What Are We Really Measuring?

The last few posts have focused on things we need to think about, or bear in mind, before we begin making measurements. In this post, the issue of what is the raw measurement being made will be considered. In many cases, what is being measured in not what you thought! The value you get is unlikely to be a raw measurement, but a derived value based on something very different being measured.

Conceptually, the simplest measurement is perhaps measuring a distance with a tape. The value on the tape may seem to be the ‘measurement,’ but it really starts with two measurements on the tape: one where the numbers are read, and the other at the zero point. Both points need to be positioned and measured to get the correct raw distance along the tape between the two points. If the ‘zero’ point isn’t actually zero, then the difference between the two readings must be calculated.

To make life easier, we usually try to align the tape’s zero point with one end of the measurement, so that the subtraction is not required. But if the zero point is not clear, as was the case with some old surveyors bands, then reading to some other point is required.

That may seem a little pedantic, but the point to note is that even the simplest measurements may not be as simple as they seem. Even with the distance along the tape known, there remains a group of ‘corrections’ that need to be made to get the corrected distance. These allow for the calibrated length of the tape to be used, and allowances can be made for changes in the tape length for temperature, tension and sag, followed by corrections to allow for the distance above the ellipsoid or sea level, and the slope of the tape.

The same thing happens with leveling, as we are just reading a value on a tape, and assuming that the zero end of the tape is on the point. With a digital level, the barcode on the leveling rod is used to determine that value on the rod. By taking a series of differences between rod readings, a series of elevation differences are determined, and by adding a known elevation, the elevations of other measured points can be calculated.

When we use EDM to measure a distance, the distance value presented has already been processed, because the actual measurement is usually phase differences between the transmitted and received signals, combined with corrections for atmospheric effects (refraction and Earth curvature), and the slope of the line. Sometimes the time of travel for the signal is measured and converted into a distance, but this is also corrected for atmospheric effects and slope.

Angle measurements are made by calculating the differences in scale readings (in older instruments), and by counting pulses around a circular track in electronic instruments. Multiple pulse counts, carefully designed to minimize errors in counts, are used to obtain the required precision.

A terrestrial laser scanner uses much the same angle and distance measuring technology as a total station, and so it’s all pulse counts and phase differences that are transformed into X, Y, Z co-ordinates. It can be considered to be a very fast total station, with similar measurement issues.

GNSS count ‘chips’ in the satellite signals to determine position using the C/A code, and wave counts at two (or more) receivers for high-precision measurement. Multiple counts across different satellites and signals are combined to determine the antenna’s location. ‘Location’ is not something that can be measured, but must be deduced from other types of measurements. In the case of GNSS, this involves many measurements.

Inertial Measurement Systems (IMS, but also Inertial Navigation Systems and Inertial Surveying Systems), by measuring linear accelerations (but actually what is required to hold the accelerometer stable) and measuring either angular acceleration or angular velocity (depending upon the technology, by measuring the phase differences of light signals), numerically integrate these values to obtain location and orientation data, and then combine these with a flexible and recursive error model to determine relative location.

Photogrammetry and other image-based systems collect light intensity measurements across an array of detectors, and the spatial relationship between the detectors and the rest of the optical system determines vectors from the detector back to the source of the radiation. Reconstituting the object space involves solving for the location and orientation of the detector systems and intersecting the vectors to allow calculation of 3-D location. Again, many measurements are involved in determining location.

Synthetic Aperture Radar (SAR) produces image-like results, but its process is significantly different to how imaging systems work. The image is therefore not really an image, and efforts to determine location need a different approach. Interferometric SAR (InSAR or IfSAR) work differently again, and also involve many measurements, not least those from GNSS and IMS.

As our measurement systems have become progressively simpler on the one hand (for a novice user’s viewpoint, a hand-held GPS is about as simple a positioning methodology as can be imagined), what happens behind the scenes gets progressively more complex. A wide variety of measurements that are connected to the final result by a complex mathematical model means that the errors also become far more complex.

We can see this as we look at the error models for more complex technologies. With taping and leveling, the errors increase with distance covered. By contrast, the error model for GNSS (as used for most surveying work) is relatively insensitive to distance, but is far more concerned with satellite configuration and potential multi-path effects. The error models for other measurement systems are often counter-intuitive and arcane, if not byzantine in their complexity.

So before we begin measuring things, we need to be aware of what the actual measurements being made are, and how they are transformed from those raw data into the values with which we are presented. GNSS measures wave counts, but presents us with a location. As measurement experts, we need to know something about how this is done, not just so we can bore people at parties, but so that we understand the errors. Many of our modern measurement systems invoke a wide variety of measurements in order to get to the value we see: what are the errors in those measurements and how do those errors impact the final results?

This writer has seen too many cases where the ‘measurement experts’ did not understand the errors involved produced poor results, while fooling themselves into believing their results were far better than they actually were. We need to be very critical and analytical of our own measurements, so that we know more about them, their strengths, weaknesses and usefulness than anyone else. Only then can we be considered true experts in this field.