Helen Burman 
  
x ESZY 
Ris 
R/AF 
INS 
(I, , I , ? M. 
shift of the GPS positions relative to the local frame due to errors in the datum 
transformation 
rotation matrix between the inertial frame and the local frame 
rotation matrix between the inertial frame and the sensor(LRF) frame 
laser shot vector in the sensor(LRF) frame 
  
For simplification, the following denotations are introduced: 
= LRF 
R =R ys Ri (2) 
5S. X LRFE 
R- R -Rns 
Laser scanning is now regarded as a technique to model terrain surface. Assume that we want to derive a rectangular 
grid of elevations, which increments are labelled ; and j. 
Z,, " f; (X, Y) - FG, J) (3) 
The gradient in Z in the X and Y direction is finite and exists for all Z. 
  
i of, is Zi, = Li 
x = = 4,1. 
ox À cie (4) 
7. = of; = Z, ju = 
=” 
oY Yo 
(X.Y), distances between nodes in grid 
Some laser scanner systems register the intensity of each reflected laser shot. Equivalent to elevation the intensity is 
continuos in at least some parts of the laser scanned area and the / (intensity value) can be expressed as function of Y 
and Y (horizontal co-ordinates). 
A laser shot, (X, Y, Z), can be related to the grid through interpolation of the four surrounding nodes. 
Z, = (01-23): 0.—32-4Z,, +xX 0) Zu) t(ü-ux-y:Z XV Linn (5) 
Goon oe CIO 
XR ———— gy P= (6) 
up Yu 
(X, Y, Z)i laser shot co-ordinates 
AM, YO) grid co-ordinates 
x, y normalised position co-ordinates within the four nodes 
Equivalent interpolation can be done for intensity. 
The observation equation for elevation measurements (combining equation 1 and 5) will after linearisation be: 
  
126 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.