GNSS Ground Localizations - Best Practices

Parent Category: Columns

Written by Joe Sass

Created on Saturday, 04 June 2011 18:32

A GNSS coordinate localization is an attempt to take space based measurements and turn them into useful northings, eastings and elevations on the ground.  There is no perfect technique to accomplish this transformation.  Several methods exist, but none are exact in the conversion and all have limitations.  This article will discuss GNSS coordinates in general and then look more closely at the method of calibrating multiple points on the ground to GNSS measurements.

GNSS positions are calculated from a theoretical center of the planet and presented as Earth Centered, Earth Fixed (ECEF) coordinates.  These ECEF coordinates are not very useful in the real world where horizontal and vertical distances need to be quickly calculated.  For the sake of convenience, these ECEF coordinates are converted to latitudes, longitudes and ellipsoid elevations.  These geographic coordinates are still not very useful for disciplines such as machine control and land surveying, so these geographic coordinates are usually converted to some type of mapping plane which then provides northings, eastings and elevations.  But, these plane coordinates are on a grid and therefore do not provide ground distances and the elevations do not account for gravitational influences.  One of the safest and most common ways to utilize GNSS derived coordinates is to perform a multi-point comparison between known ground based monuments and actual measurements with the GNSS.

This method is often called a “One-Step Transformation” even though it involves multiple steps from a mathematical sense.  The user of the equipment measures known control points on the ground with the GNSS and then the application software allows the measured point values to be compared with the control point values.  The software calculates a best fit between the two coordinate systems.  Done correctly, this technique removes the obligation of the user to understand geodesic principals such as geoid elevations, grid to ground conversions, ellipsoids, etc.  The caveats to this approach are that the routine must be done correctly, there should be good geometry between the control points and the coverage area should be limited to about 6 square miles.  Done poorly, resulting northings and eastings can be correct in some places on a project and completely wrong in others, so an understanding of the best practices for localizing a site with GNSS is important.

The key ingredients for a successful one-step transformation are:
1)    Five or more, three dimensional control points surrounding the job site.  These points should have a clear view of the sky in all directions.
2)    GNSS measurements on the control points with 1 to 2 centimeters of precision.
3)    Application software that does a good job of calibrating the two systems.
4)    Validation on additional control points throughout the job site to verify coordinate conversions.

A multi-point transformation relies on having good local coordinate values for the control points, having these points spread evenly around the perimeter or even outside of the project area and with a great view of the sky for the GNSS measurements.

If a single control point is compared to a GNSS measurement, an exact association can be made between the control northing, easting and elevation and the measured latitude, longitude and ellipsoid elevation.  The rotation of the coordinate system would probably assume a geodetic north orientation and differences between grid and ground distances would likely exist.
   

If there are two control points being compared against GNSS measurements, this manages correctly the rotation of the coordinate system and adjusts the scale difference between grid and ground distances.  But it does not lock in a three dimensional plane for the elevations.  Even though elevations are held at the two points, this does not prevent the mapping plane from tilting transverse to the line created by these points.
   

When three control points are used, this checks the orientation and scaling of the project and the software should begin to show residuals of the best fit for the northings and eastings.  Three control points also locks in the mapping plane with a “perfect” fit vertically.
   

As the fourth point is added to the localization, a truer picture of the overall horizontal fit can be observed through the residual values generated by the software.  Depending upon the presentation of the data, these should be very small values.  When expressed in RMS, a user should generally expect values in the centimeter or sub-centimeter range.  This fourth point in the localization not only tightens up the best fit horizontally, it also gives an indication of how well the fit is going vertically by producing vertical residuals.

As five or more points are added to the localization, a reliable indication of both the control values and the measured values begins to emerge. Five points provides redundancy for both the vertical and horizontal components of the localization. This redundancy exposes any misfits in the systems. The user should possess the skills to assess the quality of the calibration. Most software packages allow each localization point to be held in a horizontal and/or vertical sense.    

If the software is indicating that there is a large misclosure in the horizontal component, the user can toggle points on or off horizontally to see which point or points are causing the problem.  The same can be done in a vertical sense.  The warning is to have enough points that are held both horizontally and vertically so that there are residuals and redundancy in all three dimensions.  This means that for the horizontal component, no less than four points should be used and in a vertical sense, no less than five points should be held.
  
There will always be misclosure when using a one-step transformation with more than two points.  The goal is to manage the misclosure down to acceptable levels.  With a GNSS receiver whose specification is 1 centimeter horizontally, this is a good target.  Let’s assume that a calibration was performed using five points and all of the reported residuals are less than one centimeter.  Does this mean that the localization is good to that precision throughout the job site?  The answer depends upon the location of the calibration points.  If the five points were scattered throughout the interior of the job site, the localization is not as strong as if all of the points surround the project area as in the example above.  The misclosure of the localization is a statement about the amount of error at each particular point.  This error can be interpolated and shrink when approaching the center of the localization or it can be extrapolated and grow when leaving the bounds of the localization points.  This is the reason that calibration points need to be at the perimeter or even outside the project area.  All the error is interpolated down to zero at the center of the localization.

The methods for getting a GNSS receiver to provide local coordinates have undergone many changes since the technology came into widespread adoption.  Application software has gotten better at simplifying the process.  This evolution will continue to improve, but until it does, a practical understanding of getting from GNSS coordinates to the local job coordinates is vital.  The one-step transformation is the most widely used method due to its ease of use when executed properly.  Since GNSS is now integral to the machine control industry, it’s incumbent upon the users that deploy these systems to understand the correct procedures.  MachineControlOnline.com is committed to keeping its readers informed and educated about the industry’s best practices.

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