Sequential Detection under Correlated Observations using Recursive Method

In this paper, we propose a sequential type-based detection scheme for wireless sensor networks in the case of spatially and temporally identically and independently distributed observations. First, we investigate the optimal sequential detection rule of the proposed scheme, and then with the motivation of reducing the computational complexity of the optimal detection rule, we consider an approximation scheme and derive a suboptimal detection rule. We also compare the performances of the type-based sequential detection scheme with those of the non-sequential type-based detection scheme in terms of both average number of observations and total energy consumption, and determine the region of individual node power where the proposed scheme outperforms the non-sequential scheme. In addition, we show that the approximated detection rule provides the similar results as the optimal detection rule with a significant reduction of the computational complexity, which makes the approximated detection rule useful for real-time applications.

A modified soft combination scheme for cooperative sequential detection to achieve reduced average number of samples in cooperative sensing that is proposed here, in a fast-fading scenario. This is done to sense primary user in fast-fading environment where the samples are independent and nonidentically distributed samples (i.n.i.d.), with decreased number of samples. Log-likelihood ratio is also studied in fast-fading environment; variance of received signal and variance of noise signal are considered as random variables. First, we studied the generalized log-likelihood ratio (GLLR) considering i.n.i.d. samples caused due to fast-fading. Then, a modified rule for soft combination of test statistics for performing the cooperative sequential detection, to achieve even less number of samples, is proposed, assuming received signal variance and noise signal variances’ probability density functions are unknown. Lastly, it is shown by simulation that the proposed cooperative sequential detection with modified soft combination rule performed better in this fast-fading environment by reducing average number of samples (ANS).

Abnormal event detection with the lowest latency is an indispensable function for safety-critical systems, such as cyber defense systems. However, as systems become increasingly complicated, conventional sequential event detection methods become less effective, especially when we need to define indicator metrics from complicated data manually. Although deep neural networks (DNNs) have been used to handle heterogeneous data, the theoretic assurability and explainability are still insufficient. This article provides a holistic framework for the quickest and sequential detection of abnormalities and time-dependent abnormal events. We explore the latent space characteristics of zero-bias neural networks considering the classification boundaries and abnormalities. We then provide a novel method to convert zero-bias DNN classifiers into performance-assured binary abnormality detectors. Finally, we provide a sequential quickest detection (QD) scheme that provides the theoretically assured lowest abnormal event detection delay under false alarm constraints using the converted abnormality detector. We verify the effectiveness of the framework using real massive signal records in aviation communication systems and simulation. Codes and data are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/pcwhy/AbnormalityDetectionInZbDNN</uri> .

It is supposed that there is a multisensor system in which each sensor performs sequential detection of a target. Then the binary decisions on target presence and absence are transmitted to a fusion center, which combines them to improve the performance of the system. We assume that sensors represent multichannel systems with possibly each one having different number of channels. Sequential detection of a target in each sensor is done by implementing a generalized Wald's sequential probability ratio test which is based on the maximum likelihood ratio statistic and allows one to fix the false alarm rate and the mis-detection rate at specified levels. We first show that this sequential detection procedure is asymptotically optimal for general statistical models in the sense of minimizing the expected sample size when the probabilities of errors vanish. We then construct the optimal non-sequential fusion rule that waits until all the local decisions in all sensors are made and then fuses them. It is optimal in the sense of maximizing the probability of target detection for a fixed probability of a false alarm or minimizing the maximal probability of error (minimax criterion). An analysis shows that the final decision can be made substantially more reliable even for a small number of sensors (3-5). The performance of the system is illustrated by the example of detecting a deterministic signal in correlated (color) Gaussian noise. In this example, we provide both the results of theoretical analysis and the results of Monte Carlo experiment. These results allow us to conclude that the use of the sequential detection algorithm substantially reduces the required resources of the system compared to the best non-sequential algorithm.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A cognitive radio should be capable of finding the best spectrum band for communication depending on primary transmissions, the ambient noise level and interference. The first step in achieving this goal is to sense the existence of primary and secondary transmitters in various channels. In addition to the problem of signal detection, there is a need to distinguish between different signals at very low SNR. In this paper, the spectral correlation function is used for hypothesis testing. The sufficient statistic for feature vector based detection in the presence of timing uncertainty is derived. Sequential detection is used to decrease the average number of samples required for testing. Theoretical expressions for the stopping time at low SNR are derived for the AWGN channel. In a fading environment, the performance is evaluated using an approximate expression for the distribution of spectral correlation function. Monte-Carlo simulations verify the accuracy of the theoretical expressions.

To improve the efficiency of bandwidth usage, the cognitive radios concept has emerged. Spectrum sensing is a pivotal function in cognitive radio systems so that the secondary users can be able to access the free spectrum holes without interfering with primary users. Energy detection is the most common and easiest spectrum sensing technique for cognitive radios. In this paper, the conventional energy detection receiver operating characteristic curve and performance metrics are simulated under additive white Gaussian noise (AWGN) environment by using Monte Carlo simulation. Also, the performance of energy detection is analyzed under different types of M-ary modulation. The analysis of performance will carry the assumption of noise uncertainty. This performance gain is compared with conventional energy detection without any noise effect. In addition, the relation between a number of samples and signal to noise ratio wall (SNR wall) is provided and simulated. The simulation tool used in the analysis is MATLAB software. Finally, the implementation of energy detection technique in the time domain and frequency domain is designed on Xilinx Spartan-3E (XC3S500E-FG320) Field Programmable Gate Array (FPGA) kit by using Verilog language and Xilinx ISE Simulator version 14.1.

Sequential sampling plans based on the negative binomial distribution were developed for egg mass density of spruce budworm, Choristoneura fumiferana (Clemens), in Michigan's Upper Peninsula. Plans developed were modifications of Wald's sequential probability ratio test (SPRT) based on Monte Carlo simulation. Parameters of the negative binomial distribution were estimated by the maximum likelihood method. Sampling models developed classify egg mass populations into low and high categories using the number of egg masses on whole branch samples of balsam fir, Abies balsamifera (L.) Voss. Plans are presented for three pairs of population density hypotheses to give forest pest managers the flexibility to select a plan that best meets management objectives. Monte Carlo estimates indicated that Wald's average sample number (ASN) and operating characteristic (OC) equations underestimated the actual ASN values, and the actual alpha and beta error probabilities were smaller than the values prescribed by Wald's equations. Errors were sufficiently large to have serious economic implications during implementation of plans developed from Wald's approximate procedure. The sequential plans developed by modifying the decision boundaries of Wald's SPRT using the Monte Carlo procedure had error probabilities, OC functions, and ASN values that were approximately equal to those desired.

Because communications systems are seldom significantly interfered with by classical white Gaussian noise, it is necessary to consider other, appropriate (and tractable) interference models, if realistic estimates of system performance are to be obtained for the general spectral-use environment. For this purpose, Middleton's recently developed canonical statistical-physical model of "impulsive" interference is applied to real-world communication channels. The principal features of this model are first summarized, including the statistical relations required for the solution of signal detection problems. [Excellent agreement of these model statistics with correspondingly measured statistics is also noted.] The model for narrow-band impulsive interference (Class A noise, a subset of the overall model) is next specifically applied to an important class of coherent signal detection problems. Algorithms for error probabilities in optimum detection are then obtained, along with performance bounds, for the same error probabilities. Since it is known that in order to gain significant improvement over current receivers, the number of (essentially) independent samples of the received interference waveform must be enlarged (i.e., large "processing gains"), the performance results here are given parametrically in the number of samples, or equivalently, in the time-bandwidth product. Performance of current suboptimum receivers is then obtained and compared to the optimum performance. It is shown that very substantial savings in signal power and/or spectrum space can usually be achieved by using the indicated optimal algorithms. Since physical realization of the completely optimum detection algorithms cannot, in general, be economically realized, the somewhat more conservative, corresponding locally optimum Bayes detection (LOBD) receivers are derived. In general, these LOBD structures require adaptive, highly non-linear filters, preceding the conventional correlation detector elements characteristic of optimum receivers for Gaussian interference. Performance for these non-linear, optimum threshold systems is then determined, specifically in Part I for coherent reception.

The problem of sequential detection of spontaneous changes in equations for unobserved state variables and observations of linear and nonlinear multivariate state-space models is considered. We consider the case of new additive terms and the case of changing coefficients of these equations. The proposed nonparametric method uses the idea of the “moving window” of observations. In Theorem 4.1 the exponential rate of convergence to zero for type 1 error probability (a wrong decision about a change) is proved. In Theorem 4.2 we consider type 2 error probability and the normalized (by the volume N of the moving window) delay time in change-point detection. Asymptotic optimality of the proposed method is proved in Theorem 5.1. Experimental study includes Monte Carlo examples of sequentially detected changes in coefficients of linear and nonlinear state-space models.

Monte Carlo operating characteristic (OC) and average sample number (ASN) functions were compared with Wald's OC and ASN equations for sequential sampling plans based on Wald's sequential probability ratio test (SPRT) using the binomial, negative binomial, normal, and Poisson distributions. This comparison showed that the errors inherent in Wald's equations as a result of "overshooting" the decision boundaries of the SPRT can be large. Relative errors increased for the OC and ASN equations as the difference between the null (θ0)) and alternative (θ1) test parameter values increased. Relative errors also increased for the ASN equation as the probabilities of type I (α) and type II (β) errors increased. For discrete distributions, the relative errors also increased as θ0 increased with θ1/θ0 fixed. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN. For the values of θ0, θ1, α, and β used in many sequential sampling plans in forestry, Wald's equations may not be adequate. For those cases where the errors in Wald's equations are important compared with the other errors associated with the sampling plan, two alternative Monte Carlo OC and ASN functions are proposed.

Spectrum sensing is a key technical challenge for cognitive radio (CR). It is well known that multi-cycle cyclostationarity (MC) detector is a powerful method for spectrum sensing. However, conventional MC detector is difficult to implement due to its high computational complexity. This paper pays attention to the fact that the computation complexity can be reduced by simplifying the test statistic of conventional MC detector. Based on this simplification process, an improved MC detector is proposed. Compared with the conventional one, the proposed detector has the low-computational complexity and high-accuracy on sensing performance. Subsequently, the sensing performances are further investigated for the cases of Rayleigh, Nakagami-m, Rician and composite Rayleigh fading-shadowing channels. Furthermore, the square-law combining (SLC) is introduced to improve the detection capability in fading and shadowing environments. The corresponding closed-form expressions of average detection probability are derived for each case by the moment generation function (MGF) approach. Finally, illustrative and analytical results show that the efficiency and reliability of proposed detector and the improvement on sensing performance by SLC in fading and shadowing environments.

The problem of joint sequential change detection and isolation in a multichannel system is considered. It is assumed that a disruption occurs at some unknown time, and changes the distributions of the observations in an unknown subset of channels. The problem is to quickly detect the change, and at the same time to reliably isolate the affected channels. A novel scheme is proposed for this task, which admits a recursive structure, is scalable with respect to the number of channels, and does not require any prior information about the change-point. Its performance is analyzed in the special case that the number of affected channels is known. Specifically, explicit critical values are obtained for the control of the false alarm rate and the conditional probability of wrong isolation below arbitrary levels to be prescribed by the practitioner. Finally, the asymptotic optimality of the average detection delay of the proposed scheme is established as the error probabilities go to 0 and the effect of the prior distribution for the change point vanishes in the limit.

The performance of a cognitive radio system depends on how well it can maximize the usage of a free frequency band without causing any interference to the primary user. Thus the abilities to detect a primary user as well as to avoid any false alarm are of paramount importance for such a system. For energy detector based spectrum sensing in cognitive radios, these abilities are influenced by the threshold set to distinguish signal from noise. Conventional energy detectors are based on a fixed threshold. This may not be optimum in low SNR conditions where the performance of fixed threshold based detector can vary from the targeted performance metrics substantially. In this paper, we propose a method to change the threshold based on the number of samples, to optimize the detection parameters, namely probability of detection and probability of false alarm. We also introduce a control parameter which is used to vary the set threshold and thereby obtain a response more suited to the operational requirements than that obtained by a fixed threshold based energy detector. Simulation results are presented to show a different perspective of the importance of the sensing time to the performance metrics of the energy detector.

Of the acoustical source localization algorithms that have been proposedin the literature, mostcan be dividedinto two separate groups. While some algorithmsare robust, they are computationally complex. Conversely, the fast algorithms cannot localize robustly in real world scenarios. Recently several new algorithms have been proposed that are robust and fairly fast, including Hierarchical Localization and Hybrid Localization. A method for optimal placement of candidate locations will be presented, which reduces computational complexity of Hierarchical Localization. The performance of Hierarchical Localization and Hybrid Localization will be compared in both simulated and real scenarios. It will be shown that Hybrid Localization is more robust than Hierarchical Localization and also computationally faster.

Early detection and estimation of the spread of a biochemical contaminant are major issues for homeland security applications. We present an integrated approach combining the measurements given by an array of biochemical sensors with a physical model of the dispersion and statistical analysis to solve these problems and provide system performance measures. We approximate the dispersion model of the contaminant in a realistic environment through numerical simulations of reflected stochastic diffusions describing the microscopic transport phenomena due to wind and chemical diffusion using the Feynman-Kac formula. We consider arbitrary complex geometries and account for wind turbulence. Localizing the dispersive sources is useful for decontamination purposes and estimation of the cloud evolution. To solve the associated inverse problem, we propose a Bayesian framework based on a random field that is particularly powerful for localizing multiple sources with small amounts of measurements. We also develop a sequential detector using the numerical transport model we propose. Sequential detection allows on-line analysis and detecting wether a change has occurred. We first focus on the formulation of a suitable sequential detector that overcomes the presence of unknown parameters (e.g. release time, intensity and location). We compute a bound on the expected delay before false detection in order to decide the threshold of the test. For a fixed false-alarm rate, we obtain the detection probability of a substance release as a function of its location and initial concentration. Numerical examples are presented for two real-world scenarios: an urban area and an indoor ventilation duct.