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Experiments

In the current version of the system, images are obtained from a customized platform featuring a camera, an electronic compass, and a differential GPS system, all mounted on a tripod. In a typical image acquisition sequence, the camera platform is leveled, the compass is calibrated, and an image is taken every 10 degrees. The compass provides absolute orientation measurements; once calibrated, accuracy is $±0.5$ degree. A differential GPS device obtains ground-truth measurements of position, with accuracy of 3 meters. The images are stored in tape and played back when testing the system. Our mountain detection system takes 2 to 3 seconds per full image in the current implementation on a Sparc20 workstation, depending on the complexity of the scenes.

To extract accurate bearings from images, we measured the parameters of the camera with the calibration method proposed by Robert [10]. We repeated the calibration procedure ten times, with different images, and concluded that errors of $±2$ degrees are introduced by camera calibration inaccuracies. But the most significant source of error comes from detecting the position of peaks. We modeled the combination of the three errors (compass error, calibration errors and peak selection errors) by fixing the standard deviation of Gaussian distributions at 2 degrees.

We have run the estimation procedure with data obtained in Pittsburgh; sequences of images as illustrated by the bottom of Figure 2. Two sets of images were used to generate an estimate of position. The first set of images was acquired from the point indicated by a gray dot in the top left window of Figure 2. The second set of images was acquired 1000 meters to the southwest. Three mountain peaks are detected in the first set, two in the second. The bearings, in degrees, are ${177.6, 131.1, 92.4, 102.3, 65.3}$. A uniform distribution was chosen for the prior distribution for position.

The system estimated position with an error of 87 meters, so small that it lies inside the gray dot in the top left window of Figure 2. In comparison, errors ranging from a few hundreds of meters to 2000 to 5000 meters have been reported in previous research [12] with real data. The difference is in the scale of our features. If we constrain ourselves to a small number of very salient features, huge errors ensue. But if we allow many map features to be considered, we must impose some quantitative structure in order to manage the large number of competing interpretations that arise. The likelihood calculations in our algorithms provide this needed structure.

We have also run the system on data from Dromedary Peak; the images are shown in Figure 4. We ran the algorithm solely on the bottom image since the top image contains mountains that are not present on the Dromedary Peak quadrangle. The five bearings detected automatically are (in degrees): ${ 235.4, 209.7, 174.6, 118.1, 111.7, 107.2 }$. Based on ground truth data and the USGS map, the correct bearings are ${ 224.5, 198.8, 163.7, 107.2, 100.8, 96.3 }$. A square area of 6km by 6km was used the Dromedary Peak quadrangle, to make the test similar to the Pittsburgh tests. The system estimated position with accuracy of 95 meters, which can be compared to the 71,700m$2$ obtained by Thompson [14]. Again, we benefit greatly from our reliance on all available features, large and small, present in the image.

Next: Conclusion Up: Position Estimation from Outdoor Previous: Comparing Position Estimates

Fabio G. Cozman