4 research outputs found
Decentralized Maximum Likelihood Estimation for Sensor Networks Composed of Nonlinearly Coupled Dynamical Systems
In this paper we propose a decentralized sensor network scheme capable to
reach a globally optimum maximum likelihood (ML) estimate through
self-synchronization of nonlinearly coupled dynamical systems. Each node of the
network is composed of a sensor and a first-order dynamical system initialized
with the local measurements. Nearby nodes interact with each other exchanging
their state value and the final estimate is associated to the state derivative
of each dynamical system. We derive the conditions on the coupling mechanism
guaranteeing that, if the network observes one common phenomenon, each node
converges to the globally optimal ML estimate. We prove that the synchronized
state is globally asymptotically stable if the coupling strength exceeds a
given threshold. Acting on a single parameter, the coupling strength, we show
how, in the case of nonlinear coupling, the network behavior can switch from a
global consensus system to a spatial clustering system. Finally, we show the
effect of the network topology on the scalability properties of the network and
we validate our theoretical findings with simulation results.Comment: Journal paper accepted on IEEE Transactions on Signal Processin
Asymptotically Optimal Sampling Policy for Quickest Change Detection with Observation-Switching Cost
We consider the problem of quickest change detection (QCD) in a signal where
its observations are obtained using a set of actions, and switching from one
action to another comes with a cost. The objective is to design a stopping rule
consisting of a sampling policy to determine the sequence of actions used to
observe the signal and a stopping time to quickly detect for the change,
subject to a constraint on the average observation-switching cost. We propose
an open-loop sampling policy of finite window size and a generalized likelihood
ratio (GLR) Cumulative Sum (CuSum) stopping time for the QCD problem. We show
that the GLR CuSum stopping time is asymptotically optimal with a properly
designed sampling policy and formulate the design of this sampling policy as a
quadratic programming problem. We prove that it is sufficient to consider
policies of window size not more than one when designing policies of finite
window size and propose several algorithms that solve this optimization problem
with theoretical guarantees. For observation-dependent policies, we propose a
-threshold stopping time and an observation-dependent sampling policy. We
present a method to design the observation-dependent sampling policy based on
open-loop sampling policies. Finally, we apply our approach to the problem of
QCD of a partially observed graph signal and empirically demonstrate the
performance of our proposed stopping times
Quickest Change Detection in the Presence of a Nuisance Change
In the quickest change detection problem in which both nuisance and critical
changes may occur, the objective is to detect the critical change as quickly as
possible without raising an alarm when either there is no change or a nuisance
change has occurred. A window-limited sequential change detection procedure
based on the generalized likelihood ratio test statistic is proposed. A
recursive update scheme for the proposed test statistic is developed and is
shown to be asymptotically optimal under mild technical conditions. In the
scenario where the post-change distribution belongs to a parametrized family, a
generalized stopping time and a lower bound on its average run length are
derived. The proposed stopping rule is compared with the FMA stopping time and
the naive 2-stage procedure that detects the nuisance or critical change using
separate CuSum stopping procedures for the nuisance and critical changes.
Simulations demonstrate that the proposed rule outperforms the FMA stopping
time and the 2-stage procedure, and experiments on a real dataset on bearing
failure verify the performance of the proposed stopping time