Worst Case Detection Delay Research Articles

Algorithms for Change Detection With Sparse Signals

We consider the change detection problem where the pre-change observation vectors are purely noise and the post-change observation vectors are noise-corrupted compressive measurements of sparse signals with a common support, measured using a sensing matrix. In general, post-change probability density function (pdf) of the observations depends on parameters such as the support and variances of the sparse signal. When these parameters are unknown, we propose two approaches. In the first approach, we approximate the post-change pdf based on the known parameters such as mutual coherence of the sensing matrix and bounds on the signal variances. In the second approach, we parameterize the post-change pdf with an unknown parameter and try to estimate this parameter using two different methods, stochastic gradient descent and generalized likelihood ratio. In both these approaches, we employ the conventional cumulative sum (CUSUM) algorithm with various decision statistics such as the energy of the observations, correlation values with columns of the sensing matrix and the maximum value of such correlations. We analytically characterize the worst case detection delay and average run length to false alarm performance of pdf-approximation based approach. We also numerically study the performance and offer insights on the relevance of various decision statistics in different signal to noise ratio (SNR) regimes. We also address the problem of designing sensing matrices with small mutual coherence by using designs from quantum information theory. One such design using equi-angular lines has an additional structure which allows exact characterization of the post-change pdf of the correlation values, even when the support set of the sparse signal is unknown. We apply our detection algorithms with sensing matrix designed from equi-angular lines to a massive random access problem and show their superior performance over conventional Gold codes.

Online Change-Point Detection of Linear Regression Models

In this paper, we consider the problem of quickly detecting an abrupt change in linear regression models. Specifically, an observer sequentially obtains a sequence of observations, whose underlying linear model changes at an unknown time. Moreover, the pre-change linear model is perfectly known by the observer but the post-change linear model is unknown. The observer aims to design an efficient online algorithm to detect the presence of the change via his sequential observations. Based on different assumptions on the change-point, both non-Bayesian and Bayesian problem formulations are considered. In the non-Bayesian setting, the change-point is modeled as a fixed but unknown constant. Two performance metrics, namely the worst case detection delay and the average run length to false alarm, are adopted to evaluate the performance of detection algorithms. In the Bayesian setting, the change-point is modeled as a geometrically distributed random variable. For this case, the average detection delay and the probability of false alarm are used as performance metrics. We propose a novel algorithm, namely the parallel-sum algorithm, for the purpose of change detection. For both setups, we show that the proposed algorithm has a low computational complexity while still offering a good performance in terms of the performance metrics of the respective setting.

Second-Order Asymptotic Optimality in Multisensor Sequential Change Detection

A generalized multisensor sequential change detection problem is considered, in which a number of (possibly correlated) sensors monitor an environment in real time, the joint distribution of their observations is determined by a global parameter vector, and at some unknown time there is a change in an unknown subset of components of this parameter vector. The goal is to detect the change as soon as possible, while controlling the rate of false alarms. We establish the second-order asymptotic optimality (with respect to Lorden’s criterion) of various generalizations of the CUSUM rule; that is, we show that their additional expected worst case detection delay (relative to the one that could be achieved if the affected subset was known) remains bounded as the rate of false alarm goes to 0, for any possible subset of affected components. This general framework incorporates the traditional multisensor setup in which only an unknown subset of sensors is affected by the change. The latter problem has a special structure which we exploit in order to obtain feasible representations of the proposed schemes. We present the results of a simulation study where we compare the proposed schemes with scalable detection rules that are only first-order asymptotically optimal. Finally, in the special case that the change affects exactly one sensor, we consider the scheme that runs in parallel the local CUSUM rules and study the problem of specifying the local thresholds.

Non-Bayesian Quickest Change Detection With Stochastic Sample Right Constraints

In this paper, we study the design and analysis of optimal detection scheme for sensors that are deployed to monitor the change in the environment and are powered by the energy harvested from the environment. In this type of applications, detection delay is of paramount importance. We model this problem as quickest change detection problem with a stochastic energy constraint. In particular, a wireless sensor powered by renewable energy takes observations from a random sequence, whose distribution will change at a certain unknown time. Such a change implies events of interest. The energy in the sensor is consumed by taking observations and is replenished randomly. The sensor cannot take observations if there is no energy left in the battery. Our goal is to design a power allocation scheme and a detection strategy to minimize the worst case detection delay, which is the difference between the time when an alarm is raised and the time when the change occurs. Two types of average run length (ARL) constraint, namely an algorithm level ARL constraint and an system level ARL constraint, are considered. We propose a low complexity scheme in which the energy allocation rule is to spend energy to take observations as long as the battery is not empty and the detection scheme is the Cumulative Sum test. We show that this scheme is optimal for the formulation with the algorithm level ARL constraint and is asymptotically optimal for the formulations with the system level ARL constraint.

Diagnosis of behaviors of interest in partially-observed discrete-event systems

In this paper, we address the problem of diagnosing the behaviors of interest in discrete-event systems. To this end, we introduce the notion of language-diagnosability, based on language specifications that generalizes diagnosability based on event specifications. A polynomial-time algorithm for verifying language-diagnosability is developed. Building upon the verification algorithm, we develop a polynomial-time algorithm for computing the worst case detection delay of a given system. The computation of the worst case detection delay involves the shortest path computation of a weighted, directed graph. We exploit a special weighting structure of the graph resulting from the verification algorithm, which enables an algorithm with a lower complexity than the commonly used Bellman–Ford shortest path algorithm.