2-Point vs Multi-Point Calibration: Which Localization Is Better?

RTK surveying (real-time kinematic positioning) can obtain centimeter-level accuracy (a few centimeters (a few inches)) using GNSS satellites. However, coordinates obtained from RTK may not align with the local coordinate system used on site (design coordinates or coordinates of existing control points). Therefore, it is necessary to adjust RTK results to the site coordinate system through a procedure called localization (site calibration). When performing this coordinate alignment, which produces better results: a method that uses only two known points, or a method that uses three or more points (multi-point)? This article explains the basics of localization and the differences between 2-point calibration and multi-point calibration, and considers which method is appropriate.

Table of Contents

• What is localization?

• Characteristics of 2-point calibration

• Characteristics of multi-point calibration

• Which should you choose: 2-point or multi-point?

• Simplified surveying with LRTK

• Frequently Asked Questions (FAQ)

What is localization?

Localization (site calibration) is the process of correcting the discrepancy between global coordinates obtained by GNSS (for example, latitude/longitude and ellipsoidal height in WGS84) and the local coordinates used on site (such as plane rectangular coordinate systems or proprietary reference coordinates). Simply put, it means aligning points measured by RTK to the site’s reference coordinate system. For example, by matching RTK results to coordinate systems used in Japanese public surveys (the JGD2011 plane rectangular coordinate system) or to locally established construction references, you can ensure high consistency with design drawings and existing survey results.

Localization is necessary to eliminate offsets caused by differences in the positioning coordinate system. Typically, RTK using networks such as the Geospatial Information Authority of Japan’s Continuously Operating Reference Stations provides coordinates based on the geodetic system (world geodetic coordinates). However, construction sites already have established construction control points and plan coordinates, which are expressed in local coordinate systems (e.g., a specific zone of the plane rectangular coordinate system or an arbitrary-origin local coordinate). Because RTK results do not automatically match those plan coordinates, it is necessary to reconcile the two using known points.

The localization procedure is as follows:

• Known points preparation: Select reference points or benchmarks on site whose coordinates (X, Y, Z) are known. If possible, it is desirable to prepare three or more points, and public surveying standards also recommend "using three or more known points." The greater the number of points, the more stable the transformation becomes, and as described later, scale errors (differences in scale) can also be corrected.

• Observations with RTK: Use an RTK receiver (rover) to measure those known points on site. Coordinates obtained from GNSS are global coordinates such as latitude/longitude and ellipsoidal height, but some devices can output values converted in real time to a plane rectangular coordinate system. In any case, take correspondence between the observed coordinates and the true coordinates of the known points.

• Calculation of transformation parameters: Compare the GNSS coordinates measured at each point with the coordinates of the known points, and compute the parameters for coordinate transformation. Specifically, determine planar translation amounts (ΔX, ΔY), rotation angle (θ), and, if necessary, a scale factor (S). For optimal fitting with multiple points, a Helmert transformation (a type of 2D affine transformation) is generally used. With only one known point you can only correct translation (shift). With two known points you can correct shift plus rotation. With three or more known points you can additionally correct for scale differences.

• Apply coordinate corrections: Apply the calculated transformation parameters to the RTK system so that subsequent measured points are converted into the site coordinate system. For example, newly observed points with RTK can be automatically corrected to plane rectangular coordinates (or an arbitrary local coordinate) and recorded. This ensures that subsequent survey results are managed in the same reference coordinates as the known points, streamlining comparison with drawings and as-built control.

Characteristics of 2-Point Calibration

2-point calibration is a localization method that uses two known points. Using only two reference points A and B, RTK coordinates are transformed to the local coordinate system. Generally, the RTK coordinates are translated at point A and oriented at point B. Specifically, first match the RTK observation at known point A to its known coordinates (ΔX, ΔY shift correction), then rotate the entire solution so that known point B has the correct direction (rotation angle θ correction). In this manner, the positional relationship (distance and bearing) between the two points is adjusted to match the known coordinate system.

Advantages and disadvantages of 2-point calibration are as follows.

Advantages:

• Only two known points are required, so preparation effort is small. For limited-area surveys or urgent tasks, coordinate alignment can be completed quickly.

• The procedure is relatively simple, and the parameters to calculate are only shift and rotation, so it is easy to understand. Settings on software and devices are also straightforward.

• Because the orientation can be based on the line between the two points, it is easy to align to a locally defined coordinate axis. For example, if you want a certain baseline to align with the X-axis, two points can define that axis.

Disadvantages:

• It cannot correct scale differences. With only two points, you cannot detect or correct for stretching/compression between the RTK system and the local coordinate system, so scale discrepancies remain. For example, even a slight difference between the field distance and the RTK-measured distance between two points is difficult to reconcile with 2-point calibration. As a result, small errors may occur at locations other than the two points.

• There is little redundancy for error detection. With only two known points, there is no way to check for measurement errors at each point. If there are errors in the surveying equipment or in the known-point coordinates, those errors will directly affect the transformation parameters (risk of correcting based on incorrect references). With multiple points, outliers can be detected, but with two points you cannot judge correctness.

• The arrangement of the two points affects orientation accuracy. For example, if the two points are close to each other or lie on a north–south line, rotation calculation can be unstable and a small angle error can cause large positional offsets. When using the two-point method, it is desirable that the two points be as far apart as possible and positioned to cover the site.

Thus, while the two-point calibration is attractive for its simplicity, it is limited in what it can correct and leaves some concerns about accuracy. Especially for surveys over wide areas or where high accuracy is required, the multi-point calibration described below is recommended.

Characteristics of Multi-Point Calibration

Multi-point calibration uses three or more known points for coordinate transformation. By increasing the number of points, in addition to translation and rotation, comprehensive fitting that includes scale correction becomes possible. Surveying software performs an optimal calculation (for example, a least-squares Helmert transformation) to minimize the discrepancies between observed GNSS coordinates and the corresponding known-point coordinates, yielding transformation parameters that reduce overall error.

Advantages and disadvantages of multi-point calibration are as follows.

Advantages:

• High accuracy including scale correction. With three or more points, you can adjust not only shift and rotation but also small distance stretching/compression, enabling consistent coordinate transformation over wide areas. Particularly for distant points, errors from earth curvature or projection can become noticeable, but multi-point methods can absorb such factors into the scale coefficient.

• High redundancy and improved reliability. With three or more known points, you can compute residuals for each point to see how much each deviates. If some known points have errors or have moved, those anomalies are easier to detect through consistency with other points. Clearly outlying points can be removed from the computation. As a result, the overall survey reliability and precision control are improved.

• Suitable for wide-area work and official surveys. Calibrating with multiple control points ensures high accuracy across any point on site. For public surveys and infrastructure works, localization with at least three points is standard. Using more points (five, six, etc.) increases the stringency of accuracy checks and allows flexible re-calibration by adding control points later.

Disadvantages:

• It inevitably requires more time and effort to implement. If control points are spread out, observing each point takes time, and the more points, the greater the on-site preparation and measurement burden. However, with about three points, the additional work compared to two points is small, and the accuracy gain typically justifies the extra effort.

• The calculations are somewhat more complex. Modern surveying instruments and software perform these calculations automatically, so users do not need to compute them by hand. Nevertheless, understanding the resulting parameters (rotation angles, scale values, etc.) is important for accuracy verification.

• Attention to the balance of control-point distribution is necessary. If control points are concentrated on one side of the survey area or lie on a straight line, the transformation may not achieve its full accuracy. Ideally, place three or more known points surrounding the site to cover the entire area. The transformation performs well within the area enclosed by the known points, but accuracy is not guaranteed outside that area. Therefore, selection and planning of control-point placement are important.

Overall, multi-point calibration excels in accuracy and meets official standards. For important surveying tasks and large sites, it is desirable to perform localization using as many points as possible.

Which should you choose: 2-point or multi-point?

As seen above, both 2-point and multi-point calibrations have advantages and disadvantages. Ultimately, which is better depends on site conditions and the required accuracy. The main comparison points are summarized below.

• Required number of known points: The 2-point method can be performed with exactly two points (with only one point, rotation cannot be corrected). The multi-point method generally requires three or more points (the more points, the more stable).

• Correctable parameters: The 2-point method can correct translation and rotation only; the multi-point method can also include scale correction for a more precise alignment.

• Accuracy and reliability: The 2-point method will match perfectly at the two reference points but may show errors elsewhere. The multi-point method reduces overall discrepancies and provides consistent accuracy over a wide area. With redundancy, the multi-point method offers higher reliability.

• Work efficiency: The 2-point method wins in ease of preparation and observation. The multi-point method requires more observations, but with about three points the additional burden is small. Consider the trade-off with the improved accuracy.

• Suitable applications: The 2-point method is suitable for small-scale surveys or simple alignments. The multi-point method is essential for projects where precision control matters, public surveys, or precise coordinate integration that includes levelling benchmarks.

In summary, multi-point calibration is preferable where high accuracy and reliability are required, and official standards recommend using three or more points. Conversely, when known control is extremely limited or speed is the priority, 2-point calibration may be used as a compromise. Even in that case, it is advisable to later observe additional known points for verification and re-calibration if necessary. In short, choose the method based on site conditions and required accuracy, and use as many high-quality control points as possible to ensure safe and reliable surveying.

Simplified surveying with LRTK

So far we have discussed the importance and methods of localization, but in practice one often wants to perform RTK surveying more easily. Enter LRTK, a solution designed to simplify RTK surveying. LRTK is an RTK-GNSS system provided by Reflexia Inc., offering products and services that make traditional RTK surveying easier.

With LRTK, a small high-precision GNSS receiver that connects to a smartphone and a dedicated app enable anyone to achieve centimeter-level positioning (centimeter-level accuracy (half-inch accuracy)). For example, by attaching a device called the "LRTK Phone" to a smartphone, you can effectively upgrade the phone’s built-in GPS to RTK capability. The device includes a high-performance antenna and battery, eliminating complicated cables and bulky equipment. By configuring network RTK (Ntrip service) in the smartphone app and receiving correction data, you can obtain high-precision position information on the spot.

Why does LRTK simplify surveying? The main reason is that it minimizes specialized equipment and complicated setup. Traditionally many devices—GNSS receivers, radios, controllers—were required, but LRTK completes the workflow with just a smartphone and a compact device. Also, because correction data are obtained over the network, you do not need to set up your own base station, so you can start RTK positioning immediately even at a new site. This enables site personnel to perform quick surveys themselves at small sites or where a dedicated surveying team is not present.

LRTK’s simplified surveying can be combined with localization if needed. For example, if known points exist on site, you can use LRTK to measure those points and perform coordinate transformation within the app to obtain results in the site coordinates without complex manual computation. If there are no known points, LRTK can still obtain positions in Japan’s public coordinate system (JGD2011), allowing those results to be used as public coordinates directly (though if alignment with existing drawings is required, a post-processing shift adjustment may be necessary). In this way LRTK lowers the barrier to RTK surveying and serves as an accessible positioning tool for beginners. Making high-precision surveying more familiar and easier—LRTK is a strong solution toward that goal.

Frequently Asked Questions (FAQ)

Q: Can localization be done with only one known point? A: With only one point you can only correct translation (shift). That is, you can match that known point’s position, but the orientation (angle) remains in the GNSS north reference, and scale cannot be corrected. If possible, add a second known point or at least apply the shift with the single point and manually adjust remaining offsets later.

Q: What should I do at a site with no known points at all? A: Precise localization cannot be performed with zero known points. There are two options. One is to use the geodetic coordinates obtained from RTK (for example, JGD2011 coordinates) as-is. If the site has no existing references, you may adopt the newly obtained coordinates as an arbitrary reference. However, note that when compared with other survey results later, meter-level discrepancies (several meters (several ft)) may occur. The other option is to set up provisional control points yourself. For example, choose a convenient location on site and assign it an arbitrary coordinate (a temporary origin) to serve as a control station. Conducting relative positioning from that reference allows you to compile results within a consistent local coordinate system. Although this method lacks consistency with existing references, it is effective for work confined to the site.

Q: How do I align RTK-derived elevations (heights) to existing vertical control? A: GNSS heights are normally ellipsoidal heights and differ from orthometric (geoid-based) elevations. To align elevations, use a geoid model to convert ellipsoidal heights or measure a known elevation point on site to determine a height offset. In Japan, geoid models (such as GSIGEO2011) are provided; applying these in the RTK receiver or app allows you to correct measured elevations to standards such as the Tokyo Bay mean sea level. Alternatively, you can observe a known bench mark and apply the difference to all measured points as a simple method. In any case, don’t forget to perform vertical corrections in addition to horizontal localization.

Q: Are there cases where 2-point calibration is sufficient? A: Yes. For small-scale works or cases with low accuracy requirements, 2-point calibration may be practically sufficient. For example, site surveys within an area on the order of tens of meters (tens of ft) square where the distance between known points is short may produce nearly consistent results with two points, since scale errors are negligible over that range. However, as the area increases or accuracy requirements become strict, the limits of the 2-point method appear. For long-distance surveys or surveys subject to official inspection, it is safer to calibrate with three or more points.

Q: Does using LRTK eliminate the need for localization work? A: LRTK simplifies RTK measurements but the concept of localization (coordinate alignment) remains the same as for conventional RTK. If you need to align to known points on site, you still need to measure those known points and perform coordinate transformation as before. That said, LRTK’s app can perform such transformation calculations easily and allows immediate map-based verification of measured points, making the localization process smoother. Also, if there are no known points, you can use LRTK-obtained public coordinate system values for simplified surveying and adjust later if needed. In short, LRTK is a tool that streamlines surveying, and when used appropriately it can reduce the time and effort required for localization.