Information bounds and quickest change detection in decentralized decision systems

The quickest change detection problem is studied in decentralized decision systems, where a set of sensors receive independent observations and send summary messages to the fusion center, which makes a final decision. In the system where the sensors do not have access to their past observations, the previously conjectured asymptotic optimality of a procedure with a monotone likelihood ratio quantizer (MLRQ) is proved. In the case of additive Gaussian sensor noise, if the signal-to-noise ratios (SNR) at some sensors are sufficiently high, this procedure can perform as well as the optimal centralized procedure that has access to all the sensor observations. Even if all SNRs are low, its detection delay will be at most pi/2-1 approximate to 57% larger than that of the optimal centralized procedure. Next, in the system where the sensors have full access to their past observations, the first asymptotically optimal procedure in the literature is developed. Surprisingly, the procedure has the same asymptotic performance as the optimal centralized procedure, although it may perform poorly in some practical situations because of slow asymptotic convergence. Finally, it is shown that neither past message information nor the feedback from the fusion center improves the asymptotic performance in the simplest model

Sequential change-point detection when unknown parameters are present in the pre-change distribution

In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution $f_{\theta}$ and tries to minimize the detection delay for every possible post-change distribution $g_{\lambda}$. In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for every possible pre-change distribution $f_{\theta}$. We present asymptotically optimal procedures for one-parameter exponential families. Next, we develop a general theory for change-point problems when both the pre-change distribution $f_{\theta}$ and the post-change distribution $g_{\lambda}$ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.Comment: Published at http://dx.doi.org/10.1214/009053605000000859 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive Estimation and Detection Techniques with Applications

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection

Adaptive Estimation and Detection Techniques with Applications

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection

A New Multiple Hypothesis Tracker Integrated with Detection Processing.

In extant radar signal processing systems, detection and tracking are carried out independently, and detected measurements are utilized as inputs to the tracking procedure. Therefore, the tracking performance is highly associated with detection accuracy, and this performance may severely degrade when detections include a mass of false alarms and missed-targets errors, especially in dense clutter or closely-spaced trajectories scenarios. To deal with this issue, this paper proposes a novel method for integrating the multiple hypothesis tracker with detection processing. Specifically, the detector acquires an adaptive detection threshold from the output of the multiple hypothesis tracker algorithm, and then the obtained detection threshold is employed to compute the score function and sequential probability ratio test threshold for the data association and track estimation tasks. A comparative analysis of three tracking algorithms in a clutter dense scenario, including the proposed method, the multiple hypothesis tracker, and the global nearest neighbor algorithm, is conducted. Simulation results demonstrate that the proposed multiple hypothesis tracker integrated with detection processing method outperforms both the standard multiple hypothesis tracker algorithm and the global nearest neighbor algorithm in terms of tracking accuracy

A New Multiple Hypothesis Tracker Using Validation Gate with Motion Direction Constraint.

In multi-target tracking scenarios with dense and heterogeneous clutter, there is a substantial increase in the false measurements that originated from the clutter within the validation gate, and consequently, the number of measurement-to-track association hypothesis grows rapidly in traditional multiple hypothesis tracker (MHT), leading to a sharp decrease in data association accuracy and tracking performance. A new multiple hypothesis tracker using validation gate with motion direction constraint (MHT-MDC) is proposed to solve these problems. In the MHT-MDC, a motion direction constraint (MDC) gate is designed by considering the prior target maneuvering information, which effectively reduces the volume of validation gate and, thus, diminishes the number of false measurements in the gate when the innovation covariance is large. Subsequently, the clutter density in the MDC gate is adaptively estimated by the conditional mean estimator of clutter density (CMECD), based on which the score functions in the MDC gate can be calculated. The MHT-MDC is compared with the MHT algorithm in simulations, and the experimental results demonstrate its superior tracking performance for weakly maneuvering targets in high clutter density scenarios

Application of Classical Versus Bayesian Statistical Methods to On-line Radiological Monitoring

The on-line monitoring for illicit radioactive material with a minimum number of false detections is a critical need for homeland security. The primary objectives of this work were to apply both Bayesian and classical statistical process control chart techniques to the on-line monitoring of radiological data and to then compare the Type I and Type II error incidence rates. Two versions of the cumulative sum (CUSUM) and Shiryayev-Roberts (S-R) procedures known as total reset and alarm reset methods were developed. The best method in terms of Type I errors was the S-R total reset method. In terms of Type II errors, the CUSUM alarm reset procedure and the S-R alarm reset control scheme were most effective. At high count rates, the Shewhart (3-sigma) control chart resulted in the fewest number of false negatives independent of the amount of time a source was present