Choice and implementation of the localisation algorithm :
Finding the solution of a localisation problem thanks to tdoa (time difference of arrival) of the beeps and knowing the position of each tweeter.
Technically the problem consists in solving 3 equations of the second degree with 3 parameters (the coordinates if the position of the device).
One major advantage of an algorithm is to be able to use the fact it has redundant information if extra twitters are used.
The uncertainties in the reality come from two elements :
- detecting the exact time of arrival of a beep (this maybe difficult because of the noise and air flux)
- knowing the speed of ultrasound (which varies a lot in function of temperature, humidity, pression …)
Simulations shows that the main source of uncertainty is the speed of the ultrasound.
The algorithms we chose to implement takes all the information from the emitters and apply a least square algorithms to find a good position. The solution obtained is re-injected into the equation system to deduce an error parameter. This process is repeated to minimise the error in function of the speed of the ultrasound.
We are eager to test it in real life to see how good is the precision obtained.
I am aware I spend a great deal of time on this problem.
I am now switching to the embedded part concerning the synchronisation of the emitters.
Please feel free to leave any comments.