Stochastic Plume Estimation : Measurement Sampling for a Supermartingale Support

In this paper we use a simple a model for a stochastically moving plume center and determine sufficient measurement schemes, for three cases of measurement noise, that reduce the support of the plume center’s probability distribution. We assume a multivariate gaussian plume that moves according to a stochastic discrete-time stochastic linear time-invariant model. We also assume a measurement function that is a function of proximity to the center of the plume distribution. Using both knowledge of the dynamics and the behaviour of this measurement function a recursive probability distribution was formulated. We then found sufficient measurement schemes that reduce the support of this recursive probability distribution such that the area of the support behaves like a supermartingale.