Scenario: a small solid plate of a material yet to decide with equally spaced vibration sensors along its outer sides. An user knocks (or throws a small object) on a random point on the surface and the logic finds the point by only reading the sensors, ie time and intensity of the events.
The plate is small, 1 meter or less, and can be made of wood, acrylic etc. The number of sensors is not strictly defined as well, although I believe 6 to 8 would be ideal. If it helps, all sensors can be arranged in a circle or a square pattern. No need for precision, a 5% position error would be perfectly acceptable. OTOH speed is important: it should be able to sustain at least 50 reads per second.
(Nope, I'm not designing a machine gun target. No weapons involved, although in a broad sense we're somewhat close:*)
It doesnt' seem that hard (I thought), just read all sensors in a tight loop, find the first pulse for each sensor to discriminate against reflections and calculate the distance based on delay/intensity differences from other sensors taking into account the different speed of sound in the given material, then repeat. That would be trivial if only I wasn't a total math illiterate. After some searches the magic words I stumbled upon were "multilateration" and "TDOA", so I looked for examples, source code or anything that could be made into a small microcontroller but no cigar. One matlab example aside, I couldn't find anything practical, except for some long math papers not even my cat (way better at math than I) could understand:)
So the question is: could such a beast be implemented using low cost microcontrollers? Any pointers on similar projects with portable source code (hopefully C) to be studied? Thanks!