Sensors In Network Research Articles

Split ring resonator inspired defected ground plane dual operating band antenna for wireless LAN and RFID applications

Defected ground structure (DGS) using an array of the three split ring resonators inspired antenna for the Wireless Local Area Network(WLAN) and RFID sensor is proposed in this manuscript. The complete physical measurement for the proposed antenna is 50 X 40 mm2 (at lower operating frequency). The defected ground plane structure along with the inclusion of the square split ring resonators (SRRs) in the ground plane helps in gain and bandwidth improvement. 1 × 3 split ring resonator array is used to make the existing ground plane to be defected. The cost effective FR – 4 materials is used as a substrate for the fabrication with the standard thickness of 1.6 mm. The resonance frequencies are at 2.4 and 5.8 GHz having the average gain 2.65dBi. The impedance bandwidths for both the frequencies are 5.0 % (2.31 to 2.49 GHz) and 3.9% (4.9 to 6.1 GHz). The dipole and omni directional radiation patterns, overall gain and efficiency of around 75% make the antenna most practically possible for the RFID and WLAN devices.

Consensus-based secure and efficient compressive sensing in a wireless network sensors environment

Compressive sensing provides the optimal paradigm for data aggregation approach in wireless sensor networks as it holds the characteristics of low traffic cost and avoids the large communication overhead through a traditional approach. However, security is still considered one of the important, in recent years consensus-based approach has been one of the security highlights in compressive sensing. Moreover, a consensus is developed only with the help of genuine nodes. In this research work, a novel integrated-consensus-based secure compressive sensing (CSCS) is proposed which aims to develop a secure consensus environment to secure the network. Integrated-CSCS comprises several modules; at first certain variables are assigned to each node participating in the network. Later an algorithm is developed where each node evaluates the assigned neighbor variable and updates its states. Moreover, this phenomenon leads to the identification of genuine and compromised nodes. The proposed model is evaluated by considering the efficiency and security parameters; efficiency evaluation is carried out through energy consumption, and several node failures where as security is evaluated by considering the ability to identify the genuine node and malicious or corrupt node.

Optimizing Relay Sensors in Large-Scale Wireless Sensor Networks: A Biologically Inspired Approach

In recent years, tremendous advances in communication technologies coupled with the advent of the Internet of Things (IoT) have led to the emergence of the Big Data phenomenon. Big Data is one of the big IT challenges of the current decade. The amount of data produced is constantly increasing and makes it more and more difficult to process. Managing these masses of data requires the use of new data management systems with efficient access methods. Considered as one of the main sources of Big Data, wireless sensors used in networks offer a credible solution to the problem of Big Data management, especially its collection. Several solutions for Big Data collection based on large-scale wireless sensor networks (LS-WSN) are proposed, taking into account the nature of the applications. The hierarchical architecture is the one used for the deployment of these applications. In such an architecture, relay sensors play an important role in finding the balance of the network and maximizing its lifetime. In most LS-WSN applications, once deployed, the LS-WSN does not provide a mechanism to evaluate and improve the positions of the initially deployed relay sensors. This paper proposes, based on the growth model of physarum polycephalum and its ability to prune unnecessary links and retain only those deemed useful for food routing, a mechanism for evaluating and optimizing relay sensors in LS-WSNs. Simulation results indicate that the proposed approach significantly improves the network lifetime compared to the initial deployment and that can be a useful approach for LS-WSNs dedicated to Big Data collection. The effectiveness of the proposed technique is demonstrated by experimental results in terms of connectivity and network lifetime.

Hybrid K-Medoids with Energy-Efficient Sunflower Optimization Algorithm for Wireless Sensor Networks

Wireless sensor network (WSN) sensor nodes should have adequate energy. Reduced energy usage is essential to maximize the endurance of WSNs. Combining WSN with a more significant energy source, a cluster head (CH), is another effective strategy for extending WSN durability. A CH is dependent on the communication inside and between clusters. A CH’s energy level extends the cluster’s life for the complete WSN. Determining the energy required in WSNs while developing clustering algorithms is challenging. For maintaining energy efficiency in WSNs, this research offers K-medoids with sunflower-based clustering and a cross-layer-based optimal routing approach. An efficient fitness function generated from diverse objectives is used to choose the CH. After CH selection, sunflower optimization (SFO) indicates the best data transmission line to the sink node. The proposed protocol, SFO-CORP, increased the network lifetime by 19.6%, 13.63%, 11.13%, and 4.163% compared to the LEACH, EECRP, FEEC-IIR, and CL-IoT protocols, respectively. The experimental results showed that it performed better for packet delivery ratio, energy consumption, end-to-end delay, network lifetime, and computation efficiency.

Improving Performance Parameters of Clusters Using Density-Based Algorithm

With the advancement in technology, data generated by non-stationary in day-to-day life is massive, continuous and rapid. Many applications such as IoT, transaction systems, network sensors, video surveillance systems, and network intrusion detection systems generate a massive amount of real-time data. The data used in traditional data mining is static in nature, and it can be revised for processing and Analysis. While data in data stream mining is dynamic in nature and it never stops. Besides, the data generated may have a change imbibed in its characteristics over a long/short period of time which is called concept drift. So, analysing such data has huge inbuilt challenges that deal with the dynamism of the characteristics of data itself. This dynamic nature is because of fast and continuous changing data and its enormity. To overcome this limitation, we can use modified clustering techniques that could help us in proper data analysis. Clustering is an effective method used in data mining; but clustering data streams may add some additional challenges such as storage capacity, limited time, one pass and rate of arrival. Furthermore, data streams are fickle in nature and because of this behaviour it needs to be processed as and when it arrives. In addition to that, knowledge about the number of clusters like in K-means clustering is unknown. In view of these characteristics of the data stream, the information or the data generated in the data stream are non-deterministic. Such non-deterministic information contains noise points or outliers, so developing an effective clustering algorithm in a data stream is a crucial task. These methods can work with labelled data in data stream clustering, which has the potential to identify clusters of any shape and noise. The motivation for this research work is using the said algorithm to address and overcome the constraints of the data stream and to dig out the best knowledge from it.

Indoor Occupancy Sensing via Networked Nodes (2012–2022): A Review

In the past decade, different sensing mechanisms and algorithms have been developed to detect or estimate indoor occupancy. One of the most recent advancements is using networked sensor nodes to create a more comprehensive occupancy detection system where multiple sensors can identify human presence within more expansive areas while delivering enhanced accuracy compared to a system that relies on stand-alone sensor nodes. The present work reviews the studies from 2012 to 2022 that use networked sensor nodes to detect indoor occupancy, focusing on PIR-based sensors. Methods are compared based on pivotal ADPs that play a significant role in selecting an occupancy detection system for applications such as Health and Safety or occupant comfort. These parameters include accuracy, information requirement, maximum sensor failure and minimum observation rate, and feasible detection area. We briefly describe the overview of occupancy detection criteria used by each study and introduce a metric called “sensor node deployment density” through our analysis. This metric captures the strength of network-level data filtering and fusion algorithms found in the literature. It is hinged on the fact that a robust occupancy estimation algorithm requires a minimal number of nodes to estimate occupancy. This review only focuses on the occupancy estimation models for networked sensor nodes. It thus provides a standardized insight into networked nodes’ occupancy sensing pipelines, which employ data fusion strategies, network-level machine learning algorithms, and occupancy estimation algorithms. This review thus helps determine the suitability of the reviewed methods to a standard set of application areas by analyzing their gaps.

Analysis of Device Mismatches Effect on the Performance of UWB Receiver Front-End in Wireless Body Area Network Sensor Nodes

Today it is important to manufacture high quality integrated circuits which are insensitive to device mismatches. This paper presents an analysis of MOSFET transistors mismatches effect on the performance of UWB receiver front-end which constitute the most important part of Wireless Body Area Network sensor node. The receiver is based on Balun LNA with 25% fully differential double-balanced passive mixer. A PMOS and NMOS transistors mismatch models were proposed to determine LNA output offset voltage and mixer offset current respectively. The analysis result suggests that, to minimize NMOS current mismatch, and thus reducing second-order inter modulation distortion, the overdrive voltage must be maximized. A Monte Carlo and harmonic balance simulations were performed using 0.18µm CMOS process to evaluate the impact of mismatch as well as Vth mismatch on the receiver gain and IIP2. Simulation results show that IIP2 of the receiver is less sensitive to mixer NMOS mismatch but receiver gain is more sensitive. The receiver IIP2 confidence interval in case of NMOS mismatch is [24.674, 24.77]dBm and in case of NMOS Vth mismatch is [24.659, 24.857]dBm. This show the robustness of the proposed UWB receiver front end. Therefore the proposed circuit meets the requirement of UWB system perfectly which make it suitable for WBAN applications.

Prototype sensor system for analyzing frailty in older people: a pilot study

Introduction: Frailty syndrome is characterized by reduced physical and cognitive reserves, making older people vulnerable to adverse events. This study describes a prototype sensor system developed for assessing frailty through physiological parameters and frailty markers. Methods: A prototype combining four sensors in network and a software package was developed and tested in four long-term care facility senior residents of both sexes, aged 60 and older, showing no locomotive syndrome or severe cognitive impairment. Three of them were frail and able to walk without aid (P1), holding onto the wall (P2) or with a cane (P3), and a non-frail participant (P4) walked without aid. Results: Regarding mean acceleration, P1 and P4 showed the lowest and highest values, respectively, on the antero-posterior axis; P4 had the lowest value on the medio-lateral axis; and P3 presented the highest value on the vertical axis. All participants showed similar roll angular velocity; P4 presented the lowest pitch angular velocity; and P1 and P4 had the highest mean yaw angular velocity. A sarcopenic participant (P2) exhibited the lowest force of muscle contraction. Conclusion: The device has potential to detect frailty markers for adverse outcomes in older people, such as postural instability and increased risk of falls.

PCAS: Cryptanalysis and improvement of pairing-free certificateless aggregate signature scheme with conditional privacy-preserving for VANETs

Certificateless aggregate signature (CLAS) is an effective approach for the multiple authentications in multi-users and multi-information environments like the vehicular ad hoc networks (VANETs), which can address the certificate management issue in the traditional public key cryptography (PKC) and solve the key escrow problem in identity-based cryptography (IBC). In recent years, a new CLAS mechanism (LICLAS) is presented for the authentication of sensors in healthcare wireless medical sensor networks (HWMSNs). In this paper, we make an analysis and prove that LICLAS is not able to against forgery attacks. Thus, we present an improved CLAS scheme (PCAS) for vehicle authentication in VANETs, which satisfies the privacy and security requirements. PCAS constructs the signature algorithm based on Elliptic Curve Cryptography (ECC) to avoid bilinear pairing and Map-to-Hash function operations. In order to further improve security and efficiency of PCAS, the vehicle key generation and signature algorithm is revised. The pseudonym mechanism is also adopted to achieve conditional privacy preservation. Besides, PCAS allows to execute a batch verification of messages, where RSUs may verify the aggregated signatures from vehicles to reduce time overhead. Under the assumption that the elliptic curve discrete logarithm problem (ECDLP) is hard, PCAS is proved to be existentially unforgeable against adaptive chosen message attacks in the random oracle model. Through the performance analysis, under the same time complexity, PCAS is shown to more effective. Compared with LICLAS, for a single message and 2000 messages, the transmission overhead of PCAS is reduced by 25% and 25% respectively, and the computation overhead is reduced by 16.56% and 25.34% respectively.

Successful Alert Issuance with Sufficient Lead Time by Uttarakhand State Earthquake Early Warning System: Case Study of Nepal Earthquakes

Abstract Three moderate earthquakes on November 9, 2022, November 12, 2022, and January 24, 2023 occurred in Western Nepal region of Magnitudes 5.8, 5.4 and 5.8 respectively. The epicenters were ~100 km away from the Uttarakhand State Earthquake Early Warning System (UEEWS) network which consists of 169 seismic sensors in oval shape network with larger axis of about 280 km in East-West and 120 km in North-South in Uttarakhand-Dharchula seismic gap, a region of central seismic gap of Indian Himalaya. The strong motions recorded by UEEWS were fetched in real-time at the central server in Roorkee through dedicated private network. The central server issued notifications and warning alerts to the public of Uttarakhand on the mobile app, ‘Uttarakhand Bhookamp Alert’ installed by them. The success story of issuance of warning along with location of triggered sensors, epicenter of earthquakes and lead time people got in these events are elaborated in this article. Specially, these three moderate earthquakes albeit not triggered in the instrumented area, issuance of warning to the public by UEEWS network is noteworthy. Encouragingly, these events have been considered an example to rationalize establishment of earthquake early warning system in the other parts of the Himalayan regions.

Feature-Aided Passive Tracking of Noncooperative Multiple Targets Based on the Underwater Sensor Networks

Passive detection can work for a long time with low energy consumption in underwater surveillance. However, tracking unknown noncooperative targets with only direction angles is challenging, and the tracking performance of multiple targets is poor. Based on several passive sensors in the underwater sensor network (UWSN), a feature-aided state estimation method is used to start tracking unknown targets. The feature-aided joint probabilistic data association combined with the particle filter method is also proposed to improve the passive tracking performance of multiple targets. The track management and the fusion strategy are given to remove fake tracks and obtain correct trajectories of unknown targets. The simulation results show that the feature-aided method can quickly start and effectively track multiple noncooperative targets with passive sensors. Compared with other methods, the proposed method can track targets more accurately with the advantages of low energy consumption and less exposure in various environments.

Selecting the best location of water quality sensors in water distribution networks by considering the importance of nodes and contaminations using NSGA-III (case study: Zahedan water distribution network, Iran).

One of the most effective ways to minimize polluted water consumption is to arrange quality sensors properly in the water distribution networks (WDNs). In this study, the NSGA-III algorithm is developed to improve the optimal locations of sensors by balancing four conflicting objectives: (1) detection likelihood, (2) expected detection time, (3) detection redundancy, and (4) the affected nodes before detection. The research procedure proposed the dynamic variations of chlorine between defined upper and lower bounds, which were determined utilizing the Monte Carlo simulation model. For selecting a contamination matrix with the same characteristics and effects of all possible events, a heuristic method was applied. The coefficients of importance are introduced in this study for the assessment of contamination events and network nodes. The Pareto fronts for each of the two sets of conflicting objectives were computed for benchmark and real water distribution networks using the proposed simulation-optimization approach. Results indicated that sensors should be installed downstream of the network to maximize sensor detection likelihood; however, this increases detection time. For the benchmark network, maximum and minimum detection likelihoods were calculated as 92.8% and 61.1%, respectively, which corresponded to the worst detection time of 11.58min and the best detection time of 5.06min. So, the position of sensors regarding the two objective functions conflicts with each other. Also, the sensitivity analysis related to the number of sensors illustrated that the Pareto fronts became a more efficient tool when the number of sensors increased. The best pollution detection likelihood in the real water network increased by 18.93% and 24.66% by incrementing the number of sensors from 5 to 10 and 5 to 15, respectively. Moreover, adding more than 10 sensors to the benchmark network and more than 15 to the real system will provide little additional detection likelihood.

Rao-Blackwellized Particle Filter Algorithm Integrated with Neural Network Sensor Model Using Laser Distance Sensor

Commonly, simultaneous localization and mapping (SLAM) algorithm is developed using high-end sensors. Alternatively, some researchers use low-end sensors due to the lower cost of the robot. However, the low-end sensor produces noisy sensor measurements that can affect the SLAM algorithm, which is prone to error. Therefore, in this paper, a SLAM algorithm, which is a Rao-Blackwellized particle filter (RBPF) integrated with artificial neural networks (ANN) sensor model, is introduced to improve the measurement accuracy of a low-end laser distance sensor (LDS) and subsequently improve the performance of SLAM. The RBPF integrated with the ANN sensor model is experimented with by using the Turtlebot3 mobile robot in simulation and real-world experiments. The experiment is validated by comparing the occupancy grid maps estimated by RBPF integrated with the ANN sensor model and RBPF without ANN. Both the results in simulation and real-world experiments show that the SLAM performance of RBPF integrated with the ANN sensor model is better than the RBPF without ANN. In the real-world experiment results, the performance of the occupied cells integrated with the ANN sensor model is increased by 107.59%. In conclusion, the SLAM algorithm integrated with the ANN sensor model is able to improve the accuracy of the map estimate for mobile robots using low-end LDS sensors.

Investigation of Hillslope Vineyard Soil Water Dynamics Using Field Measurements and Numerical Modeling

Soil heterogeneities can impact hillslope hydropedological processes (e.g., portioning between infiltration and runoff), creating a need for in-depth knowledge of processes governing water dynamics and redistribution. The presented study was conducted at the SUPREHILL Critical Zone Observatory (CZO) (hillslope vineyard) in 2021. A combination of field investigation (soil sampling and monitoring campaign) and numerical modeling with hydrological simulator HYDRUS-1D was used to explore the water dynamics in conjunction with data from a sensor network (soil water content (SWC) and soil-water potential (SWP) sensors), along the hillslope (hilltop, backslope, and footslope). Soil hydraulic properties (SHP) were estimated based on (i) pedotransfer functions (PTFs), (ii) undisturbed soil cores, and (iii) sensor network data, and tested in HYDRUS. Additionally, a model ensemble mean from HYDRUS simulations was calculated with PTFs. The highest agreement of simulated with observed SWC for 40 cm soil depth was found with the combination of laboratory and field data, with the lowest average MAE, RMSE and MAPE (0.02, 0.02, and 5.34%, respectively), and highest average R2 (0.93), while at 80 cm soil depth, PTF model ensemble performed better (MAE = 0.03, RMSE = 0.03, MAPE = 7.55%, R2 = 0.81) than other datasets. Field observations indicated that heterogeneity and spatial variability regarding soil parameters were present at the site. Over the hillslope, SWC acted in a heterogeneous manner, which was most pronounced during soil rewetting. Model results suggested that the incorporation of field data expands model performance and that the PTF model ensemble is a feasible option in the absence of laboratory data.

Proportional Integral Predictive Control of High-Order Fully Actuated Networked Multiagent Systems With Communication Delays

This research is devoted to the cooperative control of high-order fully actuated networked multiagent systems (HOFA-NMASs) with communication delays between network node and sensors, and network node and actuators. A proportional integral (PI) predictive control scheme is developed to effectively implement the cooperation among HOFA-NMASs and actively compensate the communication delays. In this scheme, a local PI feedback controller is applied to stabilize the closed-loop nominal HOFA-NMASs, then a Diophantine equation is presented to establish an incremental HOFA prediction model rather than a reduced-order one, so that the optimization of cost function considered cooperative performance and the compensation of communication delays are completed via multistep output predictions, thus the optimal cooperative controllers are constructed. The further discussion provides a simple condition of simultaneous stability and output consensus of closed-loop HOFA-NMASs, which is easy to verify and extend in practice and is independent on communication delays. An experiment of formation control of air-bearing simulators is shown to prove the availability of the proposed PI predictive control scheme.

Frequency-based leak signature investigation using acoustic sensors in urban water distribution networks

Cities worldwide have been plagued by water pipe leaks for many decades, resulting in financial losses, public health risks, and environmental impacts. Current practice still relies heavily on periodic and localized inspection rather than long-term continuous monitoring, and since water pipelines are buried underground, leaks can often go undetected for prolonged periods. Noninvasive acoustic-based methods for continuous pipeline monitoring have gained increasing popularity the past decade thanks to the recent advances in sensing and communication technology. Previous research indicates that hydrophones, in particular, are capable of effectively detecting leak-induced acoustic waves inside a water pipe. However, most studies to date have been limited to either controlled or field test-bed settings; hence, findings might not generalize well to real-world complex pipe networks. Through rigorous leak tests conducted in a real water distribution network and an extensive analysis of the field-collected acoustic signals, the current study aims to test the applicability of low-cost, non-intrusive hydrophones attached to fire hydrants for continuous pipe monitoring and leak detection. Continuous wavelet transform, power spectrum, and band power analyses were employed to identify the leak signature and distinguish normal from leak acoustic data in various leak scenarios. Results indicate that the acoustic signals generated by the simulated leaks in this field study are characterized by a consistent increase in the power of the frequency band 150–450 Hz primarily, whereas background noise levels and conditions significantly vary depending on the location of the sensor in the network. Realistic conditions in urban water distribution networks, including background noise, complicated topology, and varying pipe size and material, are still posing significant challenges for cost-effective and widespread implementation of acoustic-based sensors to achieve continuous monitoring in water pipe networks for leak detection. Even though further research and development is required to handle the highly variable conditions of real systems, the low-cost hydrophones tested in this work demonstrated potential in detecting low-flow leaks in simple and complex pipe topologies.

Efficient Hybrid Fault-Management Clustering Algorithm (HFMCA) in WBANs Based on Weighted Bipartite Graph

Wireless Body Area networks (WBANs) have been adopted extensively in academic and industrial research and development in recent years. WBANs promise to provide a suitable environment for remote patient monitoring and enable caregivers to intervene in case of abnormal health conditions. However, WBANs sensors are resource-constrained and face challenges, including, for instance, sensor energy harvesting, efficient routing, parent node selection in case of two hubs links, and data security. The stringent healthcare requirements burden managing WBAN resources and sensor functionality. In this research work, we tackle the issue of total energy consumption, communication overhead, and the lifespan of WBAN. We study the effect of routing and parent node selection on the network lifespan. The study considers a cluster-based routing protocol to establish a WBAN. This approach divides the network into clusters, where each cluster consists of a cluster head called a Relay Node (RN) and a set of functional sensors. Each RN collects data from its sensor nodes and sends it to a base station. However, the relay nodes are susceptible to failures at any time due to the challenging deployment environments and resource constraints of the nodes. In addition, the network sensors are dynamic in positions due to user body movements. Therefore, improving the robustness, fault management, and reliability at different postures becomes necessary. We propose a mobility-aware, energy-efficient Hybrid Fault-Management Clustering Algorithm (HFMCA) adopting the Weighted Bipartite Graph (WBG) to handle the vulnerable RNs prone to failure. The WBG helps find the optimum path between the vulnerable RN and its members to the sink node while maintaining minimum energy consumption and transmission costs. Finally, we conducted extensive experiments, and the simulation results illustrate the proposed algorithm’s efficiency in WBANs regarding energy consumption, network lifespan, and communication overhead.

A Unified Bayesian Framework for Joint Estimation and Anomaly Detection in Environmental Sensor Networks

Advanced large-scale environmental monitoring systems relying on the emerging aerial/terrestrial technologies of wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs), and mobile crowdsensing, impose strong requirements on the reliability of the collected data. Unfortunately, sensing units can suddenly suffer unexpected anomalies due to accidental faults or malicious causes. Outlier detection methods have been widely employed to identify and discard unreliable measurements from large data sets, but further improvements in the sensing processes can be obtained by adopting advanced signal processing algorithms that take full advantage of all the collected information without rejecting the measurements. In this paper, we propose a novel unified Bayesian framework that enable simultaneous estimation of a common parameter of interest and identification of multiple and possibly different types of anomalies that can affect sensors in environmental sensor networks. Specifically, we consider two rather general error models based on Gaussian mixtures able to capture different variations affecting the quality of the collected measurements. For each model, we illustrate the optimal joint maximum-likelihood and maximum a-posteriori (ML-MAP) estimation method, which represents the benchmark for the problem at hand, and propose novel reduced-complexity two-step algorithms able to achieve almost the same performance of the joint ML-MAP, but at a fraction of its computational cost. The derivations of all the algorithms are also extended to handle the more general case in which the probability of occurrence of anomalies is unknown and should be inferred from the data using an Empirical Bayes approach. Extensive performance analyses using both synthetic and real experimental data acquired in a network of environmental monitoring stations deployed in the Apulia region, south of Italy, demonstrate the effectiveness of the proposed framework.

Jammer Location‐Aware Method in Wireless Sensor Networks Based on Fibonacci Branch Search

Due to the sharing and open‐access characteristics of the wireless medium, wireless sensor networks (WSNs) can be easily attacked by jammers. To mitigate the effects of a jamming attack, one reliable solution is to locate and remove the jammer from the deployed area within the WSN. To realize the jammer’s localization in the WSN, many range‐free methods have been proposed. However, most of these methods are sensitive to the distribution of nodes and the parameters of the jammer. For this reason, a jammer location‐aware method based on Fibonacci branch search (FBS) is proposed in this article. First, the interference region is estimated by using the interference region mapping service of sensors in wireless sensor networks. Then, the search point is selected in the jamming area and the fitness function is designed according to the average distance from the search point to the boundary sensor. According to the basic branch structure and interactive search rules, the global optimal solution is obtained in the jamming area. Finally, the position of the search point with the best fitness value is used as the estimation of the jammer position. Compared with the existing typical range‐free methods, rich simulation experiments demonstrate that the FBS algorithm is superior in the location‐aware method for jammers with a higher precision and a lower sensitivity to the distribution of nodes and the parameters of the jammer, respectively.

Asymptotic Behaviors and Confidence Intervals for the Number of Operating Sensors in a Sensor Network

In this paper, we study asymptotic behaviors of an estimator of the number of operating sensors in a sensor network based on the Good-Turing estimator. The asymptotic normality, some moderate deviations and deviation inequalities of the estimator are obtained. Our approach is based on the tail probability estimates and moderate deviations for occupancy problems. Applying these asymptotic behaviors, we give a performance analysis for the estimator of the number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> of operating nodes when the deviations of the estimator are in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\sqrt {N}, o(N))$ </tex-math></inline-formula> . These estimates also provide a method to build confidence interval of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> .