International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
alyzes the positional and height offsets as error sources and
evaluates their magnitude and their contribution to the re-
moval of the offsets between strips. The paper is organized
as follows; first the error recovery model is outlined, where
GPS offsets are modeled here as systematic errors. Follow-
ing a description of the extraction of tie information for the
adjustment results are presented and are followed by conclu-
sions.
2 Error recovery model
The error recovery model is based on modeling the system
errors and their effect on the geolocation of the laser point.
Based on the integration of the observations from the three
individual components of the laser system the geolocation
of the laser points, when transformed into a local reference
frame, is given by equation 1
VI Xo Op 0
yi{= [Yo] +Rins| 64 -ARarRs | 0 +
ZI #0 0 —p
c
=
Bi QI
R
Or
(1)
sl S
e
~
z AZ
with z;,yi,z; the footprint location; Xo, Yo, Zo location of
the phase center of the GPS receiver in the local frame; Ris
rotation from body reference frame to reference frame defined
by local vertical; d,,0,,02 offset vector between the phase
center of the GPS antenna and laser firing point; Ras the
mounting bias, which designate rotation between the altime-
ter and the body frame; p range vector measured by laser
system; €, €,, & random error components.
Introducing GPS biases that contribute offsets into the posi-
tion of the laser point, equation 1 becomes
LI Xo ô Xo Ou 0 €. ;
y | = | Yo|+|dYo |+Rins| |9y| +RaRs | 0 | |+|&
Zz Zo Ó Zo 3. ={) €,
with öXo,öYo,öZo as the GPS biases in the z,y, and z di-
rections respectively. In general, one cannot assume that the
offsets will remain constant throughout the mission as offsets
in position may vary over time. As a result the offsets are
assigned to the laser strips themselves. An error model that
covers a wider variety of error sources in the laser system is
given in Filin (2003b).
The model for solving the errors is based on utilizing natural
and man-made surfaces to recover the systematic errors. The
approach is based on minimizing the distance between the
laser point coordinates and the actual surface. By locally
approximating the surface as a plane and constraining the
laser points to lie on the plane, the following relation can be
written down.
S1X1 + SaYL + 8321 + 84 = 0 (3)
where sy, 82, 53,54 are the surface parameters. Using the
relation in equation 2 to substitute laser point coordinates by
the observations and the systematic and random errors, the
error recovery model is obtained. The formula for solving the
parameters is given in equation 4.
(4)
w; = 510X0 + 520Y0 + 53020 + S182 + S2€y + S1€;
With w;, the transformed observation. The form provides
one row in the Gauss-Helmert model
Wn = An xm Sm + Bax3n93n e n (0, oëP *! (5)
with w, the transformed observation vector; À, the coef-
ficient matrix; B, the conditions matrix; £, the vector of
unknowns; e, the observational noise vector; P, the weight
matrix; a3, the variance component; n, the number of laser
points; and m, the number of unknowns.
Following the least-squares criterion the parameters are solved
by equation 6.
És(AT(BPz!B/)y! AJ! AT(BP-!B'yw. . (6)
3 Control and tie information
Similar to photogrammetric strip adjustment errors are re-
covered by using tie and control information that register the
strips to one another and the laser block to the ground. The
model is surface based and therefore the natural control enti-
ties are control surfaces. Since not too many, if any, control
surfaces will be available, most of the control information will
be provided in the form of control points. These entities are
introduced into the model as additional surface constraints.
Control points constrain the surface to the given point posi-
tion, namely
s1(X +ex)+s2(Y +ey)+s53(Z+ez)+s=0 (7)
with X, Y, Z the control point coordinates, and ex,ey,ez
are their random error components. It is noted that linear
features can also be supported by this model.
Whereas there is little control on the type of control informa-
tion that will be available to the adjustment procedure, ob-
taining tie information is practically an implementation con-
cern. As the algorithm is surface based, surface elements that
are identified in the overlapping areas of the laser strips are
the natural candidates to serve as tie entities. In a similar
fashion to photogrammetric strip adjustment surfaces that
are introduced into the adjustment with no a priori surface
model are considered as tie objects (tie surfaces). Their ap-
proximated parameters are computed from the data and re-
fined within the process of the strip adjustment. The identi-
fication and selection of tie surfaces is part of the strip ad-
justment algorithm.
If the aim is to develop an autonomous laser strip adjustment
procedure the algorithm should identify suitable tie regions in
the data and extract the necessary information. The iden-
tification of tie surfaces in the data is conducted under the
framework of surface segmentation. Segmentation here con-
cerns with the separation of unsuitable regions and points
that are unusable for the purpose of laser strip adjustment,
e.g., vegetation points or forested regions where not too many
points are reflected from the ground, and with the partition of
the smooth regions into segments. The choice of a segmenta-
tion (and not for example a filtering method) is based on the
realization that identifying suitable points and regions for per-
forming the strip adjustment is insufficient. The dependency
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