Quickest detection in coupled systems

This work considers the problem of quickest detection of signals in a coupled system of N sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled a general Ito processes, are coupled across sensors, but that their onset times may differ from sensor to sensor. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended average Kullback- Leibler divergence criterion is used as a measure of detection delay, with a constraint on the mean time between false alarms. The case in which the sensors employ cumulative sum (CUSUM) strategies is considered, and it is proved that the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound.Comment: 6 pages, 48th IEEE Conference on Decision and Control, Shanghai 2009 December 16 - 1

Quickest Change Detection of a Markov Process Across a Sensor Array

Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general scenario is considered where the change propagates across the sensors, and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process, is considered. The problem of minimizing the average detection delay subject to false alarm constraints is formulated as a partially observable Markov decision process (POMDP). Insights into the structure of the optimal stopping rule are presented. In the limiting case of rare disruptions, we show that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened. We establish the asymptotic optimality (in the vanishing false alarm probability regime) of this threshold test under a certain condition on the Kullback-Leibler (K-L) divergence between the post- and the pre-change densities. In the special case of near-instantaneous change propagation across the sensors, this condition reduces to the mild condition that the K-L divergence be positive. Numerical studies show that this low complexity threshold test results in a substantial improvement in performance over naive tests such as a single-sensor test or a test that wrongly assumes that the change propagates instantaneously.Comment: 40 pages, 5 figures, Submitted to IEEE Trans. Inform. Theor

A particle filtering approach for joint detection/estimation of multipath effects on GPS measurements

Multipath propagation causes major impairments to Global Positioning System (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this work, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF). The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step

Nonlinear Model Predictive Control for Multi-Micro Aerial Vehicle Robust Collision Avoidance

Multiple multirotor Micro Aerial Vehicles sharing the same airspace require a reliable and robust collision avoidance technique. In this paper we address the problem of multi-MAV reactive collision avoidance. A model-based controller is employed to achieve simultaneously reference trajectory tracking and collision avoidance. Moreover, we also account for the uncertainty of the state estimator and the other agents position and velocity uncertainties to achieve a higher degree of robustness. The proposed approach is decentralized, does not require collision-free reference trajectory and accounts for the full MAV dynamics. We validated our approach in simulation and experimentally.Comment: Video available on: https://www.youtube.com/watch?v=Ot76i9p2ZZo&t=40