This work considers the cooperative sequential hypothesis testing problem in a distributed network with quantized communication channels. The sensors observe independent sequences of samples and in the meantime, exchange their local information in the form of quantized statistics at every sampling interval. The communication links are represented as an undirected graph. In this distributed setup, every sensor performs its own sequential test based on the local samples and the messages from the neighbour sensors. Our goal is to devise the distributed sequential test that comprises the quantization scheme, the message-exchange protocol and the test procedure such that every sensor in the network fully exploits the network diversity and achieves the (asymptotically) optimal performance in terms of the stopping time. In particular, two distributed sequential tests are proposed based on different quantization schemes and a quantized message-exchange protocol that satisfies certain conditions. The first quantization scheme uniformly quantizes the local statistic at each sensor and at every sampling interval; the second one hinges on a modified level-triggered quantization technique, and resembles the Lebesgue sampling of the running local statistic. Our analyses show that the uniform quantization based distributed sequential test yields sub-optimal performance, while the one based on level-triggered quantization achieves the order-2 asymptotically optimal performance at every sensor for any fixed quantization step-size. Furthermore, we generalize the proposed sequential tests to the cluster-based network. Numerical results are provided to corroborate our analyses and demonstrate the effectiveness of the proposed sequential tests.

This paper investigates the sequential hypothesis testing problem with online sensor selection and sensor usage constraints. That is, in a sensor network, the fusion center sequentially acquires samples by selecting one “most informative” sensor at each time until a reliable decision can be made. In particular, the sensor selection is carried out in the online fashion since it depends on all the previous samples at each time. Our goal is to develop the sequential test (i.e., stopping rule and decision function) and sensor selection strategy that minimize the expected sample size subject to the constraints on the error probabilities and sensor usages. To this end, we first recast the usage-constrained formulation into a Bayesian optimal stopping problem with different sampling costs for the usage-contrained sensors. The Bayesian problem is then studied under both finite- and infinite-horizon setups, based on which, the optimal solution to the original usage-constrained problem can be readily established. Moreover, by capitalizing on the structures of the optimal solution, a lower bound is obtained for the optimal expected sample size. In addition, we also propose algorithms to approximately evaluate the parameters in the optimal sequential test so that the sensor usage and error probability constraints are satisfied. Finally, numerical experiments are provided to illustrate the theoretical findings, and compare with the existing methods.

This paper analyzes the asymptotic performances of fully distributed sequential hypothesis testing procedures as the type-I and type-II error rates approach zero, in the context of a sensor network without a fusion center. In particular, the sensor network is defined by an undirected graph, where each sensor can observe samples over time, access the information from the adjacent sensors, and perform the sequential test based on its own decision statistic. Different from most literature, the sampling process and the information exchange process in our framework take place simultaneously (or, at least in comparable time-scales), thus cannot be decoupled from one another. Our goal is to achieve second-order asymptotically optimal performance at every sensor, i.e., the average detection delay is within a constant gap from the centralized optimal sequential test as the error rates approach zero for the fixed number of sensors. To that end, a type of test procedure that resembles the well-known sequential probability ratio test (SPRT), termed as distributed SPRT (DSPRT) in this paper, is studied based on two message-passing schemes, respectively. The first scheme features the dissemination of the raw samples. In specific, every sample propagates over the network by being relayed from one sensor to another until it reaches all the sensors in the network. Although the sample propagation-based DSPRT is shown to yield the asymptotically optimal performance at each sensor, it incurs excessive intersensor communication overhead due to the exchange of raw samples with index information. The second scheme adopts the consensus algorithm, where the local decision statistic is exchanged between sensors instead of the raw samples, thus significantly lowering the communication requirement compared with the first scheme. In particular, the decision statistic for DSPRT at each sensor is updated by the weighted average of the decision statistics in the neighborhood at every message-passing step. We show that, under certain regularity conditions, the consensus algorithm-based DSPRT also yields the secondorder asymptotically optimal performance at all sensors given a fixed number of sensors. Our asymptotic analyses of the two message-passing-based DSPRTs are then corroborated by simulations using the Gaussian and Laplacian samples.

This work considers the sequential hypothesis testing problem in the fully distributed sensor network. In specific, each sensor can observe samples over time, exchange information with adjacent sensors, and perform testing based on its own locally available decision statistic. Under such setting, we study the sequential probability ratio test based on the statistic that is obtained by running consensus algorithm. It is shown that, under certain regularity conditions on the data distribution and network topology, this distributed sequential test procedure yields the order-2 asymptotically optimal performance at all sensors.

This paper considers the sequential composite hypothesis test with multiple sensors. The sensors observe random samples in parallel and communicate with a fusion center, who makes the global decision based on the sensor inputs. On the one hand, in the centralized scenario, where local samples are precisely transmitted to the fusion center, the generalized sequential likelihood ratio test (GSPRT) is shown to be asymptotically optimal in terms of the expected sample size as error rates tend to zero. On the other hand, for systems with limited power and bandwidth resources, decentralized solutions that only send a summary of local samples (we particularly focus on a one-bit communication protocol) to the fusion center is of great importance. To this end, we first consider a decentralized scheme where sensors send their one-bit quantized statistics every fixed period of time to the fusion center. We show that such a uniform sampling and quantization scheme is strictly suboptimal and its suboptimality can be quantified by the KL divergence of the distributions of the quantized statistics under both the hypotheses. We then propose a decentralized GSPRT based on level-triggered sampling. That is, each sensor runs its own GSPRT repeatedly and reports its local decision to the fusion center asynchronously. We show that this scheme is asymptotically optimal as the local thresholds and global thresholds grow large at different rates. Finally, two particular models and their associated applications are studied to compare the centralized and decentralized approaches. Numerical results are provided to demonstrate that the proposed level-triggered sampling based decentralized scheme aligns closely with the centralized scheme with substantially lower communication overhead, and significantly outperforms the uniform sampling and quantization-based decentralized scheme.

This work considers the online sensor selection for the finite-horizon sequential hypothesis testing. In particular, at each step of the sequential test, the “most informative” sensor is selected based on all the previous samples so that the expected sample size is minimized. In addition, certain sensors cannot be used more than their prescribed budgets on average. Under this setup, we show that the optimal sensor selection strategy is a time-variant function of the running hypothesis posterior, and the optimal test takes the form of a truncated sequential probability ratio test. Both of these operations can be obtained through a simplified version of dynamic programming. Numerical results demonstrate that the proposed online approach outperforms the existing offline approach to the order of magnitude.

This paper considers the real-time voltage quality monitoring in smart grid systems. The goal is to detect the occurrence of disturbances in the nominal sinusoidal voltage signal as quickly as possible such that protection measures can be taken in time. Based on an autoregressive model for the disturbance, we propose a generalized local likelihood ratio detector, which processes meter readings sequentially and alarms as soon as the test statistic exceeds a prescribed threshold. The proposed detector not only reacts to a wide range of disturbances, but also achieves lower detection delay compared with the conventional block processing method. Then, we further propose to deploy multiple meters to monitor the voltage signal cooperatively. The distributed meters communicate wirelessly to a central meter, where the data fusion and detection are performed. In light of the limited bandwidth of wireless channels, we develop a level-triggered sampling scheme, where each meter transmits only one-bit each time asynchronously. The proposed multi-meter scheme features substantially low communication overhead, while its performance is close to that of the ideal case where distributed meter readings are perfectly available at the central meter.