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Kalaiyarasi.R^{1}, Rajeswari.S^{2}

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The wireless sensor node is a tiny device that is used to capture environment information. Sensor devices are used to capture temperature and pressure details from the environment. Sensors are used to cooperatively monitor physical or environmental conditions. Computing and tracking the spatialaverage of the sensor measurements are estimated over a region of the WSN. Sensor faults and heterogeneous measurement noise factors affects the sensor data average process. Robust averaging fixedpoint iteration algorithm is used to compute a weighted average of sensor measurements with noise and faults. Each sensor performs projections on its sensor measurements to produce a lower bandwidth compressed data stream. Data approximation process is used to assign relevant data values for missed or noisy data values. The sensors in the WSN use random projections to compress the data and send the compressed data to the data fusion centre. The data fusion centre only need to perform decompression once to compute the robust average to reducing the computational requirements. The compressive data collection scheme is enhanced with Bayesian approach to support projection count prediction. Sensing and transmission coverage factors are integrated in the data collection process. Data projection accuracy is improved with frequent pattern identification mechanism. The data collection scheme is tuned to support scheduling schemes to increase network lifetime.
INTRODUCTION 

A wireless sensor network (WSN) is a wireless network consisting of spatially distributed autonomous devices using sensors to cooperatively monitor physical or environmental conditions The development of wireless sensor networks was originally motivated by military applications such as battlefield surveillance In addition to one or more sensors, each node in a sensor network is typically equipped with a radio transceiver or other wireless communications device, a small microcontroller, and an energy source, usually a battery. The envisaged size of a single sensor node can vary from shoeboxsized nodes down to devices the size of grain of dust, although functioning 'motes' of genuine microscopic dimensions have yet to be created. The cost of sensor nodes is similarly variable, ranging from hundreds of dollars to a few cents, depending on the size of the sensor network and the complexity required of individual sensor nodes. Size and cost constraints on sensor nodes result in corresponding constraints on resources such as energy, memory, computational speed and bandwidth.  
A sensor network normally constitutes a wireless adhoc network, meaning that each sensor supports a multihop routing algorithm. In computer science and telecommunications, wireless sensor networks are an active research area with numerous workshops and conferences arranged each year.  
A number of data mining algorithms have been recently developed that greatly facilitate the processing and interpreting of large stores of data. One example is the association rulemining algorithm. Priori algorithm is an example of association rule mining algorithm. Using this algorithm, candidate patterns that receive sufficient support from the database are considered for transformation into a rule.  
One limitation of many association rulemining algorithms such as the Apriori algorithm is that only database entries, which exactly match the candidate patterns, may contribute to the support of the candidate pattern. This creates a problem for databases containing many small variations between similar patterns and for databases containing missing values. In the wireless sensor networks association rule mining techniques are used to fetch the data sensing patterns.  
RELATED WORK 

There are a number of papers investigating how compressive sensing can be applied in WSNs. We can classify them according to whether projections are computed “temporally” or “spatially”. The “temporal” projections are used, where each sensor computes projections of its own data and sends it to the data fusion centre. It also discusses how fault tolerance can be realized based on the framework discussed, where all signals are reconstructed at the data fusion centre. A minimal number of signals have to be reconstructed to achieve computation efficiency at the data fusion centre.  
Other works in applying compressive sensing in WSNs view the spatial data from the sensors at each time instance as an image or snapshot, and compute projections of the sensor data for each snapshot. All these works aim at obtaining a sufficient accurate snapshot of the sensor field by using as little energy as possible. The work [3] realizes this goal by using an additive radio channel to compute projections. The works in [6], [10], [5] compute projections by passing messages between sensors, while the work in [11], [9] consider random samples as projections. There is a rich literature in fault tolerance in WSNs. The work [4] discusses the types of faults that commonly appear in WSNs. The papers [7] use a Bayesian approach to detect whether sensors are faulty. The work [8] proposes to detect sensor faults by using recurrent neural networks.  
The problem of computing a robust average also appears in other fields, e.g., reputation ranking and fair assessment of students’ work in education [2]. However, this estimator experiences convergence problem, a fact which we also pointed out. The use of projection matrix as a dimensionality reduction method is fairly well known in the data mining and the machine learning communities. The framework depicted opens up the possibility of using some of the algorithms developed in these communities to WSNs, e.g., performing clustering using the compressed data. A feature of our algorithm is that it works directly with the compressed data without decompressing them. There is also some recent effort in using compressed data directly for classification and detection, see [12].  
COMPRESSIVE DATA COLLECTION SCHEME 

This paper considers the fusion of distributed compressive sensing data in a wireless sensor network (WSN). Compressive sensing is a collection of recently proposed sampling and signal reconstruction methods. A promise of compressive sensing is that it can obtain a good approximation of an unknown signal by performing a small number of generalized measurements, called projections, provided that the unknown signal is compressible. For WSNs, it means that compressive sensing can be used to reduce the bandwidth requirement and lower the energy consumption.  
Fig. 3.1 depicts a “standard” method in which distributed compressive sensing can be used to compute a robust average in a WSN. Instead of sending the original sensor measurements, each sensor performs projections on its sensor measurements to produce a lower bandwidth compressed data stream. These compressed data streams are then transmitted over the WSN to reach the data fusion centre, where these data streams are decompressed to retrieve the original signals (or more precisely, an accurate approximation of the original signals because the compression is lossy). Based on the decompressed data streams, the data fusion centre can examine which of the signals are faulty. Assuming that we are interested in calculating the average of the data, we can now use the decompressed data streams to determine suitable weights for this averaging operation, e.g., by weighting noisy signals less than the clean signals. The key advantage of this method is that bandwidth will be saved by sending compressed data streams over the network.  
In this paper, we examine the alternative method depicted for this method; the sensors again send compressed data streams to the data fusion centre. The main difference is the sequence of operations to be performed at the data fusion centre. Instead of first decompressing the compressed data to obtain the original data stream, our proposed method will work directly with the compressed data without decompressing them. Our proposed method determines a weight for each of the compressed data streams, which reflects whether the sensor which produces the compressed data stream may be faulty or not. We then apply these weights to compute a robust average of the compressed data streams. A nice property of this robust average of the compressed data streams is that, upon decompressing (or applying the compressive sensing reconstruction method to) this stream, we will obtain an approximation of the robust average of the original sensor readings. The key advantage of our proposed method is a great reduction of computation requirement at the data fusion centre. First, we work directly with the compressed data, whose dimension is only a fraction of that of the original sensor readings. Second, we only need to perform decompression (or compressive sensing reconstruction) once, this represents a huge saving in computation requirement because each decompression requires a linear programming problem to be solved. In addition, we show that our fusion algorithm can be implemented on resource limited wireless sensor nodes.  
SYSTEM MODELS 

Basic Models 

We consider a WSN with n sensors indexed by s = 1, . . . , n. We assume that the sensors are time synchronized and at each time slot t, each sensor performs a measurement. We will use xst to denote the sensor reading by sensor s at time slot t. We assume that the network works on one block of data with m consecutive data points in a block; therefore, a block of data consists of {xst} with s = 1, . . . , n and t = 1, . . .,m. Note: As depicted the sensors will not send their readings xst directly to the data fusion centre to conserve bandwidth and energy. Instead, each sensor will perform projections on its sensor readings and send only the results of the projections, which we call either the compressed data stream or the compressed data, to the data fusion centre. The action of, say sensor s, on projecting its data sequence xst (t = 1, . . .,m) can be expressed in matrix form, as follows:  
The matrix Ф is the projection matrix, and the vector ys is the result of the projection. (Note that all vector and matrix quantities are typeset in boldface in this paper.) The theory of compressive sensing says that the elements Фij can be drawn from one of these distributions: 1) Standard Gaussian distribution; 2) Symmetric Bernoulli distribution of random numbers {+1,1}; or 3) Categorical distribution whose outcomes √3, 0, and √3 occur with probability 1/6, 2/3 and and 1/6, respectively. We assume that all the sensors use the same projection matrix for each block of data. Since the network is synchronized, this can be achieved by using a time dependent seed for the pseudorandom number generators. This also means that the sink knows the projection matrix that is being used, and the sensors do not have to send this information. The parameter p (< m) here is the number of projections to be used, and we assume that all sensors use the same value of p.  
The compressed data stream {ysk} (for k = 1, . . . , p) is to be transmitted by sensor s to the data fusion centre of the WSN. For practical implementation, it is easier to use either Bernoulli distribution or Categorical distribution mentioned earlier. For Bernoulli distribution, it will be easier for the sensors to send √pysk to the data fusion centre because only integer addition and subtraction are needed to perform by the sensor nodes. Furthermore, for suitable values of p, the transmission of the sequence {ysk} will require less number of bits than {ysk}. If the analogtodigital (A/D) convertor on the sensor uses b bits, then sending the original sequence will need mb bits. However, sending the compressed sequence (assuming the aforementioned practical implementation) will require p(b + 1 +[log2 m]) bits (where [u] denote the smallest integer larger than or equal to u) because the range of ysk is [m(2b – 1); m(2b – 1). Thus, bandwidth is saved if p(b + 1 + [log2 m]) < mb (assuming that no special coding scheme is used) and we will show that using data from WSN deployments. With suitable implementation of Categorical distribution, the sensors again only have to perform integer arithmetic. Also, sampling energy can be saved if a zero is drawn from the Categorical distribution because such samples are not needed. For the rest of this paper, we will assume that either the Bernoulli or Categorical distribution is used. Note that we will continue to write projection using the convention in (2), which is commonly used in compressive sensing literature but noting that the practical implementation may be slightly different.  
Data and Fault Models for Robust Averaging 

We assume that all the sensors in WSN are measuring the same physical value at any given time but some of the sensors can be faulty. The type of faults can be bias, stuckat fault or heterogeneous measurement noise [7]. We model that by assuming that the sensor reading of sensor s at time t, xst, is generated from the Gaussian distribution with mean rt and variance σ2 s , i.e., xst N(rt, σ2 s ). In other words, the model assumes that all sensors should have the same mean reading rt at time t but the measurement noise of different sensors can be different. Our goal is, therefore, to recover the value of rt from the sensor readings. We will refer to this process of recovering rt in the presence of faults as robust averaging.  
ISSUES ON COMPRESSIVE DATA COLLECTION SCHEME 

Wireless sensor networks (WSNs) perform the data collection over a large geographic area. Computing and tracking the spatialaverage of the sensor measurements are estimated over a region of the WSN. Sensor faults and heterogeneous measurement noise factors affects the sensor data average process. Robust averaging fixedpoint iteration algorithm is used to compute a weighted average of sensor measurements with noise and faults. Each sensor performs projections on its sensor measurements to produce a lower bandwidth compressed data stream. Data approximation process is used to assign relevant data values for missed or noisy data values. The sensors in the WSN use random projections to compress the data and send the compressed data to the data fusion centre. The data fusion centre only need to perform decompression once to compute the robust average to reducing the computational requirements. The following drawbacks are identified in the existing system.  
Projection prediction is not supported by the system  
Transmission coverage factors are not considered  
Limited projection accuracy levels  
Scheduling schemes are not used  
SCHEDULING ENABLED COMPRESSIVE DATA COLLECTION SCHEME 

The compressive data collection scheme is enhanced with Bayesian approach to support projection count prediction. Sensing and transmission coverage factors are integrated in the data collection process. Data projection accuracy is improved with frequent pattern identification mechanism. The data collection scheme is tuned to support scheduling schemes to increase network lifetime. The sensor network data collection process is improved with optimal data projection schemes. Energy management is integrated with the sensor data capturing process. Sensing and transmission coverage based scheduling is applied in the system. The system is divided into five major modules. They are sensor network construction, scheduling process, data fusion center, pattern analysis and data projection process.  
Sensor network deployment process is carried out in the network construction process. Data capturing sessions are assigned in the scheduling process. Data fusion center is used to collect the data values from the sensor nodes. Pattern analysis is performed to estimate the data capture patterns. Data projection process is used to estimate the missing data elements.  
Sensor Network Construction 

Sensor networks are constructed with node count and node type information. Sensor nodes are placed with reference to the spatial coverage information. Sensing and transmission coverage details are used in the sensor networks. Spatial regions and associated sensor nodes are assigned in the deployment process.  
Scheduling Process 

Sensor node captures the environment data and updates it into the local storage. Data sensing sessions are used to manage energy levels. Sleepwakeup scheduling algorithm is used for ode scheduling process. Data capture and transmission operations are carried out with scheduling details.  
Data Fusion Center 

Data fusion center is used to collect sensor data values. Compressed data values are collected from the sensor nodes. Compressive data values are processed to fetch the aggregated data values. Projection methods are used to fetch the missing data values.  
Pattern Analysis 

Pattern analysis mechanism is used to find out the data capture patterns. Frequent pattern mining is applied on each sensor. Support and confidence levels are used to estimate frequent patterns. Apriori algorithm is used for the pattern analysis process.  
Data Projection Process 

Data projection process is performed under the data fusion center. Projection points are estimated using the Bayesian approach. Random projection method is applied to estimate the missing values. Pattern based projection scheme is applied to improve the projection accuracy levels.  
DATA COLLECTION AND WSN DEPLOYMENTS 

We have studied the behaviour of our robust averaging algorithm when it is applied to three commonly found sensor faults in WSNs, namely stuckatfaults, offset, and variance degradation fault [7]. Our study shows that our robust averaging algorithm can deal with these faults, even when a mixture of them appears in a WSNs, see Appendix C (online supplemental material). We have applied our robust averaging algorithm to data obtained from two outdoor WSN deployments. The results for the Belmont deployment (with 32 temperature sensors) are presented (online supplemental material). Note that the results presented in this section are obtained from using the symmetric Bernoulli distribution to form the projection matrix. The results from using Categorical distribution to form the projection matrix are very similar and are not shown here.  
This section describes the results of applying our robust averaging algorithm to the data obtained from an outdoor WSN test bed operated by CSIRO in their QCAT research facility in Brisbane, Australia. The WSN consists of five sensors measuring humidity and a block of data for each sensor consists of 400 points. The first four sensors have the same trend, but the fifth sensor shows completely erroneous measurements.  
CONCLUSION 

Wireless sensor network uses the data fusion centers to collect and process data values from sensor nodes. Compressive data collection methods are used to handle data collection under faulty and noisy environment. Data collection scheme is improved with Bayesian approach to predict projections. Scheduling schemes are integrated with the system to increase the network lifetime. The system achieves high computational efficiency. Communication load is reduced by the compressive data collection scheme. Efficient fault and noise handling mechanism is provided in the sensor data collection process. Data collection accuracy is improved in the pattern based model.  
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