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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
above. In the first run patch identifiers are created, in the
second run they are merely used. Accidental duplication of
patch identifiers is prohibited as one can see easily.
It is noteworthy to stress the fact that all these homologous
patch-candidates bearing the same patch identifier are of equal
rights with concern of adjustment theory since their
fundamental argument is merely the same reference point; no
correlations between the observations of different strips are
introduced.
The second run has an additional criterion in determining the
plane: compatibility of normal vectors.
Having these two sets of lists of normalized patches, they serve
as input for the adjustment programme. Patches which have no
partner are cancelled.
3. BLOCK ADJUSTMENT BY STRIPS OF LASER
SCANNER OBSERVATIONS
In the following, we describe our actual method of
simultaneously fitting laser scanner strips in 3D. The
capitalized terms in the following refer to notions used in
ORIENT (Kager, 1995). The explicit formulae of the following
— in their static form — can be found in (Kraus, 1997a, p12-43),
respective ones in (Burman, 2000).
The basic observations for simultaneous 3D-fitting:
* The polar coordinates V, Y, of the anchor points of the
patches in the overlapping areas of laser scanner strips as
delivered from the patch finding mission above (the cross
bar indicates the observation property). The accuracy of
such a polar point observation is estimated from the
scanner characteristics (for the angles) and from the
(redundant) measurement process (adjustment of plane for
the distance). They are stored in POLAR-rooms. All polar
observations of one strip are stored in one POLAR-room.
* Ground coordinates X,Y, Z of control points which are
measured geodetically terrestrially (total station and GPS)
on some of the patches as proposed in the previous section.
We recommend also to measure four points for a patch to
give it also directional support. See figure 2 for an
example. They are stored in CONPOI-rooms.
* The fictitious observations that all ground points of a patch
lie in the same (global) plane. The accuracy of such a.
plane-point was estimated in the adjustment of the patch's
plane. All points of one patch are stored in one GESTALT-
room. They stem from both runs of the patch finding
mission and from control point measuremens . This is the
essential tying information between strips and reference
frame.
* The shift-coefficients a,b,c of all (individual) strips
honouring their zero-expectation. The subscript 7
indicates the exponent of time £ in the polynomial term.
They are stored in ADPAR-OBS-rooms. Their accuracy is
chosen as to handle eventual rank-deficiencies (preventive
regularization).
* The tilt-coefficients O,,P,,K, of all (individual) strips
honouring their zero-expectation. The subscript {
indicates the exponent of time f in the polynomial term.
They are stored in ADPAR-OBS-rooms. Their accuracy is
chosen as to handle eventual rank-deficiencies (preventive
regularization).
The basic observed constants for simultaneous 3D-fitting:
e TheGPS Y 7 Z, and IMU a, ,P,,K, measurements
for the involved POLAR-points mentioned above. They
are stored in GPSIMU-rooms parallel to the POLAR-
rooms. Every polar point has one entry here with fas
common key.
The unknowns of the adjustment process are:
* Ground coordinates xX FZ for all the tie(-anchor)-
points of patches and control points mentioned above.
They are stored in the REFSYS -room.
* The shift-coefficients a;,b;,c; of all strips (common or
individual). The subscript 7 indicates the exponent of time
| in the polynomial term. They are stored in ADPAR -
rooms. The terms of order 7 = 0 handle GPS-shift, those
with / —] can handle GPS-drift (i.e. shift change linearly
with time).
e The tilt-coefficients W;,P,,K, of strips (common or
individual). The subscript / indicates the exponent of time
f in the polynomial term. They are stored in ADPAR -
rooms. The terms of order ;= 0 handle IMU-index
errors; . 7 —] can handle change of index errors linearly
with time (i.e. IMU-drift).
* Common rotations Do; Po: Ko handle bore-sight
alignment, i.e. differential rotation of IMU with respect to
the Lidar-device. They are stored in a ROTPAR -room.
* Calibration terms of the sensor covering V, A.p offsets
and scales. They are stored in ADPAR -rooms. Diagrams
showing their effect can be found in (Katzenbeisser, 2003)
* The shift-coefficients Cy Of all planes describing a patch.
They are stored in ADPAR -rooms.
* Optionally, the tilt-coefficients €,9,Co, Of all planes
describing a patch. They are stored in ADPAR -rooms.
They can handle wrong tilt of patch planes caused by
misalignment of the IMU.
The adjustment is expected to minimise the following
quantities by least squares:
* The residuals of observed polar points V, Y,p in the
strips.
® The residuals of control points RE Yo with respect to
patch planes.
* The offset of the adjusted ground points from the adjusted
global patch plane (GESTALT-residual).
* The polynomial shift-coefficients 7.0.2 - since they
are expected to have zero-values (corresponding to correct
GPS data). This yields relatively small values of the
correction polynomials (Kraus, 1997a, p37).
e The polynomial drift-coefficients a;,P;,K, - since they
are expected to have zero-values (corresponding to correct
IMU data). This yields relatively small values of the
correction polynomials (Kraus, 1997a, p37).
The incorporation of the polynomial coefficients alt, and
W,,p,,K, into the LSQ minimum condition is called
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