Efficient interpolation of LiDAR Altimeter datasets in the obtention of Digital Surface Models (DSM)

Problem raised by STEREOCARTO, S.L.

Coordinators:

Dr. Pilar Romero
(Facultad de Matemáticas, UCM)

Dr. Roberto Antolín (Stereocarto, S.L. and
Facultad de Matemáticas, UCM)

**Exposition of the problem:**

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 an interpolation.

However, filtering LiDAR
data automatically is not the main problem of this technology, there are
different commercial software that perform these analysis with very good
results. But some specifications for LIDAR 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.

**Scheme of the work to be done:**

** **

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, is it possible to get the same data to perform a
flight to capture a smaller number of points thus reducing the cost?

Hypothesized that a lower point density does not affect the LiDAR data
filtering in order to obtain digital terrain models, we consider how the loss
of density affects digital models obtained by the different interpolations
(maximum, minimum, average, polynomial or spline interpolation and stochastic
methods such as kriging).