Direct and Indirect Measurement

In the previous post, direct and indirect measurements were measured, but these were not elaborated upon. Before we go any further, we should discuss these two concepts and why they are different.

When we use ‘direct’ measurement, we are measuring the desired quantity directly, i.e., we apply a measurement device directly to the particular quantity we wish to measure. For example, to measure the length of a table, as discussed in the previous post, we might place a tape measure on the tabletop, position the zero mark on the tape at one edge of the table, and read the distance on the tape at the other edge.

By contrast, ‘indirect’ measurement is where we measures something other than the desired quantity, then use a mathematical model to transform what we actually measured into an estimate of the desired quantity. Modern measurement technology has led to increasing amounts of indirect measurements, and direct measurement is becoming much less common.

For example, in the past a chain, band or tape was used to measure the distance between two points. This was considered a direct measurement, although the value measured on the chain, band or tape had to be corrected for slope, temperature, tension, sag, calibration and elevation above sea level. As this involved a series of mathematical models of the systematic errors, it was really an indirect measurement, albeit very close to a direct measurement.

Sometimes an indirect measurement is necessary because a direct measurement is not possible. In the example above, unless we tunnel between the points of interest at sea level and bring the location of the points down to that level (which involves more indirect measurements), we cannot measure the sea level distance directly. Similarly, setting a total station over one point and a prism on a tripod over the other, we still need to reduce the slope distance measured for the slope, height above sea level, atmospheric effects, and the EDM/prism calibration values. The measurement may look direct, but again it is really an indirect measurement.

Suppose we place two GNSS antennae (identical antennae can be used) directly on the two points, and we want the ‘straight line’ vector between the two points. Is this a direct measurement? The GNSS actually measure wave counts for multiple signals from multiple satellites over time. These counts are then combined to calculate the resulting vector. The wave counts are converted to the vector components using a mathematical model, so it’s an indirect measurement.

One of the realities of modern measurement is that any given measurement is almost certainly an indirect one. This means that a mathematical model is involved, which means that additional parameters for model usually need to be measured. It also means that as measurement gets more complex, so do the mathematical models and with them, the complexity of how errors propagate through the measurements, their reduction, and then into the final results.

The examples given above are efforts to measure a simple quantity: the distance or vector between two points. But surveyors and spatial data experts measure much more than this, and measurements go well beyond spatial measurements. How do we measure customer satisfaction, when the customers themselves may not be able to quantify it?

(And in case you think this isn’t important, very few of us do surveys and measurements just for the intrinsic amusement: we usually have some particular job that needs to be done, a contract that must be completed, or someone standing there wanting results. This means there is a business function involved, and that usually has a customer or client, and to do things well, we’d like to know their level of satisfaction. It’s a measurement that all businesses should be making.)

Similarly, how do we measure attributes for a GIS in a way that has meaning and some quality estimate associated with the measurement? How do we determine all the rights pertaining to a particular piece of land? All these can be considered measurements, in that they reduce the uncertainty associated with some unknown quantity, but we would like to know just how good the quality of the estimate of the unknown quantity is.

When I started doing surveying in the 1970s, the difference between direct and indirect measurements had an additional level of importance. The regulations concerning cadastral surveys required that indirect measurements be checked by independent measurement(s). In this situation, ‘direct’ meant that the measurement was made directly between the points of interest. As EDM became more widespread, most surveyors shifted from measuring azimuths by an offset traverse and direct measurement of the boundary lines by taping between the marks. As placing the EDM over the boundary points was often difficult, all the measurement became indirect. The regulations required that the connections that determined the boundary lines were checked by independent measurements.

This is a sensible rule. Indirect measurements are fraught with greater potential for errors, as a series of additional measurements (e.g., temperature, slope angle) are made, and a slip in these measurements can cause all manner of errors to propagate through the process. So some kind of independent measurements should be made to ascertain that the various measurements being made are sensible and reasonable. For some types of measurement, this can be a little tricky, but we can often built measurement procedures that allow these checks to be done as part of the overall measurement process. Such checks are cheap insurance against errors, and a quick and easy way to ensure one’s professional reputation remain strong.

Because of the critical importance of indirect measurements, we will be returning to this topic again and again. The idea of determining the propagation of errors through the mathematical models used in all manner of geospatial processes is a central part of modern geospatial science.

While error propagation is usually discussed a bit later in a surveying or geomatics education program, it is very important to emphasize it early, when discussing the basics of measurement. This can be used as a way to introduce some different measurement techniques, e.g., tape, EDM and GNSS in this short discussion. But knowing the nature of errors is also critical from the start.