The primary purpose of airborne laser altimetry is to determine the el
lipsoidal or geoidal coordinates of a series of points on the surface
of the Earth. An aircraft that is instrumented with a laser altimeter,
an inertial navigation system, and a Global Positioning System (GPS)
receiver provides the following data: (1) laser range to the Earth's s
urface, (2) measurement platform spatial location and orientation, and
(3) aircraft kinematic trajectory in ellipsoidal coordinates. These d
ata are sufficient to determine (georeference) the three dimensional c
oordinates of the points where the beam from a pulsed laser intersects
the Earth. We develop the exact equations necessary to georeference t
he laser points. We also discuss calibrating the laser pulse timing, l
aser positioning and alignment relative to the local-level reference f
rame, correcting atmospheric refraction effects on the laser pulse, an
d time synchronizing the various data streams. We use a laser altimete
r mission flown over Lake Crowley in California to demonstrate our met
hods. For seven passes over the lake, our heights agreed with a local
tide gauge at the Lake Crowley dam to better than 10 cm with standard
deviations ranging from 1-4 cm. The horizontal accuracy of the georefe
renced points is still problematic; we have no three-dimensional contr
ol points that the laser has hit. Geometrical considerations indicate
that the measured horizontal location of the laser footprint is within
two metres of the true location when the aircraft altitude is less th
an one kilometre above the local surface.