Let's assume, hidden in a forest, there's a beacon. I walk in the forest and, at random intervals, ping the beacon. For each ping I get a lat/lng pair and the signal strength of the ping at that point (but no direction). At the end of the day I have n readings where n is a random number.
How would I compute the location (lat/lng) of the beacon?
If, at a later time, I would get another reading, how would I add this to my current estimate of the beacon's location?
Note: we do not know how the forest is affecting the signal strength, but we can assume the effect is uniform - the beacon could be in a clearing, or buried beneath a stone.
I am assuming that all my n readings can be drawn on a map as circles where the lat/lng is the center of the circle and the signal strength is the radius. If the readings are accurate then the beacon should be in that area where all the circles overlap. I have however no clue how to find the center of the overlapping areas of n circles. Can somebody help?
1. Each reading indicates the position I am currently standing in (random location)
2. The signal strength is inversely proportional to the distance between the reading and the beacon although I do not know what is the coefficient. I do however know that this coefficient is the same for all the readings
3. While from a theoretical point of view only two readings are necessary I would like to be able to incorporate as many of the readings as possible in the calculation as all these readings might not be 100% accurate