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| | It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. Thus, it is important to keep pace with this highly advanced age and have a regular interaction with your audience to keep a strong hold in the business market. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it. <br><br>As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. If you wish to sell your services or products via internet using your website, you have to put together on the website the facility for trouble-free payment transfer between customers and the company. We also help to integrate various plug-ins to expand the functionalities of the web application. Here is more in regards to [http://9ja.in/wordpress_backup_33723 wordpress backup plugin] look into the web-site. It primarily lays emphasis on improving the search engine results of your website whenever a related query is typed in the search box. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself. <br><br>This gives a clearer picture that online shoppers are familiar with the WP ecommerce system. s cutthroat competition prevailing in the online space won. all the necessary planning and steps of conversion is carried out in this phase, such as splitting, slicing, CSS code, adding images, header footer etc. Thousands of plugins are available in Word - Press plugin's library which makes the task of selecting right set of plugins for your website a very tedious task. " Thus working with a Word - Press powered web application, making any changes in the website design or website content is really easy and self explanatory. <br><br>The primary differences are in the plugins that I install, as all sites don't need all the normal plugins. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. However, you may not be able to find a theme that is in sync with your business. It supports backup scheduling and allows you to either download the backup file or email it to you. The Pakistani culture is in demand of a main surgical treatment. <br><br>Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. Mahatma Gandhi is known as one of the most prominent personalities and symbols of peace, non-violence and freedom. As a result, it is really crucial to just take aid of some experience when searching for superior quality totally free Word - Press themes, Word - Press Premium Themes for your web site. Thus, Word - Press is a good alternative if you are looking for free blogging software. Get started today so that people searching for your type of business will be directed to you. |
| | |
| '''Location estimation''' in '''[[wireless sensor networks]]''' is the problem of [[Estimation theory|estimating]] the location of an object from a set of noisy measurements, when the measurements are acquired in a distributed
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| manner by a set of sensors.
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| | |
| ==Motivation==
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| | |
| Many civilian and military applications require monitoring that can identify objects in a specific area, such as monitoring the front entrance of a private house by a single camera. Monitored areas that are large relative to objects of interest often require multiple sensors (e.g., infra-red detectors) at multiple locations. A centralized observer or computer application monitors the sensors. The communication to Power and bandwidth requirements call for efficient design of the sensor, transmission, and processing.
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| | |
| The ''[[CodeBlue system]]''[http://www.eecs.harvard.edu/~mdw/proj/codeblue/] of [[Harvard university]] is an example where a
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| vast number of sensors distributed among hospital facilities
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| allow staff to locate a patient in distress. In addition, the sensor
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| array enables online recording of medical information while
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| allowing the patient to move around. Military applications (e.g.
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| locating an intruder into a secured area) are also good candidates
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| for setting a wireless sensor network.
| |
| | |
| ==Setting==
| |
| | |
| [[Image:LocationEstimation WSN.JPG|right|370px]]
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| Let <math>\theta</math> denote the position of interest. A set of <math>N</math> sensors
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| acquire measurements <math>x_n = \theta + w_n</math> contaminated by an
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| additive noise <math>w_n</math> owing some known or unknown [[probability density function]] (PDF). The sensors transmit measurements to a central processor. The <math>n</math>th sensor encodes
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| <math>x_n</math> by a function <math>m_n(x_n)</math>. The application processing the data applies a pre-defined estimation rule
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| <math>\hat{\theta}=f(m_1(x_1),\cdot,m_N(x_N))</math>. The set of message functions
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| <math>m_n,\, 1\leq n\leq N</math> and the fusion rule <math>f(m_1(x_1),\cdot,m_N(x_N))</math> are
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| designed to minimize estimation error.
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| For example: minimizing the [[mean squared error]] (MSE),
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| <math>\mathbb{E}\|\theta-\hat{\theta}\|^2</math>.
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| Ideally, sensors transmit their measurements <math>x_n</math>
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| exactly to the processing center, that is <math>m_n(x_n)=x_n</math>. In this
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| settings, the [[maximum likelihood estimator]] (MLE) <math>\hat{\theta} =
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| \frac{1}{N}\sum_{n=1}^N x_n</math> is an [[unbiased estimator]] whose MSE is
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| <math>\mathbb{E}\|\theta-\hat{\theta}\|^2 = \text{var}(\hat{\theta}) =
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| \frac{\sigma^2}{N}</math> assuming a white [[Normal distribution|Gaussian]] noise
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| <math>w_n\sim\mathcal{N}(0,\sigma^2)</math>. The next sections suggest
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| alternative designs when the sensors are bandwidth constrained to
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| 1 bit transmission, that is <math>m_n(x_n)</math>=0 or 1.
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| | |
| ==Known noise PDF==
| |
| | |
| We begin with an example of a Gaussian noise
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| <math>w_n\sim\mathcal{N}(0,\sigma^2)</math>, in which a suggestion for a
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| system design is as follows
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| :<ref>{{cite journal
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| | last = Ribeiro
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| | first = Alejandro
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| | coauthors = [[Georgios B. Giannakis]]
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| | title = Bandwidth-constrained distributed estimation for wireless sensor Networks-part I: Gaussian case
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| | journal = IEEE Trans. On Sig. Proc.
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| | date = March 2006}}
| |
| </ref>
| |
| | |
| : <math>
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| m_n(x_n)=I(x_n-\tau)=
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| \begin{cases}
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| 1 & x_n > \tau \\
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| 0 & x_n\leq \tau
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| \end{cases}
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| </math>
| |
| | |
| : <math> | |
| \hat{\theta}=\tau-F^{-1}\left(\frac{1}{N}\sum\limits_{n=1}^{N}m_n(x_n)\right),\quad
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| F(x)=\frac{1}{\sqrt{2\pi}\sigma} \int\limits_{x}^{\infty}
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| e^{-w^2/2\sigma^2} \, dw
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| </math>
| |
| | |
| Here <math>\tau</math> is a parameter leveraging our prior knowledge of the
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| approximate location of <math>\theta</math>. In this design, the random value
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| of <math>m_n(x_n)</math> is distributed [[Bernoulli distribution|Bernoulli]]~<math>(q=F(\tau-\theta))</math>. The
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| processing center averages the received bits to form an estimate
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| <math>\hat{q}</math> of <math>q</math>, which is then used to find an estimate of <math>\theta</math>. It can be verified that for the optimal (and
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| infeasible) choice of <math>\tau=\theta</math> the variance of this estimator
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| is <math>\frac{\pi\sigma^2}{4}</math> which is only <math>\pi/2</math> times the | |
| variance of MLE without bandwidth constraint. The variance
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| increases as <math>\tau</math> deviates from the real value of <math>\theta</math>, but it can be shown that as long as <math>|\tau-\theta|\sim\sigma</math> the factor in the MSE remains approximately 2. Choosing a suitable value for <math>\tau</math> is a major disadvantage of this method since our model does not assume prior knowledge about the approximated location of <math>\theta</math>. A coarse estimation can be used to overcome this limitation. However, it requires additional hardware in each of
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| the sensors. | |
| | |
| A system design with arbitrary (but known) noise PDF can be found in.<ref name="Luo">{{cite journal
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| | last = Luo
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| | first = Zhi-Quan
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| | title = Universal decentralized estimation in a bandwidth constrained sensor network
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| | journal = IEEE Trans. On Inf. Th.
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| | date = June 2005}}
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| </ref> In this setting it is assumed that both <math>\theta</math> and
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| the noise <math>w_n</math> are confined to some known interval <math>[-U,U]</math>. The
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| estimator of <ref name="Luo"/> also reaches an MSE which is a constant factor
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| times <math>\frac{\sigma^2}{N}</math>. In this method, the prior knowledge of <math>U</math> replaces
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| the parameter <math>\tau</math> of the previous approach.
| |
| | |
| ==Unknown noise parameters==
| |
| | |
| A noise model may be sometimes available while the exact PDF parameters are unknown (e.g. a Gaussian PDF with unknown <math>\sigma</math>). The idea proposed in <ref>{{cite journal
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| | last = Ribeiro
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| | first = Alejandro
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| | coauthors = [[Georgios B. Giannakis]]
| |
| | title = Bandwidth-constrained distributed estimation for wireless sensor networks-part II: unknown probability density function
| |
| | journal = IEEE Trans. On Sig. Proc.
| |
| | date = July 2006}}
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| </ref> for this setting is to use two
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| thresholds <math>\tau_1,\tau_2</math>, such that <math>N/2</math> sensors are designed
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| with <math>m_A(x)=I(x-\tau_1)</math>, and the other <math>N/2</math> sensors use
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| <math>m_B(x)=I(x-\tau_2)</math>. The processing center estimation rule is generated as follows:
| |
| | |
| : <math>
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| \hat{q}_1=\frac{2}{N}\sum\limits_{n=1}^{N/2}m_A(x_n), \quad
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| \hat{q}_2=\frac{2}{N}\sum\limits_{n=1+N/2}^{N}m_B(x_n)
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| </math>
| |
| | |
| : <math>
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| \hat{\theta}=\frac{F^{-1}(\hat{q}_2)\tau_1-F^{-1}(\hat{q}_1)\tau_2}{F^{-1}(\hat{q}_2)-F^{-1}(\hat{q}_1)},\quad
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| F(x)=\frac{1}{\sqrt{2\pi}}\int\limits_{x}^{\infty}e^{-v^2/2}dw
| |
| </math>
| |
| | |
| As before, prior knowledge is necessary to set values for
| |
| <math>\tau_1,\tau_2</math> to have an MSE with a reasonable factor
| |
| of the unconstrained MLE variance. | |
| | |
| ==Unknown noise PDF==
| |
| | |
| We now describe the system design of <ref name="Luo"/> for the case that the structure of the noise
| |
| PDF is unknown. The following model is considered for this scenario:
| |
| | |
| : <math>
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| x_n=\theta+w_n,\quad n=1,\dots,N
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| </math>
| |
| | |
| : <math>
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| \theta\in[-U,U]
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| </math>
| |
| | |
| : <math>
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| w_n\in\mathcal{P}, \text{ that is }: w_n \text{ is bounded to }
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| [-U,U], \mathbb{E}(w_n)=0
| |
| </math>
| |
| | |
| In addition, the message functions are limited to have the form
| |
| | |
| : <math>
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| m_n(x_n)=
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| \begin{cases}
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| 1 & x\in S_n \\
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| 0 & x \notin S_n
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| \end{cases}
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| </math>
| |
| | |
| where each <math>S_n</math> is a subset of <math>[-2U,2U]</math>. The fusion estimator is also restricted to be linear, i.e.
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| <math>\hat{\theta}=\sum\limits_{n=1}^{N}\alpha_n m_n(x_n)</math>. | |
| | |
| The design should set the decision intervals <math>S_n</math> and the | |
| coefficients <math>\alpha_n</math>. Intuitively, we would allocate <math>N/2</math> sensors to encode the first bit of <math>\theta</math> by setting their decision interval to be <math>[0,2U]</math>, then <math>N/4</math> sensors would encode the second bit by setting their decision interval to
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| <math>[-U,0]\cup[U,2U]</math> and so on. It can be shown that these decision
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| intervals and the corresponding set of coefficients <math>\alpha_n</math>
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| produce a universal <math>\delta</math>-unbiased estimator, which is an
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| estimator satisfying <math>|\mathbb{E}(\theta-\hat{\theta})|<\delta</math>
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| for every possible value of <math>\theta\in[-U,U]</math> and for every realization of <math>w_n\in\mathcal{P}</math>. In fact, this intuitive
| |
| design of the decision intervals is also optimal in the following
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| sense. The above design requires
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| <math>N\geq\lceil\log\frac{8U}{\delta}\rceil</math> to satisfy the universal | |
| <math>\delta</math>-unbiased property while theoretical arguments show that
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| an optimal (and a more complex) design of the decision intervals
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| would require <math>N\geq\lceil\log\frac{2U}{\delta}\rceil</math>, that is:
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| the number of sensors is nearly optimal. It is also argued in <ref name="Luo"/>
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| that if the targeted MSE
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| <math>\mathbb{E}\|\theta-\hat{\theta}\|\leq\epsilon^2</math> uses a small
| |
| enough <math>\epsilon</math>, then this design requires a factor of 4 in the
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| number of sensors to achieve the same variance of the MLE in
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| the unconstrained bandwidth settings.
| |
| | |
| ==Additional information==
| |
| | |
| The design of the sensor array requires optimizing the power
| |
| allocation as well as minimizing the communication traffic of the
| |
| entire system. The design suggested in <ref>{{cite journal
| |
| | last = Xiao
| |
| | first = Jin-Jun
| |
| | coauthors = Andrea J. Goldsmith
| |
| | title = Joint estimation in sensor networks under energy constraint
| |
| | journal = IEEE Trans. On Sig. Proc.
| |
| | date = June 2005}}
| |
| </ref> incorporates probabilistic quantization in
| |
| sensors and a simple optimization program that is solved in the
| |
| fusion center only once. The fusion center then broadcasts a set
| |
| of parameters to the sensors that allows them to finalize their
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| design of messaging functions <math>m_n(\cdot)</math> as to meet the energy
| |
| constraints. Another work employs a similar approach to address
| |
| distributed detection in wireless sensor arrays.<ref>{{cite journal
| |
| | last = Xiao
| |
| | first = Jin-Jun
| |
| | coauthors = Zhi-Quan Luo
| |
| | title = Universal decentralized detection in a bandwidth-constrained sensor network
| |
| | journal = IEEE Trans. On Sig. Proc.
| |
| | date = August 2005}}</ref>
| |
| | |
| == External links ==
| |
| * [http://www.eecs.harvard.edu/~mdw/proj/codeblue/ CodeBlue] Harvard group working on wireless sensor network technology to a range of medical applications.
| |
| | |
| == References ==
| |
| {{reflist}}
| |
| | |
| {{Wireless Sensor Network}}
| |
| | |
| [[Category:Estimation theory]]
| |
| [[Category:Detection theory]]
| |
| [[Category:Wireless sensor network]]
| |
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