A radio signal generator is constantly transmitting from an unknown location and the most precise approximation is needed. We have two strategies at our disposal - one for each of the aforementioned antennas respectively.
### Omnidirectional Strategy(ODS)
Let `A` be the antenna and the center of the reception circle. The reception circle's radius is 2 units. These units have an unknown real life equivalent(you can imagine it as gain); However that is rather irrelevant for the scope of the experiment. A can be moved around the plane freely.
### Yagi strategy(YS)
Let `A,B,C` and `D` be individual directional antennas ordered in a rectangular formation. Each antenna has a vector with the length of 10, given that directional antennas usually have around 5 times higher gain when receiving and transmitting signal than omnidirectionals, the cost of that being that the transceiving is limited to a certain direction. The formation must be composed in a way, such that there is always at least 2 vectors intersecting each other. These points are stationary, however their respective vectors could be rotated 360 degrees.
We know the distances between each of the points.
### Solution approach
Both strategies involve direction finding of some sort. [Direction finding](https://en.wikipedia.org/wiki/Direction_finding) using vector intersection is quite self explanatory, you take the antenna in which the signal is the strongest, take the two nearest antennas and find the point in which the vectors overlap. The point left at the end is our location.
When it comes to circles, however, the strategy is different. [Trilateration](https://en.wikipedia.org/wiki/Trilateration) is a way of pinpointing a location using ranges. The approach is different from the usual, as we do not have multiple antennas, but rather a single moving one. Trilateration goes like: Get readings from 3 different points(it would help if they were polar opposites). Find the intersection of the three circles that you have. That's the point we're looking for.
YS is not as effective, however it is way more efficient than ODS on many levels. At least on paper. A list of all the theoretical pros of YS over ODS:
This is the simulation of one of the aforementioned strategy. We can take from it that, if the location we are looking for is inside of the area of the rectangle formed by connecting the antenna points, or even slightly outside - we will find it. I would say in a rather rapid manner(depending on the speed of spinning).
Would you look at that. Fueled by pure pseudorandomness, this "algorithm" is blowing the competition away. Imagine if there was a real algorithm that got closer and closer! As you can see, it takes a lot less time(given you can teleport) to cover the entirety of the rectangular area we have. But what about, scaling things up a bit...
