Fundamentals of Localization (Coordinate Transformation)

Localization is the process of comparing global GNSS coordinates—latitude, longitude, and ellipsoidal height—with the coordinates of known control points expressed in a local site grid, then applying corrections to remove any mismatch. Often called “site calibration” in surveying software, this procedure pairs each control point’s local (meter-based) planar coordinates with its GNSS-measured global coordinates (degree-based). From these pairs the software computes transformation parameters—translation (shift), rotation, and scale—so that all GNSS positions align accurately with the project’s local coordinate system.

This process enables you to assign local grid coordinates to GNSS-measured points so they match the site-specific reference frame.

To perform localization, you need to understand the reference systems involved—such as Japan’s JGD2011 datum or the global WGS 84. JGD2011 is a nationwide geodetic datum that can be expressed in regional plane-rectangular (zone) grids. For example, a project in Tokyo would use the appropriate JGD2011 Plane Rectangular Coordinate System, Zone ○. Most control-point coordinates supplied for public surveying—benchmark plaques, electronic reference stations, and so on—are published in this public grid, typically as latitude/longitude or X-Y plane coordinates.

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The standard method for utilizing known points involves the following steps for coordinate transformation:

1. Prepare the control points: Select existing benchmarks or triangulation stations on site whose coordinates are precisely known in the public grid (X, Y, Z). Ideally, use at least three control points—the standard recommendation in public surveying—although localization can be performed with fewer. The more points you include, the more robust and accurate the transformation will be.

2. Observe the control points with RTK: Using the RTK rover, measure the position of each selected control point. By default, GNSS provides global coordinates—such as WGS 84 latitude, longitude, and ellipsoidal height—although some receivers or settings can output real-time values already converted to a local plane-rectangular grid. In either case, compare the RTK-derived position of each point with its “true” published coordinates at this stage.

3. Compute the transformation parameters: From the differences between the GNSS-observed coordinates and the control points’ published values, calculate the horizontal translation (ΔX, ΔY), rotation angle θ, and scale factor S. A Helmert (similarity) transformation is commonly employed: by optimally fitting the X/Y shifts, rotation, and scale, it minimizes overall positioning error.
   With only one or two control points you can apply a simple shift—or a shift plus rotation—but three or more points enable a full solution that also corrects for scale error.

4. Apply the transformation: Load the calculated parameters into the RTK system so that every new point or point cloud is automatically converted to the public grid (or any designated local system). From that moment, all RTK-measured positions are recorded in the same reference frame as the control points. For example, raw latitude-longitude coordinates can be transformed on the fly into X-Y values in the plane-rectangular grid, making them immediately usable in design drawings, GIS layers, and other project datasets.

5. Verification: After localization, re-measure the control points—or additional check points—and compare the transformed coordinates with their known values. You can also compare the distances between neighboring control points to ensure that discrepancies before and after transformation fall within acceptable limits. If significant residual errors remain, add more control points to the adjustment or exclude any outliers and recompute the transformation.

That, in essence, is the basic localization workflow— a procedure for aligning global GNSS coordinates with the local grid used on site. In public surveying, regulations specify that the transformation must be performed in a plane-rectangular coordinate system and that at least three control points be used. Careful computation and verification are therefore essential to produce results that meet the required level of reliability.

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Localization Procedure for RTK Positioning with LRTK
By pairing an iPhone with an LRTK Phone, you can perform RTK positioning quickly and easily using LRTK.

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When paired with the dedicated iOS app, anyone can perform centimeter-level surveys with ease, and the resulting data can be managed and shared in the cloud. Below, we outline the concrete steps for applying coordinates (localization) with an LRTK device—showing how lightweight gear lets you carry out control-point measurements and localization right on site.
Please note: the in-app localization feature is still under development. Thank you for your patience until its release.

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​1. Connecting and preparing the LRTK device and smartphone:
Attach the LRTK unit to your smartphone and launch the dedicated LRTK app.

The phone connects to the device over Bluetooth, allowing you to monitor the GNSS receiver’s status directly in the app.

In environments without internet access—such as forested areas—you can receive corrections via the “Michibiki” Quasi-Zenith Satellite System’s centimeter-class augmentation service (CLAS) provided in Japan.

In the latter scenario, you can still perform RTK positioning in mountainous regions beyond mobile‐network coverage because the receiver obtains augmentation signals directly from the satellite. Once the RTK status in the app reads “Fix (Fixed Solution)”, you are ready to proceed.

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2. Set the coordinate system:
Next, choose the coordinate system to be used in the app.
The LRTK app can convert measured positions to the local plane-rectangular grid in real time. All the user has to do is select the grid zone for the region in advance; the app automatically transforms latitude and longitude into planar X-Y coordinates from that point on.

For instance, on a job site in Tokyo you would select “Plane-Rectangular Coordinate System, Zone 9 – JGD2011.” Every position measured onsite is then displayed instantly in that public grid. The vertical component is handled in the same way: the app automatically converts ellipsoidal height to orthometric height using the appropriate geoid model, outputting elevations in the JGD2011 system.

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3. Measure and register control points
After setting the coordinate system, measure the site’s known control points and register them in the app. For example, if there is an existing benchmark or survey marker on-site, place the LRTK unit over it, perform a fix, and record the resulting coordinates in the app.

For greater accuracy, remain stationary for several seconds (or up to a few dozen seconds) and use the averaging function while taking the measurement.

The LRTK app includes an “Averaged Positioning” feature that takes a user-specified number of readings and calculates their mean.

This further reduces measurement error, enabling you to obtain stable coordinate values.

Observe each additional control point in the same manner, one after another.

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4. Execute localization (coordinate transformation):
Run the localization calculation within the app.

The LRTK app provides a “Coordinate Application” feature *1 that lets you enter your measured control points and their known coordinates, then apply the coordinate correction with a single tap.

Using this feature, you register the GNSS measurements you just collected for each control point and link them to the points’ correct coordinates.

The app then calculates the discrepancies between each pair internally and derives transformation parameters—such as planar offsets and rotation corrections—that minimize overall error.

Once the calculation is complete, switch “Apply Localization” to ON. From that point forward, all coordinates displayed in the app are the corrected values—fully aligned with the site’s coordinate system.

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5. Verification and operation: 

Finally, verify the localization results. Measure the control points again and confirm that the coordinates shown in the app match the known values.

Once verification is complete, you can move on to positioning unknown points or carrying out stake-out tasks exactly as you would in a routine survey.

The LRTK app provides robust tools—including real-time readouts of distance and bearing to a target point, plus the ability to save points with names and notes—so you can carry on with field work directly in the localized coordinate grid.

In this way, the LRTK app lets you view all detailed information—including the localized coordinates—and makes it easy to add notes for each survey point and share data with others.

As an operational example, a civil engineering site used LRTK to localize two or three control points in advance; thereafter, every coordinate collected for as-built management was automatically unified in the public coordinate system.

Because the survey team could use the captured coordinates directly for electronic deliverables, they eliminated the need for post-processing conversions—achieving a substantial boost in efficiency.

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In another case, a farmland parcel survey used the coordinates of cadastral boundary markers as control points, localized the RTK solution accordingly, and then applied the unified grid for field surveys and machine-guidance in farm operations. Because localization with LRTK is a straightforward process, even novices can align site coordinates with ease, while seasoned surveyors gain a significant boost in day-to-day productivity.

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*1: This feature is currently under development. Details may change before its release. Thank you for your patience.

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Localization Troubleshooting
Discrepancy with control points not resolved:

If, after localization, you re‐measure your control points and still observe discrepancies of several centimeters or more, first suspect errors in the input of the control‐point coordinates or mistakes during the measurements.

Double-check the known coordinates (your reference values) and verify that you correctly positioned the antenna over each control point during measurement. Next, review whether you have used a sufficient number of control points.

Remedy: If possible, add additional control points and run the coordinate transformation again. If the error still persists, poor positioning conditions—such as multipath from nearby buildings or trees—may be the cause, so try adjusting the antenna mounting location or repeat the observations at a different time.

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All points are offset in the same direction:
In cases where all newly measured points are consistently offset by approximately X cm to the southwest, it may indicate that the translation parameters (shift values) computed during localization were not applied correctly.

For example, a mismatch between the base station’s coordinate system and the rover’s output reference will produce a uniform translation error across all points.

Remedy: Verify the coordinate‐system setting of your base station (or virtual reference point in network RTK). Ensure you have selected the correct plane‐rectangular coordinate zone (Zones 1–19).

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Significant height (elevation) error:
If your horizontal coordinates are correct but the elevation alone is off by more than 10 cm, the likely cause is a mismatch in the geoid model or the underlying geodetic datum.

GNSS‐derived heights are essentially ellipsoidal heights, and to convert them to orthometric heights (above sea level), you must subtract the geoid height (geoid undulation).

In Japan, models like “GSIGEO2011” are used for the geoid—but if your system isn’t applying it, you will see an elevation offset.

Remedy: Check the app and receiver settings to ensure the correct geoid correction is being applied when computing elevations.

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Use Cases and Applications
RTK localization techniques are employed across a wide range of fields—from civil‐engineering surveys to infrastructure inspections. Below are several concrete examples and potential applications.

• Control-Point Surveying in Civil Engineering: On road and bridge construction sites, high-precision surveying is essential for layout based on design drawings and for as-built management. Traditionally, coordinates were established by measuring angles and distances from known points with a total station—but introducing RTK positioning dramatically boosts efficiency. For example, if you localize your site’s control points in advance using RTK, you can then use only the GNSS rover to obtain real-time coordinates for any point. On one development site, a heavy-equipment operator measured required elevations and positions using a tablet paired with RTK, then immediately checked the depth of buried utilities on the spot. Because localization had already been applied, all measurements appeared directly in the design coordinate system, enabling instant decision-making.

• Infrastructure Inspection and Maintenance: When inspecting tunnels, bridges, and other infrastructure, pinpointing deterioration with high-precision coordinates is crucial. By leveraging RTK localization, inspectors can record cracked or damaged locations complete with public-grid coordinates, simplifying future repair planning and interdepartmental data sharing. Systems now exist—built around devices like LRTK—that automatically embed position tags into photos and sync them to the cloud. As an inspector snaps a picture on their smartphone, the exact RTK-derived coordinates are applied to the image, allowing later mapping of defect locations with pinpoint accuracy. This approach is also used for road patrol inspections and manhole‐cover management in water and sewer networks, transforming manual, paper-based workflows into fully digital processes.

• Application to Construction Management and AR Technology: High-precision localized coordinates, when combined with augmented reality (AR) technology, are giving rise to new construction‐management methods. For example, overlaying a design BIM model on a tablet’s camera view requires aligning the model to within a few centimeters—a capability made possible by RTK. One civil‐engineering firm uses an LRTK‐based AR system to visualize the design positions of buried pipelines on site, aiding pre‐excavation checks. Whereas traditional GPS‐based AR suffered meter‐level offsets, RTK localization reduces the discrepancy between the model and the real world to just a few centimeters, supporting safe and accurate construction. Furthermore, as‐built point‐cloud data acquired during construction can be immediately handled in the public coordinate system, making it easy to produce deliverables that comply with the Ministry of Land, Infrastructure, Transport and Tourism’s electronic‐submission standards.

• Agricultural Positioning & Smart Farming: High-precision RTK positioning is also transforming agriculture. Tractors with automated steering systems rely on RTK-GNSS to maintain straight paths and manage field plots with centimeter-level accuracy. By applying localization, you can further correct positioning data to match field-specific control points (e.g., the four corners of a plot), ensuring that digital field maps and on-ground reality align perfectly.

• In one ag-ICT application, soil-sensor readings were tagged with RTK-localized coordinates, greatly improving the accuracy of fertilizer-application maps. Looking ahead, using localized coordinates for tractor telemetry or drone imagery will eliminate positional discrepancies between different data sources and enable truly integrated, efficient farm management.

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In summary, RTK localization goes far beyond traditional surveying, finding applications across a wide range of industries. The advent of user-friendly devices like LRTK has created opportunities for even non-surveying professionals to leverage high-precision location data. From civil engineering and construction to agriculture, we stand on the brink of an era in which anyone can work with centimeter-accurate position information with ease.