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Dr. Les quickly explained what TULIP was doing and wanted to do a quick analysis of the same location (i.e. SLAC) using CBG with tri-laterationtrilateration. So I found a target located at SLAC (134.79.18.134) in CBG list. We ran CBG with tri-lateration trilateration for this target. The results were way off. The error distance was of the order of ~3200 km.
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Landmark 1 | Landmark 2 | Landmark 3 | Error (km) | Distance to nearest landmark (km) | Area of Region (km) | Est. Lat/Long | Actual Lat/Long36.9899 -122.06 |
|---|---|---|---|---|---|---|---|
36.9899 -122.06 (Santa Cruz) | 38.4829 -121.64 (Davis) | 37.3558 -121.954 (Santa Clara) | 25.254 | 2.5132 | 1498.5 | 37.474 -121.93 | 37.418 -122.2 |
37.4285 -122.178 (Stanford) | 37.3762 -122.183 (Palo Alto) | 37.3558 -121.954 (Santa Clara) | 2.5156 | 2.5132 | 1048.8 | 37.429 -122.18 | 37.418 -122.2 |
CBG with tri-lateration trilateration seems to be performing well.
Points to consider
These results prove that tri-lateration trilateration works. So the question is why is TULIP failing so miserably?
CBG
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multilateration vs CBG
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trilateration comparison
Spreadsheet shows a comparison of error (in km) between CBG with multi-lateration multilateration and CBG with tri-laterationtrilateration. The technique I've followed:
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- Avoiding duplicate landmarks.
- Reason: If you look at the spreadsheet you will notice that there are duplicate entries for multi-lateration multilateration as well. You can infer this from matching Estimated Lat/Longs to Actual Lat/Longs and by observing the distance to the nearest landmark values. Also a few targets don't have more than two landmarks and in all such cases those are duplicates (in terms of Lat/Longs). So in such a case I don't have an option but to use the duplicate ones. However I do require comments on this - whether I should remove duplicates or not. The two reasons of my concern are that multi-lateration multilateration uses duplicate landmark values and a few targets having none but duplicate landmarks.
- Avoiding landmarks present within a target's vicinity.
- Reason: Closely related to the point mentioned above.
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In the ??spreadsheet we have made various calculations in order to understand the results.
1. Amount of NaNs (in error distance) for
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multilateration and trilateration
67/171 for multi-lateration multilateration and 11/171 for tri-laterationtrilateration.
NaN (Not a Number) is a value of numeric data-type representing an undefined or unrepresentable value, especially in floating point calculations. More here.
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2. Some results have enormous errors (|error|>1000)
This is true for both multi-lateration and tri-laterationmultilateration and trilateration. And reasons could be one or more of the following:
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I've inferred these from looking at the Target files.
3.
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Trilateration is performing better than
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multilateration in some cases
There are 23 instances where tri-lateration trilateration performs better than multi-laterationmultilateration, 29 instances where multi-lateration multilateration performs better than tri-lateration trilateration and in the rest both perform equally well. The reason as far as I understand is:
We sorted the Target files on the basis of RTT between the target and landmarks. This promoted those lat/long values to the top of the list which had least RTT from the target. Though any such sorting technique on these values doesn't affect multi-lateration multilateration results but it makes a huge impact on tri-lateration trilateration results. The reason being the way these two techniques use these values. Multi-lateration Multilateration considers all values and figures out regions of intersection whereas tri-lateration trilateration simply takes three values to find an intersection region.
So If we have say 10 landmarks and 4 of them had relatively lower RTT to the target, multi-lateration multilateration will give good results. Even if some values aren't really good, it won't cause multi-lateration multilateration to behave in an entirely different way. However in case of tri-laterationtrilateration, better the landmark estimates we have, the better the results are. Since tri-lateration trilateration considers three values, even a single one of those three values can make a big difference.
CBG trilateration vs Improved trilateration (by Farrah) comparison
Spreadsheet here shows comparison between CBG's trilateration and Farrah's improved trilateration. A few important points:
- There are a total of 174 targets for CBG out of which 131 remain after ignoring values that either have error in the range "0<error<1" or contain "NaN".
- Improved trilateration by Farrah produced results for only 78 targets so far. Her method produced 7 "NaN" values which she ignored.
- Only 74 targets overlap between CBG trilateration and improved trilateration.
- If I don't ignore CBG's values that have estimate error in the range "0<error<1" then CBG trilateration performs 64/74 times better and improved trilateration performs only 10/74 times better.
- Even if I ignore values with error estimate "0<error<1" then CBG performs 32/74 times better, improved trilateration performs 10/74 times better and rest are unaccounted for.