Optimal Bayesian Quickest Detection for Hidden Markov Models and Structured Generalisations

In this paper we consider the problem of quickly detecting changes in hidden Markov models (HMMs) in a Bayesian setting, as well as several structured generalisations including changes in statistically periodic processes, quickest detection of a Markov process across a sensor array, quickest detection of a moving target in a sensor network and quickest change detection (QCD) in multistream data. Our main result establishes an optimal Bayesian HMM QCD rule with a threshold structure. This framework and proof techniques allow us to to elegantly establish optimal rules for several structured generalisations by showing that these problems are special cases of the Bayesian HMM QCD problem. We develop bounds to characterise the performance of our optimal rule and provide an efficient method for computing the test statistic. Finally, we examine the performance of our rule in several simulation examples and propose a technique for calculating the optimal threshold

Bayesian Non-parametric Hidden Markov Model for Agile Radar Pulse Sequences Streaming Analysis

Multi-function radars (MFRs) are sophisticated types of sensors with the capabilities of complex agile inter-pulse modulation implementation and dynamic work mode scheduling. The developments in MFRs pose great challenges to modern electronic reconnaissance systems or radar warning receivers for recognition and inference of MFR work modes. To address this issue, this paper proposes an online processing framework for parameter estimation and change point detection of MFR work modes. At first, this paper designed a fully-conjugate Bayesian non-parametric hidden Markov model with a designed prior distribution (agile BNP-HMM) to represent the MFR pulse agility characteristics. The proposed model allows fully-variational Bayesian inference. Then, the proposed framework is constructed by two main parts. The first part is the agile BNP-HMM model for automatically inferring the number of HMM hidden states and emission distribution of the corresponding hidden states. An estimation error lower bound on performance is derived and the proposed algorithm is shown to be close to the bound. The second part utilizes the streaming Bayesian updating to facilitate computation, and designed an online work mode change detection framework based upon a weighted sequential probability ratio test. We demonstrate that the proposed framework is consistently highly effective and robust to baseline methods on diverse simulated data-sets.Comment: 15 pages, 10 figures, submitted to IEEE transactions on signal processin

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

Quickest Change Detection in Autoregressive Models

The problem of quickest change detection (QCD) in autoregressive (AR) models is investigated. A system is being monitored with sequentially observed samples. At some unknown time, a disturbance signal occurs and changes the distribution of the observations. The disturbance signal follows an AR model, which is dependent over time. Before the change, observations only consist of measurement noise, and are independent and identically distributed (i.i.d.). After the change, observations consist of the disturbance signal and the measurement noise, are dependent over time, which essentially follow a continuous-state hidden Markov model (HMM). The goal is to design a stopping time to detect the disturbance signal as quickly as possible subject to false alarm constraints. Existing approaches for general non-i.i.d. settings and discrete-state HMMs cannot be applied due to their high computational complexity and memory consumption, and they usually assume some asymptotic stability condition. In this paper, the asymptotic stability condition is firstly theoretically proved for the AR model by a novel design of forward variable and auxiliary Markov chain. A computationally efficient Ergodic CuSum algorithm that can be updated recursively is then constructed and is further shown to be asymptotically optimal. The data-driven setting where the disturbance signal parameters are unknown is further investigated, and an online and computationally efficient gradient ascent CuSum algorithm is designed. The algorithm is constructed by iteratively updating the estimate of the unknown parameters based on the maximum likelihood principle and the gradient ascent approach. The lower bound on its average running length to false alarm is also derived for practical false alarm control. Simulation results are provided to demonstrate the performance of the proposed algorithms

Secret key establishment from common randomness represented as complex correlated random processes: Practical algorithms and theoretical limits

Establishing secret common randomness between two or multiple devices in a network resides at the root of communication security. In its most frequent form of key establishment, the problem is traditionally decomposed into a randomness generation stage (randomness purity is subject to employing often costly true random number generators) and an information-exchange agreement stage, which relies either on public-key infrastructure or on symmetric encryption (key wrapping). This dissertation has been divided into two main parts. In the first part, an algorithm called KERMAN is proposed to establish secret-common-randomness for ad-hoc networks, which works by harvesting randomness directly from the network routing metadata, thus achieving both pure randomness generation and (implicitly) secret-key agreement. This algorithm relies on the route discovery phase of an ad-hoc network employing the Dynamic Source Routing protocol, is lightweight, and requires relatively little communication overhead. The algorithm is evaluated for various network parameters, and different levels of complexity, in OPNET network simulator. The results show that, in just ten minutes, thousands of secret random bits can be generated network-wide, between different pairs in a network of fifty users. The proposed algorithm described in this first part of this research study has inspired study of the problem of generating a secret key based on a more practical model to be explored in the second part of this dissertation. Indeed, secret key establishment from common randomness has been traditionally investigated under certain limiting assumptions, of which the most ubiquitous appears to be that the information available to all parties comes in the form of independent and identically distributed (i.i.d.) samples of some correlated andom variables. Unfortunately, models employing the i.i.d assumption are often not accurate representations of real scenarios. A more capable model would represent the available information as correlated hidden Markov models (HMMs), based on the same underlying Markov chain. Such a model accurately reflects the scenario where all parties have access to imperfect observations of the same source random process, exhibiting a certain time dependency. In the second part of the dissertation , a computationally-efficient asymptotic bounds for the secret key capacity of the correlated-HMM scenario has been derived. The main obstacle, not only for this model, but also for other non-i.i.d cases, is the computational complexity. This problem has been addressed by converting the initial bound to a product of Markov random matrices, and using recent results regarding its convergence to a Lyapunov exponent