A Stochastic Sensor Selection Scheme for Sequential Hypothesis Testing With Multiple Sensors

Abstract

We study the problem of binary sequential hypothesis testing using multiple sensors with associated observation costs. An off-line randomized sensor selection strategy, in which a sensor is chosen at every time step with a given probability, is considered. The objective of this work is to find a sequential detection rule and a sensor selection probability vector such that the expected total observation cost is minimized subject to constraints on reliability and sensor usage. First, the sequential probability ratio test is shown to be the optimal sequential detection rule in this framework as well. Efficient algorithms for obtaining the optimal sensor selection probability vector are then derived. In particular, a special class of problems in which the algorithm has complexity that is linear in the number of sensors is identified. An upper bound for the average sensor usage to estimate the error incurred due to Wald's approximations is also presented. This bound can be used to set a safety margin for guaranteed satisfaction of the constraints on the sensor usage.

Sequential Hypothesis Test With Online Usage-Constrained Sensor Selection

“…As such, we arrive at the following 1 One can also use the weighted sum of type-I and type-II error rates as the error probability. Here we adopt the formulation in [15], and consider them individually. Nevertheless, the method developed in this work can be applied to the former case.…”

“…Similar teniques were later applied to the quickest detection with stochastic surveillance control [14]. Recently, focusing on the binary-hypothesis test, [15] further imposed constraints on the sensor usages, i.e., sensors, on average, cannot be selected more than their prescribed limits, and obtained the selection probabilities for SPRT with random sensor selection.…”

“…That is, certain sensors in the network are not allowed to be selected more than a prescribed number of times on average. The usage constraints naturally arise when one intends to restrain the sensors from being overused due to their limited battery/lifetime, or if the fairness for all sensors in the network is important [15]. We summarize the contributions as follows:…”

“…• To the best of our knowledge, this is the first work that jointly solves for the optimal sequential test and online sensor selection when sensor usage constraints are considered. Moreover, this work distinguishes from [15], where the usage-contrained sensor selection is also studied, in terms of its online/closed-loop setup.…”

On Real-Time Fault Detection in Wind Turbines: Sensor Selection Algorithm and Detection Time Reduction Analysis

“…For instance, Chepuri and Leus [6] propose convex relaxations techniques to select the best subset of sensors that guarantees some recommended performance. Similarly, Bai et al [7] suggest a sensor selection schedule to minimize the observation cost on a sequential probability ratio test (SPRT). With respect to a more precise problem, Miao et al [8] investigated the performance of combinations of several metal-oxide sensors for the discrimination of a set of ginsengs.…”