Abstract
GNSS relative positioning uses simultaneous observations from a reference station and a monitoring station to eliminate or reduce errors shared by both sites. With a shorter baseline, the signal paths through the ionosphere and troposphere are usually more alike. As the distance grows, residual atmospheric delay often increases and reliable integer ambiguity resolution may become more difficult.
There is, however, no universal rule that converts each additional kilometer into a fixed loss of accuracy. Results also depend on satellite geometry, frequencies and constellations, ionospheric activity, height difference, obstruction, multipath, antenna calibration, observation duration, the correction service and the processing model. The sound approach is to understand these mechanisms and then validate the proposed configuration against the project’s measurement objective.
The discussion below first uses an engineering reference model from published guidance to illustrate the distance term, then uses anonymized operational data to show the measured relationship between baseline length and 24-hour apparent displacement. Because the two use different statistics, they are shown separately rather than overlaid.
1. Why baseline length matters
The baseline length in this article is the spatial distance between the reference station and the monitoring station. In single-base relative positioning, more similar observations generally leave smaller residuals after differencing. As the baseline grows, that similarity tends to weaken.
This does not mean that every short baseline performs well or that every long baseline is unusable. Multipath, obstruction, antenna installation or an unstable reference can dominate a short baseline. Multi-frequency observations, atmospheric estimation, network corrections or longer observation periods can improve a long-baseline solution. Baseline length is an important design variable, but it is not the only one.
For an overview of high-precision positioning methods, see High-Precision GNSS Techniques Compared. The satellite systems and basic error sources are covered in GNSS Systems and Positioning Principles.
2. What double differencing removes—and what remains
2.1 The double-differenced carrier-phase model
Relative positioning commonly forms carrier-phase double differences between two stations and two satellites. Omitting smaller terms that have already been modelled, the observation can be represented conceptually as:
λ·∇Δφ = ∇Δρ + λ·∇ΔN − ∇ΔI + ∇ΔT + ∇ΔεHere, ρ is geometric range, N is the integer ambiguity, I and T are ionospheric and tropospheric delays, and ε includes measurement noise and multipath. Sign conventions vary with the order of differencing, but the practical points are the same:
- Time-aligned common-view observations remove receiver and satellite clock terms in the first-order model.
- Atmospheric delays cancel substantially only when the conditions seen by the two stations are sufficiently similar; double differencing does not make them vanish automatically.
- Multipath, antenna installation and monument motion are site-specific effects and are normally not removed by observations at the other station.
2.2 Spatially correlated and site-specific errors
| Class | Examples | Typical effect as the baseline grows |
|---|---|---|
| Spatially correlated errors | Ionosphere, troposphere, part of the orbit error | Commonality usually decreases and double-difference residuals may increase |
| Site-specific errors | Multipath, obstruction, antenna phase center, monument stability | Not determined by baseline length; a short baseline can still perform poorly |
Shortening the baseline mainly addresses the first class. Siting, monumentation, antenna calibration and quality control address the second. Blaming every error on distance leads to the wrong order of corrective work.
3. The main distance-dependent mechanisms
3.1 Ionosphere
Ionospheric delay is frequency-dependent. Dual- or multi-frequency receivers can form an ionosphere-free combination or estimate the ionospheric state, but spatial gradients and rapid disturbances can still leave residual errors.
Taiwan is in an active low-latitude ionospheric region. A distance rule observed at one location or during one period should therefore not be treated as a year-round guarantee [1]. Quiet and disturbed conditions should be assessed separately, including cases in which a solution becomes unavailable or must reconverge.
3.2 Troposphere and height difference
Tropospheric delay is not frequency-dependent and cannot be removed by a dual-frequency combination in the way first-order ionospheric delay can. The dry component is generally easier to model; the wet component is harder because water vapour changes rapidly in space and time.
As horizontal separation or height difference increases, the atmospheric profiles above the stations may diverge. The remaining error often appears most clearly in the vertical component. Garrido et al. [2] also found that tropospheric modeling directly affected GNSS vertical results. Mountain sites, dams and deep excavations require more than a plan-view distance check.
3.3 Satellite orbits and correction products
The effect of orbit error in relative positioning generally grows with baseline scale, but its actual magnitude depends on ephemeris quality, satellite geometry and the processing model. Broadcast ephemerides, precise ephemerides and real-time State Space Representation (SSR) corrections are not equivalent conditions.
Orbit uncertainty therefore belongs in a long-baseline error budget, but a simplified proportional rule cannot establish that it is the dominant source. It usually has to be interpreted together with the ionosphere, troposphere and site environment.
4. How baseline length affects solution quality
4.1 Ambiguity availability and reliability
High-precision carrier-phase positioning requires resolving integer ambiguities. Larger unmodelled residuals weaken the float solution and its stochastic model, making ambiguity resolution more difficult. Methods such as LAMBDA efficiently search the integer candidates [3], but obtaining a fixed solution does not prove that the accepted integers are correct.
A monitoring system should evaluate the following together:
- availability of the fixed or target solution and time to reconverge;
- the assumptions behind ambiguity validation statistics;
- residuals, satellite geometry, data completeness and consistency across time;
- stability of the reference station itself.
No single indicator—including fixed status, ratio, solution sigma or PDOP—describes more than one part of solution quality. None can independently prove that a displacement is real.
4.2 Time-series quality and detectable deformation
For deformation monitoring, a single coordinate epoch matters less than whether the entire time series is stable, continuous and interpretable. Distance-dependent residuals may cause outages, reconvergence or environmentally correlated biases. Site-specific multipath can also produce repeating signals.
The minimum detectable displacement therefore cannot be derived from receiver specifications or baseline length alone. Observation interval, temporal correlation, data gaps, deformation rate, evaluation window and acceptable false-alarm and missed-detection risks all matter.
4.3 Literature model: how the distance term enters positioning accuracy
Engineering specifications often express typical single-epoch positioning accuracy as a + bL: a is a distance-independent constant term, while bL is a ppm distance term that grows with baseline length. USGS guidance summarizes typical single-base RTK reference values as horizontal 10 mm + 2 ppm and vertical 20 mm + 2 ppm, with a recommended operating distance below 10 km and an approximate maximum of 40 km [4]. Figure 2 extends the same formula to 60 km only to make the distance term easier to read; the segment beyond the recommended range is neither an operating recommendation nor an accuracy guarantee.
Swipe horizontally to view the full chart.
Published repeated measurements show the same direction, but the magnitude depends on the method. Baybura et al. compared long-baseline RTK, network RTK and long-session static results at 5, 10, 20, 30, 40 and 60 km; differences within 40 km were broadly within 3 cm horizontally and 4 cm vertically, and at 60 km were about 3 cm horizontally and 5 cm vertically [5]. These values are results under that study’s conditions, not validation points for the Figure 2 formula or upper bounds for all sites.
When moving from single-coordinate uncertainty to apparent displacement between two epochs, the variance of the difference is σ₁² + σ₂² − 2Cov(x₁,x₂); when the two uncertainties are equal, this becomes the √[2(1−ρ)] × σ expression shown in the figure [6]. GNSS observations have temporal correlation, and ignoring it makes accuracy assessment overly optimistic [7]. This article therefore does not assign an arbitrary value to ρ or convert the single-epoch RTK reference line directly into a 24-hour displacement line.
4.4 Our measured data: baseline length and 24-hour apparent displacement
To answer the deformation-monitoring question directly, our data use valid coordinate solutions separated by 24 hours, transform them to local ENU, and calculate horizontal and vertical apparent displacement. For each station, we calculate p95 from a 30-day sample, then take the median within each baseline-length group. This is not the same statistic as the single-epoch RTK reference value in Figure 2, so the results are presented separately.
Swipe horizontally to view the full chart.
Both horizontal and vertical results increase monotonically across the four distance groups; station-level rank correlations point in the same direction, at +0.647 horizontally and +0.615 vertically. This supports baseline length as an important explanatory factor in this sample, but does not mean distance causes every station’s difference. Satellite visibility, obstruction, multipath, equipment and site environment also remain present, so Figure 3 is suitable for viewing the trend, not for promising a new site’s result from one bar.
5. Why there is no universal distance-to-accuracy table
Studies often report the performance of relative positioning, reference networks or precise point positioning for a particular baseline range, but each result is tied to its test conditions. Such findings help define technical boundaries; they are not universal guarantees.
For single-reference relative positioning, physical distance directly affects how much error remains common between the stations. When an external reference network or regional correction service is used, the correction content changes the effective error model. A map distance alone is therefore insufficient; the observations, correction representation and coordinate frame must also be identified.
6. How a project should validate its design
6.1 Define the measurand first
Before discussing distance, make the requirement testable. Is the project observing horizontal, vertical or three-dimensional motion? Does it concern sudden events, daily change or a long-term trend? How much latency and missing data are acceptable? Which stable reference frame must the result represent?
6.2 Test candidate configurations under the same protocol
Compare candidate reference stations, antenna sky view and height differences across different times and weather conditions. If an external reference network, regional corrections or precise products are used, record the data mode, correction age, communication interruptions and reconvergence behavior.
6.3 Report accuracy, availability and integrity separately
At a minimum, report separately:
- horizontal and vertical bias and dispersion;
- availability of the fixed or target solution type;
- initial convergence and reconvergence after interruption;
- data gaps, periodic effects and discontinuities;
- external checks against an independent reference or known-stable point.
Mean, RMS, standard deviation and percentiles answer different questions. State the statistic, sample period and exclusion rules before comparing results. A model coefficient from one site must not be carried directly to another.
6.4 Check the reference independently
Motion of a single reference station enters relative-position results with the opposite sign. Critical projects should use an independent method or redundant references to check reference stability and should record antenna replacement, firmware changes, environmental changes and earthquakes.
How RST diagnoses baseline effects from measured data
RST has accumulated operational observations across multiple sites, long periods and varied environments—not only equipment specifications. These data let us separate the mechanisms hidden behind “a longer baseline” instead of blaming distance whenever a time series degrades.
1. Separate GNSS observations from the processing pipeline
Raw epochs, observation-period solutions and final monitoring time series do not have the same statistics. Ambiguity state, sliding windows, quality selection and aggregation can all change the distribution and temporal correlation. We compare these layers so that smoothing, overlap or latency introduced by processing is not mislabeled as a physical limit of GNSS.
2. Do not treat fixed, ratio or sigma as truth
Measured data can enter an incorrect integer state while familiar quality indicators still appear normal. We therefore combine residuals, geometry, continuity across time, reference stability and independent checks instead of using one threshold as proof of validity.
3. Identify the source of periodic behavior before correcting it
Repeating motion can come from site multipath, regional atmosphere, a shared reference or the processing window itself. RST compares phase consistency between stations, reference grouping, time-frequency signatures and environmental records before attribution. Stronger smoothing or blind common-mode removal can delay an event or remove genuine regional deformation.
The engineering value is a site-calibrated error budget that identifies the dominant error and the intervention justified by measured evidence. Project validation documents the samples, settings, model coefficients and decision thresholds used to reach and accept that conclusion.
The following de-identified internal examples illustrate qualitative patterns only. Because this public article does not include the sample size, observation period or full analysis method, the bar lengths should not be read as performance specifications or universal ratios.
Interpreting measured symptoms
| Observed symptom | What it does not prove | What to check next |
|---|---|---|
| Fixed, ratio or sigma appears normal, but the coordinate jumps | The movement must be real deformation | Residuals, geometry, continuity over time, reference stability and an independent reference |
| Several stations in one region show a similar period | It must be single-site multipath, or it must be global atmosphere | Cross-region phase, reference grouping, environmental records and the time spectrum |
| A short baseline still produces an unstable series | Atmosphere or distance must be the only cause | Obstruction, multipath, antenna, monument and construction environment |
| Stronger smoothing makes the curve flatter | Data quality must have improved | Event latency, serial correlation and whether genuine common movement was removed |
7. Conclusion
Baseline length affects whether errors at two stations remain common; it does not directly determine one fixed accuracy. Greater distance usually increases ionospheric and tropospheric decorrelation and can affect ambiguity resolution, solution availability and time-series quality. A short baseline, however, cannot remove multipath, obstruction, antenna effects or instability of the reference station.
GNSS deformation-monitoring design should treat the baseline, site, atmosphere, correction service and processing method as one error budget and validate that budget with field data. A distance-and-performance result becomes useful when its measured conditions are stated, reproduced and carried into the project acceptance criteria.
RST Ltd.’s near-real-time differential GNSS monitoring service evaluates reference configurations against the site and measurement objective. Each project establishes its acceptance method from field conditions and records the validated samples, settings, coefficients and criteria in the project documentation.
GNSS monitoring series
This article focuses on baseline effects; the adjacent articles compare positioning methods and explain how to assess a monitoring site.
Previous: Comparing differential positioning methods | Series 3 of 7 | Next: GNSS monitoring site assessment
References
- Balan, N., Liu, L., & Le, H. (2018). A brief review of equatorial ionization anomaly and ionospheric irregularities. Earth and Planetary Physics, 2(4), 1–19. DOI: 10.26464/epp2018025
- Garrido, M. S., de Lacy, M. C., & Rojas, A. M. (2018). Impact of tropospheric modelling on GNSS vertical precision: an empirical analysis based on a local active network. International Journal of Digital Earth, 11(9), 880–896. DOI: 10.1080/17538947.2017.1367040
- Teunissen, P. J. G. (1995). The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. Journal of Geodesy, 70, 65–82. DOI: 10.1007/BF00863419
- U.S. Geological Survey. Global Positioning Application and Practice: Typical Accuracy of Survey-Grade GNSS. USGS GNSS guidance
- Baybura, T., Tiryakioğlu, İ., Uğur, M. A., Solak, H. İ., & Şafak, Ş. (2019). Examining the accuracy of network RTK and long base RTK methods with repetitive measurements. Journal of Sensors, 2019, 3572605. DOI: 10.1155/2019/3572605
- Ku, H. H. (1988). Statistical Concepts in Metrology—With a Postscript on Statistical Graphics. NBS Special Publication 747. NIST publication
- Miller, C., O’Keefe, K., & Gao, Y. (2012). Time correlation in GNSS positioning over short baselines. Journal of Surveying Engineering, 138(1), 17–24. DOI: 10.1061/(ASCE)SU.1943-5428.0000057
Frequently asked questions
Q: How close should the reference station be? No single distance works for every project. Validate the proposed baseline against the target displacement, vertical requirement, site, height difference, ionospheric environment, correction service and processing method. For single-reference relative positioning, a shorter baseline is generally favorable, but the reference must also be stable and have a good observing environment.
Q: Can a better receiver compensate for a long baseline? Only in part. Multiple frequencies, constellations and a better antenna improve observations and modeling, but they cannot make distant stations observe the same atmosphere. Long baselines still require suitable atmospheric estimation, network corrections or longer observation periods.
Q: Does a fixed solution prove that the displacement is trustworthy? No. Fixed status means that the processor accepted one integer ambiguity set. Model error, multipath or an unsuitable stochastic model can still produce a wrong fix. Residuals, geometry, continuity, reference stability and external checks are also required.
Q: Can an external reference network replace a dedicated reference station? It depends on the measurement objective. An external network can reduce some distance-dependent errors and support a coordinate frame. Local high-rate relative deformation, tolerance of service interruption and reference traceability may impose different requirements. Compare them under the same acceptance criteria rather than assuming one is always superior.
Q: How can I tell whether an existing system is affected by baseline length or the atmosphere? Compare solution availability, reconvergence, residuals and time-series repeatability under different atmospheric conditions and times of day. Diagnose those effects separately from obstruction, multipath and reference stability. A displacement curve or a single sigma value cannot identify the cause.
Need help evaluating a reference configuration and acceptance method? Contact RST Ltd. or learn about our near-real-time differential GNSS monitoring service.