for the same stipulated signal. Applying the wavelength twice scales the observation incorrectly; omitting it when a length is required leaves incompatible units inside the calculation.
Real signals have their own defined frequencies, wavelengths and observation conventions. Our round0.200-metre value is chosen for transparent arithmetic and is not a specification for GPS L1 or any other actual carrier. Use authoritative signal and format definitions when processing real records rather than substituting the classroom constant into a production workflow.
CHAPTER 4 OF 12
4. Show how an integer jump enters a time difference
Suppose the fictional accumulated phase changes from500.00 to501.50 cycles while the relevant geometric contribution increases by0.300 metres and all omitted terms are held fixed. With λ=0.200, the phase difference also corresponds to0.300 metres. Under this complete stipulated fixture, continuity and geometric change agree.
Now add a five-cycle ambiguity change at the later observation. Its phase becomes506.50 rather than501.50. The apparent phase-derived length change is6.50×0.200=1.300 metres, containing the original0.300 plus an extra1.000 metre. The extra term came from the declared ambiguity change, not from another metre of physical movement.
If a processor assumes no slip, it must account for that unexplained term somewhere else or reject the observation. The actual response depends on the estimation model. It is not responsible to predict one universal final coordinate jump from the toy observable alone. The fixture establishes the measurement inconsistency, not a particular software failure outcome.
Reverse the question: if a real phase difference looks about one wavelength too large, has a cycle slip been proved? No. You need the relevant model and supporting observations to separate possible causes. The fictional case is identifiable because its omitted terms were explicitly held fixed. Real data does not acquire those simplifying conditions merely because the arithmetic looks close to an integer.
CHAPTER 5 OF 12
5. Keep a wrapped phase display separate from a lost cycle count
A display limited to one cycle can move from a fraction0.95 to0.05 as the phase advances through the wrap point. Under a known small forward increment, that represents+0.10 cycle rather than−0.90. A visible numerical jump in a wrapped representation is therefore not automatically a loss of tracking or an integer ambiguity change.
The fraction alone is incomplete. The same displayed transition could also accompany1.10 or2.10 forward cycles if the missing whole-cycle information were not otherwise established. A continuity assumption, additional observations or a suitable motion model supplies the information needed to choose among those possibilities. The display does not contain that information by itself.
This is a generic wrapped-phase teaching picture, not a claim that standard RINEX carrier observations are always stored as fractions between zero and one. Read the actual observable definition and representation. A large accumulated phase value, a wrapped display and a coordinate estimate are different products, even when the interface places them near one another.
For transfer, compare an ordinary clock face crossing noon. The hands’ displayed angle wraps without time running backward. But a photograph of the face alone may not identify which day it is. The analogy highlights the difference between cyclic representation and continuous counting; it does not replace the radio, timing and propagation models used in GNSS.
CHAPTER 6 OF 12
6. Read loss-of-lock and status indicators as evidence with scope
A loss-of-lock indication can be important evidence about phase continuity. It is not itself a coordinate correction, an instruction to delete a fixed number of cycles or proof that the monument moved. Its precise interpretation depends on the applicable observation format and receiver or processing context. Preserve the indicator and the relevant version rather than translating it into an invented repair.
The existing RINEX guide explains why observation codes, time systems and quality fields must retain their machine-facing meaning. A language or table conversion that drops a relevant flag can remove evidence needed to distinguish arcs. Equally, a blank field should not be silently rewritten as a good-status value simply to make a downstream column complete.
A fixed ambiguity status also has limits. It reflects the result of a particular algorithm under its inputs and assumptions. It is not an unconditional guarantee that every ambiguity is correct or that every physical interpretation is valid. The connected RTK terminology guide separates such statuses from broader accuracy and acceptance claims.
Use indicators together with observation consistency and suitable independent evidence. A warning may identify where to investigate without establishing the cause or size of every affected error. A missing warning is not positive proof of continuity if the data path omitted the relevant information or the detector has known limits.
CHAPTER 7 OF 12
7. Understand what a detector actually compares
A detector responds to a quantity that should behave in a specified way under its model. It may compare time differences, combinations of frequencies or relationships with other observables. Its threshold and assumptions determine which departures are flagged. A flag is therefore evidence of inconsistency relative to that test, not a universal classification of the physical cause.
Make a fictional test in which normal phase-derived increments are0.020 metres and the deliberately chosen alarm threshold is0.050 metres. An increment of0.820 is flagged. That is correct for the stipulated fixture. The threshold is not a recommended GNSS setting, and the successful example does not establish how the detector behaves under different noise, dynamics or sampling intervals.
Now remove an observation so the elapsed time becomes longer. The same physical speed produces a larger total change. A detector that compares increments without accounting for time can flag ordinary motion as an anomaly. Alternatively, a very broad threshold can miss smaller discontinuities. The test needs the actual expected behaviour, not just a convenient fixed number.
Preserve false-positive and false-negative cases in validation. Testing only large artificial slips makes almost any detector look successful. Add ordinary dynamics, changing data cadence, signal-specific effects and difficult combinations appropriate to the real task. Record the scope of the demonstrated performance rather than converting a small test set into a claim that all slips will be found.
CHAPTER 8 OF 12
8. Expose a combination’s blind spot with a two-signal fixture
Different combinations remove different common terms. That can make some discontinuities easier to see while also leaving particular changes undetected. Inspect the algebra of the actual combination. A detector based on one transformed quantity cannot establish everything about all of the original observations simply because it cancels a nuisance term.
For an explicitly fictional two-signal example, let λ1=0.200 metres and λ2=0.250 metres. A five-cycle change in signal1 adds1.000 metre, while a four-cycle change in signal2 also adds1.000 metre. A simple difference of the two phase-derived lengths does not change under those simultaneous stipulated jumps.
This demonstrates a blind direction in that toy difference. It does not assert the behaviour of a detector using actual GNSS wavelengths, additional combinations, quality flags or other observables. The point is to ask which changes a test mathematically cannot distinguish before using a quiet residual as proof that every input remained continuous.
A physical range change shared by both idealised lengths can also leave their difference unchanged. That is precisely why combinations are useful for some purposes and insufficient for others. Keep independent tests that retain information removed by a particular combination. The value of several checks lies in their different sensitivities, not merely in having several plots of closely related quantities.
CHAPTER 9 OF 12
9. Distinguish a physical displacement from an observation artefact
A genuine ground displacement can change the observations. An ambiguity change, antenna alteration, clock-related issue or processing revision can also affect reported results. The final coordinate step alone does not decide among those possibilities. Investigate the time sequence, signal-level evidence, equipment history and spatial coherence using information appropriate to the actual scientific question.
If neighbouring stations and independent measurements support a coherent physical event, that evidence matters. If a discontinuity appears only after one tracking interruption in one observation stream, the investigation starts differently. Neither situation permits an automatic verdict. A cause should follow from the combined evidence rather than from the analyst’s preference for smooth or dramatic results.
Do not smooth away a jump merely because it is inconvenient. Likewise, do not describe every retained jump as a hazard signal. A fitted trend can absorb a step and make its history difficult to see. Preserve the original observations and justified processing decisions so later reviewers can distinguish what was measured from what the model inferred.
The root Geodesy guide introduces equipment steps as a model-selection problem. Carrier-phase continuity adds a specific observation mechanism to that wider question. Keeping those levels connected helps prevent a receiver diagnostic from becoming an unsupported geophysical explanation or a physical event from being dismissed solely because a quality flag also appeared nearby.
CHAPTER 10 OF 12
10. Segment or repair only through a justified processing path
A processing workflow may separate ambiguity arcs, estimate additional parameters, exclude observations or use a supported slip-repair method. Those choices have different consequences for the resulting estimate and its uncertainty. The appropriate action depends on the evidence and algorithm; this educational guide does not prescribe a universal automatic repair.
Do not subtract an integer merely because it makes a plot look continuous. A plausible-looking correction can erase a genuine displacement or compensate for another modelling error. Preserve the original observation, the detected event, the proposed correction, the evidence supporting it and the software’s actual treatment. The distinction between a detected discontinuity and a justified repair should remain visible.
A new ambiguity arc may contain useful information even when its absolute offset relative to the earlier arc is unresolved. The analyst can sometimes use within-arc changes while refusing an unsupported cross-arc difference. State that limited capability clearly rather than choosing between discarding everything and pretending the entire series has one continuous ambiguity.
Validate the final saved processing result and its record of excluded or changed observations. A temporary preview showing a continuous curve is not the delivered artifact. Reproducibility requires enough source and decision history to understand why each arc, flag or correction entered the final coordinate estimate.
CHAPTER 11 OF 12
11. Build an independent continuity workshop
A useful teaching fixture includes a continuous arc, an integer jump, an ordinary wrapped display transition, an observation gap and a simultaneous two-signal jump that one combination cannot detect. Give expected outcomes before running the test. The learner should identify which assumption changes in each case instead of applying one rule to every visible step.
Then change the question from detecting an inconsistency to estimating displacement. The evidence requirement becomes stronger. A detector can correctly flag an anomalous phase difference without identifying the ground-motion contribution. Ask what extra information would distinguish ambiguity change, physical motion and other model terms in the new task.
Keep signal identity and units attached during the workshop. Swap a cycle-valued column with a length-valued one deliberately and ask which check exposes the mistake. This ordinary unit test is useful because specialist-looking diagnostics can distract reviewers from a basic conversion error that changes every subsequent numerical comparison.
The final exercise should use unseen values, not just repeat the original five-cycle example. A learner who can explain the new length increment, the cancelled term and the unresolved cause has transferred the concept. A learner who merely remembers that one metre means five cycles under every system has mistaken the classroom fixture for a universal physical constant.
CHAPTER 12 OF 12
12. Report continuity and displacement as separate claims
A useful result states which observations and arcs were used, how continuity was assessed, what indicators were retained, which processing decisions were applied and which independent evidence supports the final displacement interpretation. It should identify uncertainties and unresolved cross-arc relationships rather than hiding them inside a single quality adjective.
Use precise wording. The tested detector flagged an inconsistency is different from a slip was independently established; both are different from the monument moved by the reported amount. A careful report does not need to sound hesitant. It needs to attach each positive claim to the evidence that actually supports it.
Keep the antenna and frame checks in the same evidence chain. Correct carrier continuity does not prove the mechanical reference point was measured correctly, and a well-documented antenna setup does not prove the frame and epoch comparison is compatible. These controls complement one another because they address different ways that a plausible coordinate can acquire the wrong meaning.
The endpoint is an interpretable observation history. You can explain which phase count remained connected, where that relationship became uncertain, what the processor did and why the final movement claim is justified or limited. That is more useful than treating every jump as ground motion or every smooth curve as evidence that nothing went wrong.
Independent worked case and evidence checks
Try an independent fictional four-epoch arc with λ=0.200 metres. Its continuous accumulated phases are100.00,100.10,100.20,100.30 cycles. Hold all other terms fixed except a geometric contribution increasing by0.020 metres between successive epochs. Every continuous phase increment agrees with that stipulated change.
Now introduce a four-cycle jump before the third epoch. The reported phases become100.00,100.10,104.20,104.30. The phase-derived length increments are0.020,0.820,0.020 metres. In this fully specified fixture, the middle increment contains0.020 of geometric change and0.800 of ambiguity change.
A fictional0.050-metre increment alarm flags the middle transition. That demonstrates the expected behaviour for these inputs, not a recommended detector threshold. If the sampling interval changed or the physical motion were different, the detector’s expected increments would need to be re-established before the same alarm could be interpreted responsibly.
Next give the reviewer only the four final coordinate estimates, without phase observations or tracking information. Can they recover the exact ambiguity change from that table alone? Not in general. The coordinate estimation has combined several inputs and assumptions. Restoring the observation and processing evidence is necessary before claiming that a particular signal mechanism caused the apparent step.
For a changed-context case, show a wrapped phase display moving from0.95 to0.05. Under a stipulated small forward change, that is0.10 cycles or0.020 metres for our toy signal. It is not the same numerical representation as the accumulated four-cycle jump. Explain why the wrap point and a lost whole-cycle count require different reasoning.
Finally apply simultaneous fictional jumps of five cycles on the0.200-metre signal and four cycles on a0.250-metre signal. Each length changes by1.000 metre, leaving their simple difference unchanged. A quiet difference is therefore insufficient evidence that both original signals remained continuous. Identify an additional independent check rather than declaring the pair automatically safe.
Write a handoff separating what was stipulated, detected, inferred and left unresolved. Retain the toy nature of the wavelengths and thresholds. The exercise is successful when another reader can apply the continuity logic to a new observation pattern without borrowing our invented constants as real receiver specifications.
Add a cadence test with the same stipulated physical speed of0.020 metres per second. An interval of four seconds now produces0.080 metres of ordinary geometric change. The earlier fixed0.050-metre increment alarm would flag it despite uninterrupted phase under this fixture. A time-aware comparison should recognise the changed expected increment. This demonstrates why a detector’s validation must include observation times and modelled dynamics, not just a list of artificial integer jumps. The numerical threshold remains a classroom choice, never an operational recommendation.
Worked comparison
| Evidence or operation | What it can establish | What it does not establish alone |
|---|---|---|
| Continuous ambiguity model | A term can cancel within a supported arc | Continuity across every stored row |
| Cycle-to-length conversion | Scale under a declared wavelength | An equal coordinate displacement |
| Loss-of-lock information | Relevant tracking evidence | A complete repair or physical cause |
| Detector flag | Inconsistency under a defined test | Unique identification of ground motion |
| Quiet observation combination | No detected change in that combination | No change in every original observable |
| Smooth repaired series | Appearance after processing | Independent validity of the correction |
Questions and practical checks
Is a cycle slip the same as a ground displacement?
No. It concerns phase continuity and ambiguity. A physical displacement requires a supported interpretation of the full observation chain.
Does a loss-of-lock flag supply the correction?
No. Preserve it as evidence and use the applicable supported processing and validation.
Is every phase wrap a slip?
No. A cyclic display can wrap during ordinary continuous evolution. Read the actual observable representation.
Does a quiet two-signal combination prove no slip occurred?
Not universally. A combination can have changes to which it is insensitive, as the fictional equal-length-jump example shows.
May I smooth a jump until the series looks right?
Not as evidence of a valid repair. Preserve the original observations and justify any correction or arc treatment independently.
Continue with the connected subjects
Keep observations and statuses interpretable
RINEX records: signal codes, missing observations and loss-of-lock evidence
RTK status language: fixed, float and the limits of accuracy claims
Connect signal behaviour with the wider measurement model
Phase-locked loops: tracking behaviour, feedback and jitter
Geodesy overview: positions as estimates and the need for reference evidence
GNSS–acoustic displacement: distinguish observations, model terms and Earth movement
Sources and scope
ESA Navipedia: integer-cycle discontinuities and families of carrier-phase detection methods
IGS ANTEX: antenna-response terms remain distinct from phase-continuity evidence
The numerical cases in this guide are original fictional teaching examples, not measurements from a real site. This is an educational explanation, not a field safety instruction, engineering approval or an official certification. For a real project, use qualified practitioners, current product documentation and site-specific evidence. Sources were checked on 31 October 2026.
Connect the geodetic checks
These guides examine different links in one position claim. A correct time model does not prove the antenna setup, and a correct instrument model does not establish the reference or uncertainty. Follow the unresolved link rather than treating one passing check as complete validation.
Coordinate epochs: separate the clocks and moving-frame model. Establish compatible frames and epochs before treating a coordinate difference as movement.
Antenna reference points: connect setup geometry with the reported point. Identify the actual physical endpoint and which reductions have already been applied.
Height differences: geoid variation, shared errors and covariance. State the target height difference and supported dependence assumptions before claiming differential precision.