(avec J.L. Boimond and L. Hardouin (LISA)),
Let us consider a plane where ten acoustic transmitters (see figure below). Each transmitter emits an indiscernible impulse sound at date 0.
A robot, whose position x,y has to be estimated, is equipped with a sound sensor and records a dater the component of which corresponds to dates at which a sound is detected. It is assumed that ten dates have been recorded. : (1,2.24,3,3.6,4.12,4.47,5,5.1,5.38,6.4), with an error on each measurement which is known to belong to the interval [-1,1]. The propagation delay associated with the ith transmitter is assumed to be proportional to the distance between the robot and the transmitter: the algorithm SIVIA brackets the feasible set (i.e., consistent with sur mesurements and acceptable errors) as represented on Figure, in less than 5 seconds on a PC DX4-100.
