Noticias y eventos

The Faculty of Mathematics of the UCM and the UCM Research Group "Mathematical Models in Science and Technology: Development, Analysis, Numerical Simulation & Control" organize this event within the framework of the Master of Mathematical Engineering of the UCM.

The purpose of this event is to use mathematics as a tool to solve problems arising out of the industry. The presentations and exhibitions will take place on 22nd and 30th and attendance is free for all interested    

Efficient interpolation of LiDAR altimeter datasets in the production of Digital Elevation Models (DEM's)

The Airborne Laser Scanning (ALS) technology is based on the ground survey from an airborne laser telemeter. The telemeter measures the distance between the emission point, A, and the echoing point, B, which is a generic ground point hit by the laser ray. Thus, the laser telemeter measures the distance between the instrument and the echoing surface.

However, the ground point coordinates are actually wanted. The measure of these coordinates implies the knowledge of the airplane position and attitude at each instant. For this purpose, an integrated sensor GPS/INS (Global Positioning System/Inertial Navigation System) is provided.

This instrumentation basically consists of an inertial sensor which is composed of three accelerometers and three gyroscopes, a GPS receiver and an electronic device to synchronize and to archive the data of the instruments. The accelerometers and the gyroscopes are lead to measure the linear acceleration and angular velocity. Once the measuring session is over, the data is pre-processed by a Kalman filter to calculate the aeroplane position and attitude at each singular moment of the flight.

Thus, the GPS/INS sensor is able to determine the aircraft coordinates and its normal vector direction; The point distance from the telemeter and the angle between the emitted ray by the telemeter and the aircraft normal vector are also known. Thus, the coordinates of the surveyed point can be achieved.

Some of the most important laser scanning capabilities are:
1. High accurate measurements: 30cm in planimetric components; and 15cm in height component.
2. High resolution, (function of the height and velocity of the flight, and the scanning frequency) between 0.5 and 5 point/m2.
3. High velocity survey. From a few up to 50km2/h.

The final data from a LiDAR survey is a great amount of planimetric coordinates, sorted by the points retrieved instant, and the corresponding ellipsoidal heights. Since LiDAR is often able to measure the intensity echo, this kind of signal attribute is also archived.

From LiDAR data, it is easy enough to develop a Digital Surface Model (DSM) as a simple raw data interpolation. DSM just represents the trend of the terrain and of the objects over it. However, the principal aim is to develop a Digital Terrain Model (DTM) by filtering (or .removing) points that represent objects (buildings or vegetation) and performing a final interpolation.

However, filtering LiDAR data automatically is not the main problem of this technology, for there are different comercial softwares that perform these analysis with very good results. Besides, some specifications for LIDAR flights are demanding for point densities about 5 points/m². This leads to two main problems. The first is how to manage such volumes of data without an increase in resources consumption and therefore without an increase of costs. The second is that such a density of a data automatically implies a more restrictive flight in terms of height and time of survey, and therefore it also implies a more expensive project.

However, solving one problem leads to solve the other. Thus, the following problem can be presented: is there a way to reduce the density of the data so that data loss does not represent? Or seen from another angle, is it possible to get get the same data to perform a flight to capture a smaller number of points thus reducing the cost?

Hypothesizing that a lower points density does not affect the LiDAR data filtering in order to obtain digital terrain models, we consider how the loss of density on time to end digital models obtained from an interpolation.