Now and then you will come across a claim of companies offering sub centimeter accuracy LiDAR from a drone. I know you will like me to, but no I will not name and shame the biggest culprits in this article. Instead I will demonstrate with the use of some simple mathematics that this is simply not possible.
First let’s look at the major error sources present in drone LiDAR. These are:
The first three errors are inherent to the system that you will use, the error caused by the reflection is project specific and depends on the type of material, the shape and angle of the object from which the LiDAR signal is reflected. If I claim that sub centimeter accuracy is a myth, then we should look at an ideal (the most perfect) situation so for the sake of this article we will disregard this last error.
In order to get sub cm accuracy with a drone-based LiDAR the combined effect of all three errors should be less than 1 cm. The total error is not the sum of the three individual error sources. This is only the case in a freak situation whereby the maximum error occurs in all three situations. In order to estimate the total error we will use the method of least squares.
This method aims to create a more realistic outcome of the total error that minimizes the sum of the squares of the errors that are generated by the individual errors 1, 2 and 3.
Now first the error caused by the positioning of the drone. A LiDAR will calculate the X, Y, Z position of a laser reflection by measuring the time interval between sending the laser pulse and when its reflection is received as well as the angle under which the reflection was returned. The angle and distance of the reflection are applied to the position of the LiDAR scanner.
If this position contains an error than this will directly influence the calculated position of the reflection, i.e. the accuracy of your measurement. Note that this statement does not apply to a SLAM based LiDAR!
How is the position of the LiDAR scanner calculated? Most likely by RTK or PPK GNSS. Under ideal situations this will be accurate to 2 cm in X, Y and 3 cm in Z. By a variety of factors, it can occasionally be better or worse, but these figures give a good average for an optimal situation.
If we cannot calculate the position of the LiDAR scanner during flight more accurate than 2 cm how then can we calculate the X,Y,Z position of the LiDAR reflection to sub centimeter? The answer is we can’t. And so far we have only calculated the error for error source 1.
The second source of error, the orientation of the drone, is the cause for the biggest error. If the position of a LiDAR reflection is calculated and a very small error in the angle is made by assuming a wrong orientation of the drone then this results in a large error. The cause of this error is the Inertial Measurement Unit (IMU). Here we will disregard the error of mounting the LiDAR scanner not a 100% in line with the IMU and GNSS.
Assume the accuracy of the IMU to be 0.025 degrees. And I am being generous here as this is the specification for the top of the range Applanix APX-20.
If the LiDAR is scanning at a height of 50 meters (typical flying height for a LiDAR under a multirotor drone) then assume a slant range (distance of LiDAR scanner to the point whose reflection is being measured) of 60 meters. The error will then be 60 m * tan 0.025° = 2.6 cm.
The third error is the accuracy of the LiDAR scanner itself. This is normally an error in the order of a few mm. Many people frequently quote the accuracy of the LiDAR scanner as the total error and thereby disregarding the two errors explained earlier. Again lets be generous and take 3mm, the specifications of a top of the range scanner.
So now if we estimate the total error using the least squares method we will get:
From personal experience I have been able to get accuracies as good as 2 cm. This is however an optimal situation whereby extremely good GNSS was available. But claiming sub cm accuracies is misinforming your customers.
USing a zoom lens for aerial drone surveys is not a good idea. Why? This has to do with the base height ratio. I have made a short video explaining this concept.
12th March 2020
You will frequently come across statements from drone vendors or GNSS equipment manufacturers that when using their equipment, you will not need ground control for photogrammetric drone surveys.
Away with those time-wasting ground control points! Why bother if your drone can tag the position of where images were taken within centimeters using the latest RTK, PPK or even PPP algorithms?
Sorry to be the spoilsport but there are two very good reasons why you should still use ground control points. The first is the more complex to understand and is about establishing the interior orientation of the camera. The second is more common sense. You should take a GNSS receiver with you to perform quality control measurements and while you are there you might as well measure Ground Control Points since this will make your survey more accurate.
When we perform an aerial survey based on photographs, i.e. photogrammetry, we rely on the basic principle of stereoscopic parallax. This may be defined as the change in position of an object with height, from one image to the next, relative to its background, caused by the imaging’s platform motion. You can observe this yourself by looking at a close by object first using one eye and then only the other. You will observe an apparent shift of position of the object. Digital photogrammetry uses this parallax to compute the height (Z coordinate) and planar position (X and Y coordinates) of the pixels in aerial photographs. To obtain the correct coordinates of the pixels (i.e. a point cloud) the photogrammetric software must know or compute both the internal orientation and the external orientation of the camera.
The external orientation defines the position and angular orientation of the camera that took the image. This means that the external orientation is different for each and every image taken during the survey! If we do not add the exterior orientation then the derived coordinates are not referenced in a world coordinates system such as OSGB 36, UTM, WGS84 or RD-NEW. These coordinates would be in a local non scaled system.
A high grade GNSS receiver can compute the position of where each image in the survey was taken to an accuracy of a couple of centimetres. This part is not up for discussion but that does not mean that the end products of your survey will have an accuracy of a couple of centimetres! There is a whole list of factors that will influence the accuracy apart from the exterior orientation such as the sharpness of the images, exposure of the images, ISO setting, the Ground Sample Distance, type of sensor used, type of lens used and last but not least the internal orientation.
The internal orientation describes the geometry of the camera at the time of capture. Unless you change something during a survey (like change a lens or set a new aperture value) then the interior orientation will be the same for all images in that survey. Every lens used in (aerial)photography will distort the image in varying degrees depending on the type of lens used. This means that each and every lens must be calibrated prior to being able to compute accurate 3D positions of objects. Calibration is the process to find the true parameters of the camera.
Modern day photogrammetry that relies on the Structure for Motion (SfM) needs a high percentage of overlap between all the images (minimum 60%). This high overlap ensures a high degree of redundancy and allows for the calibration of the camera purely based on the images taken during the survey, i.e. the camera does not need to be separately calibrated.
However, this is true for most parameters but the most important one, the focal length, is very hard to derive. And it is this parameter that is the most important one to obtain accurate survey results.
The most accurate way to determine the focal length would be to calibrate the camera separately. Since we use cheap, light and inexpensive cameras (compared to the $1 million. Vexcel aerial cameras for manned aircraft) the parameters of the internal orientation will change simply by banging the camera on a table. Unless you are very careful with the camera before or after a separate calibration there is no way of getting these parameters accurately except by…. Yes, you guessed right by performing a calibration during the flight and that is exactly one of the functions of a ground control point (GCP).
Theoretically you will need just one GCP to calculate the focal length accurately, but what if you made a small error measuring the GCP… No self-respecting surveyor will ever rely on a single measurement, so he will take at least three measurements or 3 GCP’s. While you are at it you might as well measure some more since the more GCP’s you measure the more accurate your survey will become. Up to a point of course! 1000 GCP’s on one square km will not make a more accurate survey than 10 GCP’s. How many are optimal? well that is unfortunately beyond the scope of this article.
Coming back to a point previously made. A surveyor never relies on a single measurement. Most photogrammetric software will take all the inputs such as the images and their position and then create a point cloud in a semi ‘black box’ manner. If you have made a mistake somewhere in the process, then the saying garbage in gives garbage out will apply. But there is a good chance you will never notice this error, nor will you be able to make a statement about the accuracy of your end results.
The best way to overcome this is by measuring extra points (using RTK GNSS). These points should not be used for the data processing but kept apart. Once the end products are made you can then check these against the extra points measured. You should measure a sufficient amount if you want to make a statistical claim on the obtained accuracies. If you are out measuring these extra points you might as well measure ground control points, it will be very little extra effort and the reward is a more accurate survey.
Is there no benefit in using these high end (RTK or PPK) GNSS receivers on your drone? Yes there is! The first is that you will need a lot less GCP’s than if you would not tag the position of where the images are taken accurately.
The second is that your survey area might not be 100% accessible by foot in for example an inter tidal area, a portion cut off by a river etc. Using these high-end receivers on the drone will allow you to get accurate survey results even if the ground control points do not cover the entire survey area.