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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
and s<e, the relative transformations f. 1» Sie between each
1.1
pair of successive GPS/INS updates are adjusted to achieve
global matching between 7, and 7,’, while maintaining local
consistencies.
Relative transformations ;,,,, s«i«e are adjusted in an
4
iterative way, where in the kth iteration, a Ar a is calculated
LN
for each i p 5sise. It is updated as follows.
Ut 1.
-l -
A
i-li
Art. sant ut 3 Ai, as uti siut
Hi ele e s ssl
e-s
(8)
HW eM un (9)
Ei INES! Lil
The process continued until |r JT | is smaller than a
e e
given threshold or can never be minimized any more, where
| is the norm of the vector. Denote i and T. as the
it 7
l
rectified Le and T respectively. 7 , S< j<e are obtained
by sequentially aligning {88s follows.
IT, =T5 1), (9)
AU AGT,
s.s] id4l J-LJ
ES
Jai
y
Since GPS/INS parameters drift in a non-linear way
according to the local surroundings, they are rectified using the
ground truths at a number of updates. Let T X demie due
xx
g2 gn
represents the n true transformations at the GPS/INS updates
#gl, #g2, ..., ign, where g/ «g2«... «gn. Correction of T's at all
GPS/INS updates is conducted as follows.
Algorithm Rectification of GPS/INS parameters using a
number of ground truths
Input GPS/INS measured transformations msi N}
1
< S =< N}
> ^. 4 ^ ce {iq t
Input » ground truths { T [iso So;
Output Rectified transformations T, |1</<N}
for k=1:n
if k=/
let A7 = ri SP
for i-1:N (7 =7 AT)
else
calculate {7 | 24 ST $ 2; — 1}
frigus 7l AT ST f
let AT” Tl
fori 0, N (T zT-AT!
3.2 Obtaining the ground truths
In this research, the true transformations at a number of
GPS/INS updates are obtained in two levels, so that GPS/INS
parameters are rectified in two subsequent steps, horizontal and
vertical registration. True values of the horizontal parameters,
Le. o,,0, andk, are obtained using a number of manually
assigned tie-points, which reflect the correspondences between
the laser points of VLMS and a DSM that is treated as the
ground truth. On the other hand, true values of the vertical
parameter, i.e. o_, are obtained by horizontally registering the
laser points of VLMS to the data source of ground truth, and
sampling the elevation values of the data of ground truth along
497
the vehicle's measurement course.
Obtaining the true values of horizontal parameters: A set of
tie points consists of two pairs of closely located corresponding
points. Figure 6 shows an example, where p, and p, are
VLMS measurements to building corners from the vehicle
positions o, and o,, respectively. p,' and p,' corresponds to
P and pss which are represented by a DSM. Let (0,50, 3K)
denote the horizontal position and orientation parameters
obtained from GPS/INS combination at 0, and (0,50, K,)
denote their true values. Suppose o, and o, are near to each
other, so that the difference of GPS/INS drifts ( Ax , Ay, AK )
between them are ignored. Let 0, '= 0, 4x so, mort AY.
x, kt AK, (Ax, Ay, Ak) are obtained by matching p, p,
to p, p, as follows, where 75 and p,' Serve as the
directional points in finding the orientation drift of Ax, p, and
p, are the axis points, the resulted Ax, Ay, Ax are treated as
the GPS/INS drift at 0,-
Considering the horizontal parameters of Formula 7,
P; and P; ', i=1,2 are represented as follows.
COS”, —sinxw _
2, = =p +0, (11)
SINK, COS;
pot
COSK, + AK Ay
7
eum 7 —sink, + Ax Ax (12)
sink; + Ax
= 5. ' ' = = 1
Let V, T P» = Pr V, HET P» -P 2 and V, 705 0,» it has
cosk, -—cosk, Y P., -sinx, sink, YP.»
v, = ; . dd a dy
sink, -sink, AP, cosx, -—cosK, / P.
(13)
COSÁK —sin AK 14
Ya al (973) (14)
sinAK | cCOSAK
Thus Ax, Ay, A« are obtained as follows.
Ak = cos” lq vv, =v, p] (15)
Axe pco. - BOT cose 4 Ax). P. "sine ^ Ax) (00)
Ay p 0,75. sin + Ar) 5. “cost, Ax) (17)
yl
Where, |v| denotes the normalized vector of v.
Obtaining the true value of vertical parameter: Vertical
registration is conducted, after the position and orientation
parameters of GPS/INS updates are horizontally rectified, and
the laser points of VLMS are horizontally registered to the
DSM. GPS/INS updates of VLMS are equally sampled, and at
each sampled vehicle position, the ground truth is calculated as
follows. Let (050,50, ) be the vehicle position of GPS/INS
measurement, o. ' be the elevation value at (9 0) obtained
from the DSM, 7 is the height from the origin of HISS
coordinate system to the ground surface, which is measured
previously in calibration process, o.'=0_.'+h is treated as the
true value of o, at(o.,o.).
