Photogrammetry Surveys Understanding Accuracy, Precision and Error
What are accuracy, precision and error?
Many people get rather confused when talking about accuracy, precision and error, and quite often they use the terms interchangeably without really understanding the implications. Some applications will require high precision, and others will require high accuracy. When we start talking about UAV photogrammetric data, we really need to fully understand what these terms really mean.
There is an example that is commonly used to explain the difference between accuracy and precision…the dart board principal. In the example below the player is aiming to hit the bullseye which can be thought of as the reference, or real value. Each throw can be thought of as taking a measurement and this measurement ideally wants to fall on the real value or bullseye. By evaluating multiple throws, we are able to calculate the accuracy and precision of that player. See Figure 1
Author: James Dunthorne
Published: 12 August 2016
Figure 1 – Accuracy Vs Precision Dart board
It can be seen that precision is all about the spread of the data. To obtain high precision all the measurements (or throws) must be grouped together in a tight cluster. They could miss the board completely, but if they are grouped close together, the precision of the throws is still high. The precision of a measurement is quantified by its variance, which is found by calculating the difference between each individual measurement from the mean of all the measurements. More specifically the variance, σ, for a normally distributed variable can be calculated as follows
Where X is the value of each measurement, μ is the mean of all the measurements, and N is the number of measurements taken.
Accuracy on the other hand is all about the positioning of the measurements (or throws) with respect to the reference (bullseye). The spread of these measurements can be extremely large but still be very accurate if they are centred on the real value. By averaging a series of measurements to find their mean, we can eliminate the variance, and calculate the accuracy of the throws. This is done by finding the difference between the mean value of the throws and the reference.
Error is the sum of the accuracy AND the variance in any single measurement. The root mean squared error (RMSE) is a well-known measure of the error distribution used by many surveyors and means that approximately 68.3% of samples fall within +/- the value of the RMSE. The National Standard for Spatial Data Accuracy (NSSDA) is another quoted measure of error distribution and is very similar to the RMSE except that it encompasses 95.5% of the sampled points. It should be noted at this stage that by averaging multiple samples, the variance component of error can be eliminated to reduce the overall error of the measurement. This shall be explained in more detail later on
Do I require accurate or precise data?
We have found out that precision is all to do with the spread of data, and accuracy is to do with the average position of the measurements from the reference point, but what is important for your application? Figure 2 below is an illustration of a tennis court and the goal is to survey the corners of the court. The measurements on the top half are all high precision and low accuracy. The measurements on the bottom half are higher accuracy and lower precision.
Figure 2 – Tennis court illustration
Figure 2 shows multiple measurements for each point; however to evaluate the effect of precision and accuracy it is often better to look at a single measurement. We can then start to see why the difference between accuracy and precision are so important. See Figure 3
Figure 3 – Tennis court illustration with single measurement
The two main types of measurement that are commonly required in surveys are:
- Global measurements – the measurement of something with respect to an external reference (i.e. position measurement with respect to British National Grid)
- Relative measurements – the measurement of something with respect to something else within the same survey (the position of one point in a survey with respect to another)
If we wanted to measure the position of the corners of the tennis court to a given grid/ datum, it is fairly clear that the high accuracy measurements give a better result. Applications such as topographical surveys require high accuracy since they are in reference to an external grid that is not part of the survey.
If we are trying to measure the length of the tennis court however, the story is quite different. The high precision data is much better suited at tackling these kinds of relative measurements since the variance between measurements is low. Examples of relative measurements include measuring distances between two points in a survey and when conducting volumetric calculations.
So in summary, if you are looking for measurements with respect to an external reference such as British National Grid, high accuracy is required. If you are only interested in measuring a property of something relative to something else within the survey, high precision is required. Achieving high precision and high accuracy is not always required and can affect the cost of a survey, so understanding which you require can save you money