On the Performance of Quickest Detection Spectrum Sensing: The Case of Cumulative Sum

Quickest change detection (QCD) is a fundamental problem in many applications. Given a sequence of measurements that exhibits two different distributions around a certain flipping point, the goal is to detect the change in distribution around the flipping point as quickly as possible. The QCD problem appears in many practical applications, e.g., quality control, power system line outage detection, spectrum reuse, and resource allocation and scheduling. In this paper, we focus on spectrum sensing as our application since it is a critical process for proper functionality of cognitive radio networks. Relying on the cumulative sum (CUSUM), we derive the probability of detection and the probability of false alarm of CUSUM based spectrum sensing. We show the correctness of our derivations using numerical simulations.Comment: This paper is accepted for publication in IEEE Communication Letters Jan 202

A Binning Approach to Quickest Change Detection with Unknown Post-Change Distribution

The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions distinguishable from a discretized version of the pre-change distribution. A sequential change detection procedure is proposed that partitions the sample space into a finite number of bins, and monitors the number of samples falling into each of these bins to detect the change. A test statistic that approximates the generalized likelihood ratio test is developed. It is shown that the proposed test statistic can be efficiently computed using a recursive update scheme, and a procedure for choosing the number of bins in the scheme is provided. Various asymptotic properties of the test statistic are derived to offer insights into its performance trade-off between average detection delay and average run length to a false alarm. Testing on synthetic and real data demonstrates that our approach is comparable or better in performance to existing non-parametric change detection methods.Comment: Double-column 13-page version sent to IEEE. Transaction on Signal Processing. Supplementary material include

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 $2$-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

Centralized moving-horizon estimation for a class of nonlinear dynamical complex networks under event-triggered transmission scheme

Data availability statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.This article is concerned with the problem of event-triggered centralized moving-horizon state estimation for a class of nonlinear dynamical complex networks. An event-triggered scheme is employed to reduce unnecessary data transmissions between sensors and estimators, where the signal is transmitted only when certain condition is violated. By treating sector-bounded nonlinearities as certain sector-bounded uncertainties, the addressed centralized moving-horizon estimation problem is transformed into a regularized robust least-squares problem that can be effectively solved via existing convex optimization algorithms. Moreover, a sufficient condition is derived to guarantee the exponentially ultimate boundedness of the estimation error, and an upper bound of the estimation error is also presented. Finally, a numerical example is provided to demonstrate the feasibility and efficiency of the proposed estimator design method.National Natural Science Foundation of China. Grant Numbers: 61873148, 61933007, 62033008, 62073339, 62173343; Natural Science Foundation of Shandong Province of China. Grant Number: ZR2020YQ49; AHPU Youth Top-notch Talent Support Program of China. Grant Number: 2018BJRC009; Natural Science Foundation of Anhui Province of China. Grant Number: 2108085MA07; China Postdoctoral Science Foundation. Grant Number: 2018T110702; Postdoctoral Special Innovation Foundation of Shandong Province of China. Grant Number: 201701015; Royal Society of the UK; Alexander von Humboldt Foundation of Germany