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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. [ABSTRACT FROM AUTHOR]

Geometric-optical (GO) model suitable for forest plantation (GOFP) is a GO model for forest plantations at the stand level developed in this study based on a four-scale GO model a Geometric-Optical Model for Sloping Terrains-II (GOST2), which simulates the bidirectional reflectance distribution function (BRDF) for natural forest canopies. In most previous GO models, tree distributions are often assumed to meet the Poisson or Neyman model in a forest; therefore, these models are suitable for simulating BRDF for natural forest canopies. However, in forest plantations, tree distributions are proven to meet the hypergeometric model rather than the Poisson or Neyman model at the stand level. GOFP, in which the tree distributions are described using the hypergeometric model, is proposed to simulate the bidirectional reflectance factor (BRF) of forest plantations at the stand level. The area ratios of the four scene components (sunlit foliage, sunlit ground, shaded foliage, and shaded ground) of GOFP compare well with those simulated by a 3-D canopy visualization technique. A comparison is also made against discrete anisotropic radiative transfer, showing that GOFP has the ability to simulate BRF of forest plantations. Another comparison is made against operational land imager and Moderate Resolution Imaging Spectroradiometer surface reflectance, showing that GOFP with the hypergeometric model outperforms GOST2 with the Poisson and Neyman models. The results further show that the differences in BRFs between GOFP and GOST2 pronouncedly increase with the difference between the reflectance of sunlit foliage ( RT ) and the reflectance of sunlit ground ( RG ), as well as the distances among trees and the number of crowns in a forest plantation, suggesting that GOFP significantly outperforms GOST2 for simulating BRF of forest plantations. [ABSTRACT FROM PUBLISHER]

Spectrum sensing is a key technology enabling the cognitive radio system. In this paper, the problem of how to quickly and accurately find an unoccupied channel from a large amount of potential channels is considered. The cognitive radio system under consideration is equipped with a narrow band sensor, hence it can only sense those potential channels in a sequential manner. In this scenario, we propose a novel two-stage mixed-observation sensing strategy. In the first stage, which is named as scanning stage, the sensor observes a linear combination of the signals from a pair of channels. The purpose of the scanning stage is to quickly identify a pair of channels such that at least one of them is highly likely to be unoccupied. In the second stage, which is called refinement stage, the sensor only observers the signal from one of those two channels identified from the first stage, and selects one of them as the unoccupied channel. The problem under this setup is an ordered two concatenated Markov stopping time problem. The optimal solution is solved using the tools from the multiple stopping time theory. It turns out that the optimal solution has a rather complex structure, hence a low complexity algorithm is proposed to facilitate the implementation. In the proposed low complexity algorithm, the cumulative sum test is adopted in the scanning stage and the sequential probability ratio test is adopted in the refinement stage. The performance of this low complexity algorithm is analyzed when the presence of unoccupied channels is rare. Numerical simulation results show that the proposed sensing strategy can significantly reduce the sensing time when the majority of potential channels are occupied. [ABSTRACT FROM PUBLISHER]

We consider linear regression problems for which the underlying model undergoes multiple changes. Our goal is to estimate the number and locations of change-points that segment available data into different regions, and further produce sparse and interpretable models for each region. To address challenges of the existing approaches and to produce interpretable models, we propose a sparse group Lasso based approach for linear regression problems with change-points. Under certain mild assumptions and a properly chosen regularization term, we prove that the solution of the proposed approach is asymptotically consistent. In particular, we show that the estimation error of linear coefficients diminishes, and the locations of the estimated change-points are close to those of true change-points. We further propose a method to choose the regularization term so that the results mentioned above hold. In addition, we show that the complexity of the proposed algorithm is much smaller than those of existing approaches. Numerical examples are provided to validate the analytical results. [ABSTRACT FROM PUBLISHER]

In this paper, Bayesian quickest change detection problems with sampling right constraints are considered. In particular, there is a sequence of random variables whose probability density function will change at an unknown time. The goal is to detect this change in a way such that a linear combination of the average detection delay and the false alarm probability is minimized. Two types of sampling right constrains are discussed. The first one is a limited sampling right constraint, in which the observer can take at most \(N\) observations from this random sequence. Under this setup, we show that the cost function can be written as a set of iterative functions, which can be solved by Markov optimal stopping theory. The optimal stopping rule is shown to be a threshold rule. An asymptotic upper bound of the average detection delay is developed as the false alarm probability goes to zero. This upper bound indicates that the performance of the limited sampling right problem is close to that of the classic Bayesian quickest detection for several scenarios of practical interest. The second constraint discussed in this paper is a stochastic sampling right constraint, in which sampling rights are consumed by taking observations and are replenished randomly. The observer cannot take observations if there are no sampling rights left. We characterize the optimal solution, which has a very complex structure. For practical applications, we propose a low complexity algorithm, in which the sampling rule is to take observations as long as the observer has sampling rights left and the detection scheme is a threshold rule. We show that this low complexity scheme is first order asymptotically optimal as the false alarm probability goes to zero. [ABSTRACT FROM AUTHOR]

Electromagnetic wave radiation from a SLF/ELF underground horizontal electric dipole (HED) related to seismic activity is discussed. In order to estimate the effects on the electromagnetic waves associated with the seismic activity, SLF/ELF waves radiated from a possible seismic current source modeled as a electric dipole, are precisely computed by using a speeding numerical convergence algorithm. In 1999, Barrick proposed an algorithm, which was only suitable to solve the electromagnetic problems under the ideal electric conductor condition. To solve the problems under the non-ideal electric conductor condition, we have further developed Barrick's method and proposed a speeding numerical convergence algorithm. The variations of the electromagnetic field along the propagation distance and the altitude, as well as the frequency during day and night are analyzed and calculated. It takes 0.5 minute to calculate the sum of the series by my algorithm, while it needs 15 minutes by calculating directly the sum of the series. Our algorithm is compared with the calculation directly the sum of the series algorithm, and two algorithms agree with each other very well. Therefore, our algorithm is correct. Schumann resonance is also verified. [ABSTRACT FROM AUTHOR]

This paper presents a new design of wide slot antenna for various wideband applications. The proposed printed antenna consists of a slot and a turning stub, both formed by a binomial curve function; thus, various bandwidths (BWs) can be obtained based on the structure with different binomial curves. Some key parameters affecting the antenna performance have been analyzed and discussed in detail as an antenna design guideline. To validate the theoretical design, six prototypes of various binomial-curved slot antennas were designed, fabricated, and measured. Good agreement between the simulated results and the measured ones is observed. The results demonstrate that the proposed type of antenna can obtain a BW range from 9.8% to 99.7% for VSWR \leq 2 by selecting various binomial-curved slots, which may provide a convenience for various wideband antenna designs. Moreover, the proposed type of antenna owns a simple structure and a stable gain of about 3–5.5 dBi, which is very suitable for wideband wireless system applications. [ABSTRACT FROM AUTHOR]