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"spatial autocorrelation factor". The spatial autocorrelation factor will affect the scanner model and the trajectory 
perturbations used in the PMIIM method. 
3.3.3 Scanner Model Design: The airborne scanner model mimics the characteristics of NASA's Airborne Terrestial 
Applications Sensor (ATLAS). This sensor is a whiskbroom, multispectral scanner and is flown aboard a Learjet 
(NASA, 2000). However, unlike the ATLAS sensor, only one band (channel) was modeled. Since the reference image 
is derived from panchromatic digital orthophotos, this band is essentially a panchromatic band. Relevant characteristics 
of ATLAS are provided in Table 1. 
Name Value . . Units _ 
| Field-of-View (FOV) 72 Pon | HOBE IIT TGRSERS. 
Instantaneous Field-of-View (IFOV) 0.0020 Radians 
Samples per Scanline 640 i iis 
Scan Speed 6 - 50 Revolutions per Second (Scans per Second) 
Scan Direction -1 counter-/clockwise (+1/-1) about flight direction axis 
= Table 1. Characteristics of the ATLAS scanner. 
Two scanner models are needed for this work. The first is called the "full resolution" scanner model, and is defined by 
the values in Table 1. The second is called the "reduced resolution" scanner model. This model is defined by a reduced 
number of samples per scanline, calculated by dividing the samples per scanline of the full resolution scanner model by 
the spatial autocorrelation factor. Therefore, the reduced resolution scanner model has 178 samples per scanline. 
3.3.4 Aerial Survey Design: A hypothetical airborne survey was defined to acquire one flight line over the study area 
in a north to south direction down the center of the study area extents. The nominal GSD was set at 10 meters per pixel 
to match that of the reference image and DEM. Since the IFOV is 2.0 milliradians, the nominal flying height was set to 
5,000 meters AGL. The average elevation of the DEM is 306 meters, so the nominal flying height was set to 5,306 
meters above MSL. The flight line starts at the point (N 293,175 [m], E 545,400 [m], 5,306 [m] above MSL) and ends 
at the point (N 285,675 [m], E 545,400 [m], 5,306 [m] above MSL). The ground speed of the platform was set to 150 
meters per second, which is close to the NASA Learjet's actual ground speed of 300 knots for an ATLAS aerial survey 
at this flying height (LMSO, 1997). The nominal scan line overlap was set to 0 percent, such that scan lines would abut 
each other. Therefore, the scan speed was set to 15 scans per second. The number of scan lines to be acquired was set 
to 750. Therefore, the flight line length was 7,500 meters and the acquisition time was 50 seconds. 
3.3.5 Trajectory Generation: Two trajectories for the hypothetical airborne scanner mission were created. The first 
represents the "actual" trajectory, and is considered to be error free. The second trajectory represents the error prone 
measurement of the "actual" trajectory. This second trajectory will be referred to as the "measured" trajectory. Each 
trajectory consists of a file containing the x, y, z, roll, pitch, and yaw of the scanner at discrete points in time from 0 
seconds to 50 seconds at 1/15 second intervals (i.e. one record per scan line). Parameters governing the trajectory 
generation were estimated from examination of the exterior orientation parameter variations observed during actual 
aerial surveys and forming a "worse case scenario" (Ethridge and Mikhail, 1977; Zhang, Albertz, and Li, 1994; Breuer 
and Albertz, 1996; Schlapfer, 1998). The "actual" trajectory was generated from sine functions. The frequency was set 
to 1 cycle every 10 seconds such that 5 cycles were completed in the 50 seconds it took to complete the flight line. 
Phase shifts were added such that the exterior orientation parameters were out-of-phase from each other by 30 degrees. 
The amplitude of the position parameters was set to 50 meters. The amplitude of the orientation parameters was set to 2 
degrees. The "measured" trajectory was generated by adding correlated noise to the "actual" trajectory through the use 
of first-order autoregressive (ARI) functions (Wei, 1994). The mean of the ARI functions was set to 0. The standard 
deviations of the ARI functions were set equal to the change in exterior orientation parameter values which would give 
rise to a planimetric error of 3 GSDs (30 meters) for level flight at a scan angle of 36 degrees when applied 
independently (Roy et al., 1997). These values are provided in Table 2. 
Exterior Orientation Parameter Error Value Units 
OX 30.000 Meters 
oY 30.000 | Meters 
oZ 41.222 Meters 
cRoll 0.2248 | Degrees 
oPitch 0.3438 | Degrees 
oYaw 0.4731 Degrees 
Table 2. Change in exterior orientation parameter values giving rise to a planimetric error of 3 GSDs. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 735