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Environmental monitoring is often performed through wireless sensor networks, by randomly deploying sensor nodes over the geographical region of interest. Sensors sample a physical phenomenon (the so-called field) and send their measurements to a sink, which is in charge of reconstructing the field from such irregular samples. In this work, we focu...
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... the case of massively dense networks, the LSD of VV H is given by (16) and from (17) we know that the MSE tends to 0 as β → ∞. This result is confirmed by the plot in Figure 4, which shows the AESD f (n) λ,x (2, β n,m , z), for |A| = 1, a = 5 dB, and n = 10. The behavior of such a function is compared with the density g x (z) as β varies. ...
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... There are some existing results in the literature that analyze the wireless sensors distribution in the threedimensional space such as in [21][22][23]. These scenarios analyze the distribution of the sensor networks under certain conditions that are not considered in this research work. ...
Location information for wireless sensor nodes is needed in most of the routing protocols for distributed sensor networks to determine the distance between two particular nodes in order to estimate the energy consumption. Differential evolution obtains a suboptimal solution based on three features included in the objective function: area, energy, and redundancy. The use of obstacles is considered to check how these barriers affect the behavior of the whole solution. The obstacles are considered like new restrictions aside of the typical restrictions of area boundaries and the overlap minimization. At each generation, the best element is tested to check whether the node distribution is able to create a minimum spanning tree and then to arrange the nodes using the smallest distance from the initial position to the suboptimal end position based on the Hungarian algorithm. This work presents results for different scenarios delimited by walls and testing whether it is possible to obtain a suboptimal solution with inner obstacles. Also, a case with an area delimited by a star shape is presented showing that the algorithm is able to fill the whole area, even if such area is delimited for the peaks of the star.
... The disk coverage model, however, is a simplistic sensor coverage model, which does not consider the spatial correlation of physical phenomena and information processing paradigm via the collaboration of sensors. Motivated by the precision agriculture applications [5,6] and based on the theory of field reconstruction [7], we have proposed a new sensor coverage model, called confident information coverage (CIC or Φ-coverage), in our previous study [8]. We will briefly introduce the CIC model in Section 3. ...
Coverage and connectivity are two important performance metrics in wireless sensor networks. In this paper, we study the sensor placement problem to achieve both coverage and connectivity. Instead of using the simplistic disk coverage model, we use our recently proposed confident information coverage model as the sensor coverage model. The grid approach is applied to discretize the sensing field, and our objective is to place the minimum number of sensors to form a connected network and to provide confident information coverage for all of the grid points. We first formulate the sensor placement problem as a constrained optimization problem. Then, two heuristic algorithms, namely the connected cover formation (CCF) algorithm and the cover formation and relay placement with redundancy removal (CFRP-RR) algorithm, are proposed to find the approximate solutions for the sensor placement problem. The simulation results validate their effectiveness, and the CCF algorithm performs slightly better than the CFRP-RR algorithm.
... . Such function can be computed numerically by using the result in[23, Corollary 4.2]. This result links η R β, u , computed in the case where the distribution of the estimates P is uniform over the entire sampling area. ...
The dramatic increase in the number and sensing capabilities of mobile devices
is fostering opportunistic sensing as a paramount data collection paradigm in
smart cities. According to this paradigm, sensing of large-scale phenomena is
autonomously performed by mobile devices that provide irregular samples in time
and space. The collected data is then transferred to a central controller, and
processed so as to obtain a representation of the
phenomenon. In this paper, we investigate the factors that impact the accuracy
of mobile opportunistic sensing. Specifically, we characterize the accuracy of
a phenomenon representation obtained from samples collected by mobile devices
and processed through the popular LMMSE filter. We do so by drawing on random
matrix theory, which allows us to deal with irregularly spaced samples.
Our analytical expressions capture the fundamental relationships
existing between the accuracy and the parameters of mobile opportunistic
sensing. We apply our analytical results to a realistic scenario where
atmospheric pollution samples are collected by vehicular and pedestrian
users. We validate the proposed analytical framework, and then exploit the model
to investigate the impact on mobile sensing accuracy of a number of
parameters. These include the pedestrian and vehicle density, the participation
ratio to the sensing application, the type of phenomenon to be sensed, and the
level of noise and position errors affecting the collected samples.
... When this condition is not met, the uncovered region(s) in this union is called the coverage hole(s). In addition to the obvious security concerns of such uncovered regions, coverage holes also effect the accuracy of the field estimation of the phenomenon to be sensed as analyzed in [20]. Such detrimental effects due to coverage holes may be remedied to a certain extent given the knowledge of location of the coverage hole within the network. ...
The state estimation problem is investigated in this paper for discrete-time general complex dynamical networks with packet loss happening in transmission channel between original network and observer network. A set of random variables satisfying the Bernoulli distribution is used to describe the phenomenon of the packet loss. In order to eliminate the influence of packet loss, we substitute the observer outputs for the missing original network outputs when the packet loss happens. By applying the Lyapunov stability theory and the stochastic analysis method, a sufficient condition for state estimation is derived in terms of linear matrix inequalities (LMIs). Based on the bisection method, we propose an algorithm to obtain the maximally allowable packet loss probability for state estimation. If the real packet loss probability is smaller than the maximally allowable value, the state estimation problem is feasible. Finally, it is demonstrated by simulation that the proposed scheme is feasible and effective.
Finding the optimal placement pattern to provide complete area coverage is of great theoretical and practical significance. Most of the current studies on placement problem are based on the simplest disk coverage model. In this paper, we study the optimal placement pattern based on the confident information coverage (CIC or Φ-coverage) model [1], which is much more complicated than the disk coverage model. Based on the reconstruction theory, the CIC model takes into consideration of not only the collaboration of sensors for information processing but also the spatial correlation of physical phenomena. We first analyze Φ-coverage of one sensor and two sensors, and then Φ-coverage of n sensors for n ≥ 3, where n sensors are deployed at n vertices of a regular n-sided polygon. We prove that the regular triangular lattice is the optimal placement pattern among all the placement patterns consisting of regular polygons. We also extend our analysis to acute cyclic polygons, and prove that the regular triangular lattice is still the optimal placement pattern among all the placement patterns consisting of acute cyclic polygons.
Wireless sensor networks (WSNs) consist of hundreds or thousands of small energy-constrained nodes with sensing, computation, and wireless communication capabilities, which are spatially deployed at different locations to sense the physical conditions of the surrounding environment. As a result, WSNs are usually applied to many applications that require unattended operations. However unlike many other networks, sensor nodes on the WSNs are resource constrained. In addition, data exchange is common among these sensor nodes over the WSNs. It is a challenging task to ensure the content or meaning of data information, due to the nature of WSNs, such as the delay uncertainty, latency and dynamic reliability. In order to ensure the reliability, integrity and continuity of data transmission, a novel application oriented frame is specifically designed for the WSNs in this paper. This frame is built on ZigBee technology because of its low-power, which remains redundant sampling information on screen, such as sampling time and information types.
In flat wireless sensor networks, one fundamental issue is region coverage, which usually addresses whether the given region is sufficiently covered by sensing disks of sensor nodes or not. Although numerous research works have been carried out on region coverage, it still lacks in-depth understanding on the relations between region coverage and sensing topology defined with the intersections of sensing areas of sensor nodes. In this paper, we consider the region coverage problem by using the sensing topology proposed in our previous work. Based on the notion of sensing topology, we prove that the given region can be partitioned into a number of the smallest cells, each of which is defined by sensing links among sensor nodes. Then, we investigate the sufficient and necessary conditions for the existence of coverage holes for the specific polygon graph residing in the partitioned cells. Further, two polynomial time algorithms are presented for dividing the given region covered by the whole network and detecting the coverage holes existing in the interior area of the partitioned cells, respectively. The experiment results show that our proposed algorithms are effective for detecting the coverage holes.
Coverage is one of the fundamental issues in wireless sensor networks, yet most of the current studies on coverage are based on the simplest disk coverage model. Based on the theory of field reconstruction, we proposed a novel coverage model called confident information coverage in our previous study. In this paper, based on the confident information coverage model, we study the critical sensor density to achieve complete coverage in randomly deployed sensor networks. We first use the average vacancy to measure the degree of coverage, and compute the average vacancy through the computation of the probability that an arbitrary point is not covered by randomly deployed sensors within its correlation range. We then propose a numerical computation method called discrete approximation algorithm to compute this probability, and prove that this probability is actually the limit of the output of the proposed algorithm. Furthermore, we derive the upper and lower bound for the average vacancy as a function of sensor density, which provides a useful insight for the critical sensor density to achieve complete coverage. The simulation results validate our theoretical analysis.
Tracking mobile targets is one of the most important applications in wireless sensor networks (WSNs). Traditional tracking solutions are based on fixed sensor nodes and have two critical problems. First, in WSNs, the energy constraint is a main concern, but due to the mobility of targets, lots of sensor nodes in WSNs have to switch between active and sleep states frequently, which causes excessive energy consumption. Second, when there are holes in the deployment area, targets may fail to be detected while moving in the holes. To solve these problems, this paper exploits a few of mobile sensor nodes to continuously track mobile targets because the energy capacity of mobile nodes is less constrained. Based on a realistic detection model, a solution for scheduling mobile nodes to cooperate with ordinary fixed nodes is proposed. When targets move, mobile nodes move along with them for tracking. The results of extensive simulations show that mobile nodes help to track the target when holes appears in the coverage area and extend the effective monitoring time. Moreover, the proposed solution can effectively reduce the energy consumption of sensor nodes and prolong the lifetime of the networks.
