Identification of Simple Product-Form Plumes Using Networks of Sensors With Random Errors

Abstract

We consider a class of simple, idealized plumes which are specified by a product of injection and distance decay terms. The plume propagates with a constant velocity, and its distance term decays exponentially with respect to distance in a planar region. If the intensity sensors are error-free, the difference triangulation method can identify the origin of plume both in time and space within a specified precision. In our case, the sensors are subject to random, correlated errors with unknown distributions in measuring the plume intensity. The sensors are available or in place to conduct controlled experiments and collect measurements. We present a training method that utilizes the plume equation together with controlled sensor measurements to identify the plume's origin with distribution-free probabilistic performance guarantees. The training consists of utilizing the measurements to compute a suitable precision value for the difference triangulation method to account for sensor distributions. We present a distribution-free relationship between the training sample size and the precision and probability with which plume's origin is identified