Towards Fast and Reliable Localization of an Underwater Object: An Interval Approach

To localize an underwater object, we measure the distance to this object from several sonar sensors with known locations. The problem is that the signal sent by some of the sonars is reflected not by the desired object(s), but by some auxiliary object and thus, the values measured by these sensors are drastically different from the distance to the desired object. To solve this problem, currently probabilistic methods are used; however, since we do not know the exact probability distributions, these methods may miss the actual location of the object. There exist interval-based methods which provide guaranteed (reliable) bounds on the object’s location, but these methods sometimes require too much computation time. In this paper, we propose a new faster algorithm for reliable localization of underwater objects. 1 Formulation of the Problem Localizing an underwater object: general idea. In some practical situations, we need to find the spatial location x⃗ = (x1, x2, x3) of an underwater object: for example, of a mobile underwater robot or an adversary’s submarine. To locate this object, we can use a network of stationary omnidirectional sonars whose locations s⃗1, . . . , s⃗n are known. A sonar emits an acoustic signal. This signal is reflected by the object, and the reflection is detected by a sensor attached to the sonar. The sensor measures the time that passes from the