can be calculated from its left and right image coordinates. 
After mathematically correcting the position and rotation 
offsets, the local coordinate can be transferred into a 
global coordinate system. In the following, the positioning 
procedure of the GPSVision is presented. 
3.1 Differential GPS Positioning 
Depending on the type of GPS receiver, the GPS 
processing software varies. In the first generation of the 
GPSVision system, the code-phase submeter receiver is 
used. The C/A peudoranges are used for differential 
positioning. We process the GPS data by first forming the 
distance double difference between two satellite ( 1), (] ) , 
base receiver ( b ) and the rover GPS receiver (1) by : 
Ri<R -R —-R +R (1) 
The double difference of the pseudo range distance equals 
the double difference of calculated distance using their 
coordinates: 
Ra = py, @) 
The unknowns parameters are the three coordinate of the 
rover GPS receiver, since the location of satellite and base 
station are known. We get the observation equation for 
one double difference observable after linearizing (2): 
  
  
ILE AM, AS A 
hls gli dll yy, 
P Ph 
fly ET A 
En 6) 
P P 
Zi xu uu 
+( : b b WZ, 
Pr P 
At least three double difference observations are needed to 
solve three unknowns. This requires at least four common 
satellites in view. As the GPSVision is moving, its position 
is calculated on an epoch by epoch basis whenever four or 
more satellites are tracked. 
3.2 INS Positioning 
The measurement of an inertial system come from two 
sensor triads, an accelerometers block and a gyro block. 
They are defined as three components of the specific force 
vector f and three component of the body rotation rate. 
The body rotation rates are measured as angular velocities 
with respect to the inertial frame. All measurements are 
given in body frame coordinate. 
According to the Newton's second law of motion in the 
gravitational field of the earth (i-frame): 
p! = f tg (4) 
156 
where r is the position vector, f is the specific force and g 
the gravitation in inertial frame (i). After considering the 
earth rotation, the equation (4) can be written in a local 
coordinate system (n-frame) defined by Easting, Northing 
and Upward in the ellipsoid with a set of first order 
differential equations as : 
«N H 
F y 
wis ARÜÁ'-(QQ"O')eg"| (S5 
} " N Rr Q A 
where the n represent the local coordinate system, r is 
. . * FK - . . 
position vector and v is velocity, A, is rotation matrix 
from body frame (b) to local frame (n), and Q is the 
skew matrix of the body rotation rate with respect to the 
local frame. . 
3.3 GPS/INS integration 
The integration of GPS/INS can be performed at different 
levels and using different methods. The kalman filter is 
considered as a common method. The state vector 
includes attitude, position, velocity, accelerometer biases 
and gyrodrifts: 
X - (&,0,,0,.d,b). (6) 
The linear dynamic model for the kalman filter is formed 
by linerizing equation (5) and adding the error model of 
gyrodrifts and accelerometer biases: 
X=FX +W (7) 
or for the discrete measurement: 
AQ m OX, W, (8) 
where X is the state vector, W is the system noise and 
is @ is the transition matrix. For a short time interval 
(f — £5), F can be considered as a constant and ¢ is 
defined by : 
o -I-4P( C) (9) 
The kalman filter consists of a prediction and an update. 
From time k to k+1, the prediction is: 
Vr o, X, 
EMO (10) 
Pat=0, A020) 
were (+) represents the updated value and (-) the 
predicted value. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996 
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