Positioning Errors—Managing Project Accuracy Budgets

A 723Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

In the positioning domain, there is no such thing as a perfect measurement or an exact location. Digits can be added to any number to increase its precision to a point where error can be seen. Understanding the precisions of the various positioning devices that are used on modern machine control systems must be taken into account when project accuracy requirements are close to the system performance levels. This article will look at various sources of positioning errors and discuss ideas for managing project accuracy budgets.

A botanist that is delineating the edge of a forest with a project accuracy budget of 5 meters, while using a GPS unit precise to ½ meter, has a large buffer. She/ He does not need to be very concerned about the system performance to meet the accuracy requirements of the project. But a machine controlled grader that must rough grade dirt to within a 10th of a foot vertically needs to consider the total error of all the positioning sensors and hardware being used. Tilt sensors, GNSS, lasers, total stations and inertial guidance systems have the potential to contribute some amount of error. Add to this any changes that occur with the machine or in the environment. Cutting edges wear down; offset distances can change; and hysteretic variations and environmental extremes can contribute additional errors to the final positioning result. Does the sum of these errors exceed the accuracy requirements of the project?

GNSS can be the single largest contributor of error to final positioning results when considering the various sensors used on a typical machine control system. GNSS relies on external data to take an autonomous precision of 10 meters down to an RTK fixed position of 1 or 2 centimeters (0.03 ­ 0.06 ft.). This represents a 500 times increase in performance but is completely reliant on an external data source for this precision.

If the data stream fails or is not relevant (such as the base station being too far away), positioning results degrade. GNSS is also affected by the amount of sky that is visible and is sensitive to reflective objects in the vicinity. If the sky is partially blocked by trees or other structures and/or there are reflective objects nearby such as mirrored buildings or industrial plants, accuracies will degrade. A typical real-time GNSS specification claims a 1 centimeter precision in the horizontal plane and 2 centimeters in the vertical sense. This specification is in a perfect world. Imagine a grassy field in all directions with a GNSS set up on a tripod. Most machine control installations and project sites do not resemble this so it is likely that this 1 ­ 2 centimeter specification will not be met all the time using GNSS only. For a waste disposal site with accuracy requirements in the +/- 6 inches range, real time GNSS accuracy is ample for their compactors. But for a cement contractor pouring pads for tilt-up buildings, the difference between +2 centimeters and -2 centimeters of grade can amount to $1,000's of difference in material costs. GNSS for vertical positioning is likely not the right tool for this task.

A cement contractor is more likely to use lasers to position his machine. Lasers provide some the highest vertical accuracies in the machine control domain. Total stations do a good job with verticals; lasers do a better job. Accuracies using either of these tools are going to be in the 1 to 2 millimeter range when used properly. "When used properly" is an important consideration. Every time a total station or a laser is moved from one location on a site to another, there is an introduction of error in the setup when compared to the previous setup. The instrument may not be precisely positioned over its control point or the height of the instrument may not have been measured properly. The instrument may be out of calibration or the orientation of the coordinates may have been slightly misaligned. There will be error.

Station setup error can be a significant disadvantage when using total stations or lasers compared to a GNSS. Although a GNSS is only accurate in the 2 ­ 3 centimeters range, it still may provide better results than a laser or total station depending upon the size of the project. For a typical construction site, it's obvious that lasers and total stations are the most precise. But for certain corridor projects spanning tens or hundreds of miles, GNSS will reduce significantly the number of station setups that are required and is coupled with the ability to tie the project datum together through post-processing during the development of the control.

Total stations and GNSS express their vector accuracy in terms of an absolute value plus an accumulated value. A typical total station distance specification is 2 mm + 2 ppm. Every measurement will have a random 2 millimeters of error and as the distance increases (total station to prism) an accumulation of error will be added at the rate of 2 millimeters per kilometer. Since most machine control systems are not going further than 500 meters from the total station that is tracking it, every measurement will have 2 to 3 millimeters of error associated with it. GNSS real-time vertical accuracy is typically 2 cm + 2 ppm. Every measurement will have a random 2 centimeter of error plus another 2 millimeters for every kilometer of distance between the machine and its base station. This distance can be a bit confusing to estimate since most machine control systems do not display base station information.

Total stations, lasers and tilt sensors are graded in terms of angle accuracies. Most total stations are specified 1 to 5 seconds of arc accuracy. A well calibrated, 3 second total station will aim within +/- 0.003 feet of the correct line at 2000 feet. Tilt sensors are typically in the 10th of a degree range. Rotating lasers usually express accuracy as a tolerance at a certain distance. For instance, a laser specification might be expressed as +/- 2 mm @ 30 meters. When an operator is 100 feet from the laser, the vertical position will be reported within a 4 millimeter range of the correct value.

The cost of inertial sensors has declined over the past few decades. It makes sense to employ these sensors into machine control systems. Inertial sensors can add a great deal of redundant assurance that the machine control system is performing as expected and can also augment performance in areas that are not optimized for visual or GNSS positioning techniques. Inertial systems rely on periodic calibrations; position computations gracefully degrade between calibrations. The accuracy of inertial systems is limited by the precision of the calibration sensor (GNSS for instance), the period of time between calibrations and the quality of the inertial sensor.

There is also the actual machine hardware to consider. When using GNSS, how is the position of the geodetic antenna related to the blade cutting the dirt? Has the blade worn down? Has the antenna model changed? Is the antenna on a mast that swings around in relation to the machine? For a total station system, are the prism type and height correctly accounted for and have the offsets to the blade maintained their initially surveyed precision?

Another error source that must be considered is the human element. North's and East's get transposed. Ditto with feet and meters. Ellipsoidal heights are treated as orthometric or geoid models get changed. Poor survey practices are used, equipment does not get serviced, and operators do not get trained properly. Hardware components get changed but the software knows nothing about these changes. Designs get amended in the office but don't make it out to the field. The human error contribution is real and must always be considered as a possible error contributor.

Mostly, primary sensor errors are compensated by secondary sensors. A GNSS which meets the horizontal accuracy requirements of a project may be augmented by a laser system that manages the vertical positioning more accurately. Hardware error sources tend to be in addition to sensor errors. It's an accident when a blade wearing down actually corrects a sensor that is measuring a little high for some reason. More often, the hardware contributions of error are in addition to the actual sensor positioning errors.

What is the best method for managing these errors sources? Redundant measurements, system awareness and frequent check shots are key tools for managing an accuracy budget.

On every project, there are key points or key areas that are critical to the project's success or profitably. These are money shots. The question should be asked, "If the position is wrong, will it cost money?" If the answer is yes, redundant measurements may be in order.

System awareness can only be mastered with time, training and experience. Operators that are intimate with all aspects of the machine control system can tell when something is amiss. They may not recognize the source immediately, but they recognize a change which can be the first and not so obvious indication of a problem.

Check shots should be mandatory. There should be several control points surrounding a project that are available to check precisions. A noted land surveyor, Phil Stevenson, is famous for saying "The proof is in the dirt." There is no better method for determining system performance in terms of accuracy than comparing measured to known. Setting the blade directly on a control point with a known location and comparing that value to the position being measured by the system is an excellent indication of project precision. Check your control as frequently as convenience allows and reasonable in respect to the type of working being done.

There is no such thing as an exact location or measurement. Nor is there a perfect method for dealing with positioning errors. Site logistics, project accuracy requirements and available resources must be factored together when choosing the best positioning techniques. This article has discussed several positioning error contributors but has not covered all sources; the list and this article would be too long. Instead, the intent was to highlight the major contributors to positioning errors, suggest factors that should be considered when using the various positioning tools, and provide some ideas to consider when managing your own accuracy budgets on current and future machine control projects.

Joe Sass has more than 15 years experience in GNSS. He currently works as a Field Applications Engineers for Spectra Precision with a mission to bridge the gaps between customers, marketing and engineering.

A 723Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

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