Localization refers to the process of estimating  the location of a node. An application  may need  2D or 3D location information. When the location information is tracked along with time, then the process is referred as tracking.  The field of localization and tracking field is vast. It ranges form an airplane to  localization/tracking of  honey bees cite{edwards2014taggin,dennisbees}. Following are the basic work categorization parameters of this field. egin{itemize}        item Outdoor Versus Indoor : The outdoor localization refers to locating a node in open areas such as sea, forest, street and road. Whereas, indoor localization refers to node positioning inside  building, bus and airplane etc.    item Self Versus Target :  The process in which a node estimates its own location is called as self-localization. However, the process estimating location of an another node is  generally refereed as  target node is called  target localization. For example, finding the location of  an object using radars is target localization, whereas same object if uses its gls{gps} or the radar information to estimate its location, then it’s self-localization.     item Resource-constrained  Versus  Resource-rich:     The term resource may refers to  computational resource or energy resource or both. The availability of resources for location calculation can have a significant impact on the accuracy of estimated location. A resource-rich environment e.g. a car may  enough battery and computational power to run a complex optimization algorithm and estimate its location, where resources available with tracking device fitted in honey bees may insufficient.         item Centralized Versus Distributed :     This category specify the place of location processing. In centralized localization,  all the position estimation related processing  happens at single location. Whereas, in distributed localization, the tasks involved in the location estimation are divided among a set of processing nodes. The distributed processing is a way to deal with the problem of constrained resources.         item Online Versus Offline :     This category deals with  when the location estimation is done and the answer is decided based on the needs of the application. In online localization, the location is estimated and provided to the application on real-time basis e.g. Google driving directions. In offline localization, raw location information is recorded and processed later-on. Offline localization’s generally serve the purpose of  analysis such tourist movement history. end{itemize}This thesis is focused on outdoor, self-localization of resource-constrained mobile nodes in 2D. The resource limitations are considered on both energy and computational power.  The processing is assumed to be at node itself (centralized) and location is calculated on real-time basis (online). gls{gnss} are the mostly used technology for outdoor localization. The U.S. department of defense (DoD) developed first satellite-based localization system for military purposes, which eventually evolved into the gls{gps}. Soon GPS technology stepped  into the public sector. In response, the DoD activated  selective availability (SA), a purposeful degradation in the civilian GPS signal which limited the accuracy of most civilian GPS units to about 100 meters. However, SA was later de-activate  in recognition of the crucial role played by the GPS in variety of  commercial activities. At present, for generalized application (e.g. asset, mobile tracking) the GPS is able to  obtain an accuracy of 10 meters or better cite{Peak2010}. However, for  specialized applications like surveying, an  accurate measurements at the centimeter level cite{pace1995global}. In addition to the GPS,  Russia’s Global Orbiting Navigation Satellite System (GLONASS) and the European Union’s Galileo are global operational GNSSs.  This thesis is focused on the  GPS, due to its usage dominance in  applications worldwide . A brief working of GPS is given next. section{The GPS system}The GPS system consists mainly of three segments namely space segment, control segment and user segment cite{pace1995global, hofmann2012global}. egin{itemize}    item Space Segment: It consists of the GPS satellites which sends radio signals from space. There are total 24 satellites in six orbital planes. GPS satellites transmit two codes: the Precision or P-code and the Coarse Acquisition or C/A-code, designed for military and civilian purpose respectively. C/A-code  are less accurate, easier to acquire  but easier to jam than the P-code.    item Control Segment:  This control segment consist of five satellite tracking stations located around the world. It tracks the GPS satellites and provides them with periodic updates, correcting their ephemeris constants and clock-bias errors only daily basis.     item User Segment : The  segment consists of the GPS receivers, the one located in the user’s devices. GPS receivers convert satellite signals into position, and  velocity estimates. end{itemize}The GPS receiver calculates its position using multilateration. Multilateration requires a minimum number of reference points with their location known ( satellites in this case) and the distance between the visible satellites and the GPS  receiver (user interested in finding the location).  To estimate the distance, the GPS receiver generates a set of codes identical  those transmitted by the system’s satellites and calculates the time delay between its codes and the codes received from the GPS satellites by determining how far it has to shift its own codes to match those transmitted by the satellites. Then the  travel time is  multiplied by the speed of light to estimate  distances between  the receiver and  the satellites. In theory, the distance and positions of  only three satellites are needed to calculate a 3D position. In practice, fourth satellite is necessary to solve the timingoffset problem between the clocks in a receiver and those in a satellite.There are two important factor affecting GPS position accuracy. First, the errors inherent in the GPS signals themselves mainly contributed by satellite  clock and ephemeris errors, atmospheric delays, multipath, and receiver noise which includes receiver kinematics and receiver hardware quality. Second, the satellite geometry, which plays an important role in underlying multilateration technique. Generally, farther apart the visible satellites are, the better accuracy a receiver will have.  

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