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In the spreadsheet we have made various calculations in order to understand the results.
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1. Amount of NaNs in error for multi-lateration and tri-lateration
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67/171 for multi-lateration and 6/171 for tri-lateration.
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I've inferred these from looking at the Target files.
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3. Tri-lateration is performing better than multi-lateration
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There are 37 instances where tri-lateration performs better than multi-lateration, 26 instances where multi-lateration performs better than tri-lateration and in the rest both perform equally well. Reason??The reasons for this could be one or more of the following:
- We sorted the Target files on the basis of distance between the target and landmark. This promoted those lat/long values to the top of the list which were closer to the target. Though any such sorting technique on these values doesn't affect multi-lateration results but it makes a huge impact on tri-lateration results. The reason being the way these two techniques use these values. Multi-lateration considers all values and figures out regions of intersection whereas tri-lateration simply takes three values to find an intersection region. If we have more landmarks and some of them fairly close to the target multi-lateration will give good results. Even if some values aren't really good, it won't cause multi-lateration to behave in an entirely different way. However in the case of tri-lateration the better the landmark estimates we have the better the results are. Since we are only considering three values here, even a single one of those three values can make a big difference.
I'm inferring this from sorted Target files for tri-lateration. Before sorting Target files we were getting way-off results. We then tested our approach of taking RTT into account and manually re-arranged values to produce fairly accurate results. Later sorting on the basis of RTT failed as RTT isn't always directly related to distance. Our latest try involved sorting on the basis of distance instead of RTT, which proved to be quite successful.
So in short for those Target files which have both good and not-so-good landmark values, tri-lateration performs better than multi-lateration because good values are moved to the top of the list and are exploited by tri-lateration whereas multi-lateration takes into account all values.