In this paper, the consensus problems of the continuous-time integrator systems under noisy measurements are considered. The measurement noises, which appear when agents measure their neighbors' states, are modeled to be multiplicative. By multiplication of the noises, here, the noise intensities are proportional to the absolute value of the relative states of agent and its neighbor. By using known distributed protocols for integrator agent systems, the closed-loop system is described in the vector form by a singular stochastic differential equation. For the fixed and switching network topologies cases, constant consensus gains are properly selected, such that mean square consensus and strong consensus can be achieved. Especially, exponential mean square convergence of agents' states to the common value is derived for the fixed topology case. In addition, asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied. Simulations shed light on the effectiveness of the proposed theoretical results.In reality, communication processes are always corrupted by various uncertain factors, such as random link failures, transmission noises and quantization errors. These are outcomes of the use of sensors, quantization and wireless fading channels in the network. Recently, the consensus problems that concern corrupted communication processes between agents have attracted many researchers. In [9], the authors model the measurement noises to be additive, which means that the noises additively input the communication processes. To attenuate this type of measurement noises, a decreasing consensus gain is designed to reduce the detrimental effect of the noises. For fixed network topology, mean square consensus and strong consensus results are presented. Furthermore, in [10], the authors deal with randomly varying topology, while [11] considers the Markovian and arbitrary switching topologies. In [15], the authors consider continuous time first-order integrator model with Gaussian additive standard white noise. To be exact, in [15], firstly, for noise-free cases, necessary and sufficient conditions are given on the network topology and consensus gains to achieve average-consensus; secondly, for the cases with measurement noises, necessary and sufficient conditions are given on the consensus gains to achieve asymptotic unbiased mean square average-consensus. In addition, [16] considers the time-varying topology case, while [19] deals with the leader-follower consensus control problem. It is worth noting that most existing literatures are for additive measurement noises.In this paper, we model the measurement noises to be multiplicative, which may be viewed as the complement to those considered in [9,15,19]. Our modelling comes from a simple intuition. To be exact, as the states of agents (say, for example, mobile vehicles) may be viewed as the positions, intuitively, the closer the vehicles are to each other, the smaller the intensities of measurement noises should be related t...
Rapid urbanization and economic development inevitably lead to light pollution, which has become a universal environmental issue. In order to reveal the spatiotemporal patterns and evolvement rules of light pollution in China, images from 1992 to 2012 were selected from the Defense Meteorological Satellite Program Operational Linescan System (DMSP/OLS) and systematically corrected to ensure consistency. Furthermore, we employed a linear regression trend method and nighttime light index method to demonstrate China's light pollution characteristics across national, regional, and provincial scales, respectively. We found that: (1) China's light pollution expanded significantly in provincial capital cities over the past 21 years and hot-spots of light pollution were located in the eastern coastal region. The Yangtze River Delta, Pearl River Delta, and Beijing-Tianjin-Hebei regions have formed light pollution stretch areas; (2) China's light pollution was mainly focused in areas of north China (NC) and east China (EC), which, together, accounted for over 50% of the light pollution for the whole country. The fastest growth of light pollution was observed in northwest China (NWC), followed by southwest China (SWC). The growth rates of east China (EC), central China (CC), and northeast China (NEC) were stable, while those of north China (NC) and south China (SC) declined; (3) Light pollution at the provincial scale was mainly located in the Shandong, Guangdong, and Hebei provinces, whereas the fastest growth of light pollution was in Tibet and Hainan. However, light pollution levels in the developed provinces (Hong Kong, Macao, Shanghai, and Tianjin) were higher than those of the undeveloped provinces. Similarly, the light pollution heterogeneities of Taiwan, Beijing, and Shanghai were higher than those of undeveloped western provinces.
Surface water bodies, such as rivers, lakes, and reservoirs, play an irreplaceable role in global ecosystems and climate systems. Sentinel-2 imagery provides new high-resolution satellite remote sensing data. Based on the analysis of the spectral characteristics of the Sentinel-2 satellite, a novel water index called the Sentinel-2 water index (SWI) that is based on the vegetation-sensitive red-edge band (Band 5) and shortwave infrared (Band 11) bands was developed. Four representative water body types, namely, Taihu Lake, Yangtze River, Chaka Salt Lake, and Chain Lake, were selected as study areas to conduct a water body extraction performance comparison with the normalized difference water index (NDWI). We found that (1) the contrast value of the SWI was larger than that of the NDWI in terms of various water body types, including purer water, turbid water, salt water, and floating ice, which suggested that the SWI could achieve better enhancement performance for water bodies. An (2) effective water body extraction method was proposed by integrating the SWI and Otsu algorithm, which could accurately extract various water body types with high overall accuracy. The (3) method effectively extracted large water bodies and wide river channels by suppressing shadow noise in urban areas. Our results suggested that the novel method can achieve efficient water body extraction for rapidly and accurately extracting various water bodies from Sentinel-2 data and the novel method has application potential for larger-scale surface water mapping.
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