Millimeter precisie met lidar en drone is een mythe
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 error caused by the positioning of the drone
- The error caused by the orientation of the drone
- The error caused by the accuracy of the LiDAR scanner
- The error caused by the reflection of the LiDAR pulse
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 minimises the sum of the squares of the errors that are generated by the individual errors 1, 2 and 3.
What we will look at is the a-priori error calculation, which is taking the equipment specifications and calculating from there as opposed to a practical case.
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. In addition we will look at just the error introduced by just one angle (pitch or roll).
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:
So based on equipment specifications the expected accuracy is 3.3 cm. Some people might object here and claim to have obtained better accuracies in practical examples. Yes that is of course possible. From personal experience I have been able to get accuracies as good as 2 cm. This is however in an optimal situation whereby extremely good GNSS was available.
You might have been extremely lucky in getting sub cm accuracies with a drone based LiDAR in the past. That is similar to having measured a point using one RTK GNSS observation with sub cm accuracy. It is possible but not likely that you can repeat this over and over.
So claiming sub cm accuracies for drone based LiDAR is either misinforming your customers or demonstrates a poor understanding of the basic survey principles.
Artikel van Pieter Franken via Linked in.