Dp ( , f, M) = S in VS .NET

Paint Denso QR Bar Code in VS .NET Dp ( , f, M) = S
2 Dp ( , f, M) = S
Reading QR In Visual Studio .NET
Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in .NET framework applications.
2 2 fM
Make QR In VS .NET
Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code image in Visual Studio .NET applications.
i=1 k=1
QR Code Decoder In Visual Studio .NET
Using Barcode recognizer for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
4 S e 3di / s 2 2 S e 2di / s + N tk di /c / t
Barcode Maker In .NET
Using Barcode printer for .NET framework Control to generate, create bar code image in VS .NET applications.
t 2 e +
Bar Code Recognizer In VS .NET
Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET applications.
2 N fM 2 M
QR-Code Generator In C#
Using Barcode encoder for .NET Control to generate, create QR Code 2d barcode image in VS .NET applications.
tk +di /c
Printing QR Code In Visual Studio .NET
Using Barcode creation for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications.
e
Creating QR Code In Visual Basic .NET
Using Barcode creation for .NET Control to generate, create Quick Response Code image in Visual Studio .NET applications.
4 S e 2di / s 2 2 S e di / s + N M M f f 2
Bar Code Creator In .NET
Using Barcode creation for .NET Control to generate, create barcode image in Visual Studio .NET applications.
+ where =
Creating Code 128C In Visual Studio .NET
Using Barcode creation for VS .NET Control to generate, create Code 128 image in Visual Studio .NET applications.
1 2f 2M2
Encoding Bar Code In .NET Framework
Using Barcode generator for .NET framework Control to generate, create barcode image in Visual Studio .NET applications.
(i, j, k, l)
Drawing Code 11 In .NET
Using Barcode drawer for VS .NET Control to generate, create Code 11 image in .NET applications.
i=1 j=1 k=1 l=1
Code-128 Encoder In Java
Using Barcode generation for Java Control to generate, create Code 128 Code Set A image in Java applications.
(5.34)
Recognizing UPC-A In VS .NET
Using Barcode decoder for VS .NET Control to read, scan read, scan image in .NET framework applications.
8 S e 2(di +dj )/ s 2 2 2 2 S e di / s + N S e dj / s + N
Recognizing GTIN - 13 In .NET
Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
SPATIOTEMPORAL CORRELATION THEORY FOR WIRELESS SENSOR NETWORKS
Paint Bar Code In VB.NET
Using Barcode printer for .NET Control to generate, create barcode image in .NET applications.
and di = (xi + yi ), and (i, j, k, l) is the spatiotemporal correlation function given in (5.27). Spatiotemporal Characteristics of Field Sources. In some WSN applications such as temperature monitoring and seismic monitoring, the physical phenomenon is dispersed over the sensor eld and, hence, can be modeled as a eld source. Thus, here we explore the spatiotemporal characteristics of observing such a phenomenon in WSNs. As in Section 5.3.3, the event signal f (x, y, t) is assumed to be a Gaussian random 2 process with N(0, s ). The sink is interested in estimating the signal f (x0 , y0 , t) over the decision interval at location (x0 , y0 ). Assuming that the observed signal f (x, y, t) is wide-sense stationary (WSS), the expectation of the signal over the decision interval [i.e., S( )] can be calculated by the time average of the observed signal as S( ) = 1
Recognize Code 128 Code Set B In VS .NET
Using Barcode scanner for .NET Control to read, scan read, scan image in .NET applications.
f (x0 , y0 , t) dt
UPC Symbol Printer In Visual C#
Using Barcode drawer for .NET framework Control to generate, create UPC-A image in .NET framework applications.
(5.35)
UPC Code Generation In Java
Using Barcode drawer for Java Control to generate, create UPCA image in Java applications.
where (x0 , y0 ) is the event location. The signal Si [k] received at time tk by a sensor 2 node at location (xi , yi ) is de ned as in (5.26), and the Si [k] s are JGRV with N(0, s ). The covariance of two samples, Si [k] and Sj [l], is given by
Creating Code 128C In VS .NET
Using Barcode encoder for ASP.NET Control to generate, create Code 128 image in ASP.NET applications.
2 cov{Si [k], Sj [l]} = S s (i, j) t ( )
(5.36)
where s (i, j) = e di,j / s and t ( ) = e | |/ t (5.37)
are spatial and temporal correlation functions, respectively, = (k l)/f , f is the sampling rate, di,j = (xi xj )2 + (yi yj )2 is the distance between two nodes ni and nj , and s and t are spatial and temporal correlation coef cients, respectively. Following the discussion and derivations in Section 5.3.3, the noisy version of the signal, Xi [k], and the transmitted signal, Yi [k], are given by (5.29) and (5.30), respectively. The estimation Zi [k] can be found as
2 S Si [k] + Ni [k] 2 2 S + N
Zi [k] =
(5.38)
After collecting the samples of the signal in the decision interval from M nodes, the sink estimates the expectation of the signal over the last decision interval as given in (5.32). As a result, the distortion achieved by this estimation is given as in (5.33). Using the de nitions above and substituting (5.35), (5.38), and (5.32) into (5.33), the distortion function can be derived as [2]
COROLLARIES AND EXPLOITING CORRELATION IN WIRELESS SENSOR NETWORKS
2 Df ( , f, M) = S f
2 2 S 2 2 2 fM ( S + N )
s (i, s)
k t f / t
t 2 e k/(f t ) e
6 4 2 S S N + 2 2 2 2 fM ( S + N )2 ( fM ( S + N ))2 M f f
s (i, j) t (|k l|/f )
i=1 j=1 k=1 l=1
(5.39) In order to provide further insight into the spatiotemporal correlation characteristics and distortion analysis derived in this section, next we discuss possible approaches that can be used in the design of ef cient communication techniques exploiting the spatiotemporal correlation observed in the wireless sensor networks.
5.4 COROLLARIES AND EXPLOITING CORRELATION IN WIRELESS SENSOR NETWORKS Spatiotemporal correlation, in addition to the collaborative nature of the WSN, bring signi cant potential advantages for the development of ef cient communication protocols well-suited for the WSN paradigm. In this section we discuss possible approaches exploiting spatiotemporal correlation to achieve energy-ef cient medium access and reliable event transport in WSN, respectively. 5.4.1 Spatial Correlation and Medium Access Control The shared wireless channel between sensor nodes and energy considerations of the WSN make the medium access control (MAC) a crucial part of the wireless sensor networking. Furthermore, the scarce energy sources of sensor nodes necessitate energy-aware MAC protocols. Hence, MAC protocols for WSN should be tailored to the physical properties of the sensed phenomenon and the speci c network properties so that the access to the channel is coordinated with minimum collisions without affecting the connectivity throughout the network. In WSNs, many individual nodes deployed in large areas sense events and send corresponding information about these events to the sink. As discussed in Section 5.3.1, due to the physical properties of the event, this information may be highly correlated according to the spatial distribution of the sensor nodes. Intuitively, data from spatially separated sensors are more useful to the sink than highly correlated data from closely located sensors. Hence, it may not be necessary for every sensor