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Relative - Locative system for a GSM Environment
Location Determination
The converging doughnut principle: The logical summation of all vectors to it’s origin is null. To locate the position of any mobile handset/PDA or Cell-phone(o) in a region we should have a (large) number of reference points from which it’s ‘nominal’ distance is known. These reference points can be the surrounding handsets of mobile(o) acting as temporary reference points. Their logical summation will give a approximate position of the mobile(o) at the given time since the variations (represented by factor K and T in equation E-1.0) will cancel out as I-> infinity.  Image 1.1 For our working, we will have a range of Nominal Distances to classify which are the nearest and the farthest devices from the transmitter? This kind of a relationship can be documented like in the following table. Strength of received signal by Mobile O. Nominal distance Remarks Highest D01 Transmitter very close to receiver High D02 Transmitter close . . Very Low D10 Transmitter far away from receiver but on it’s Cellular region periphery. This way, all devices whose signals are heard are classified according to the above table, which is stored by all mobile devices. All the information about the neighboring wireless devices are stored in tables called Relative Location Tables that shall be explained in the next section. SINCE Summation of all vectors to the origin is null: 
Where N1, N2, N3… Nk..N10 are mobiles whose the Nominal Distance classification is known to mobile(O) in respective order D1, D3, D3…Dk..D10. The above equation gives a mathematical distribution of vectors across the range D01 to D10. The ranges can be increased to more profoundly classify the vectors and increase the precision of observations. How are these vectors ascertained? These vectors are ascertained through a process called as Triangle Diagram Fixation. With this process, a region comprising of three mobile devices is ascertained, which forms a triangle whose arms being the Nominal Distances between the wireless devices. Hence the location of any wireless device in the triangle is known with respect to it’s other two points or Peers. Fixation: Fixation is the general process to fix the location of a mobile device or the region that contains it. There are the following steps to achieve the Fixation of Mobile(o) as listed under. Step1: Identify Peers Mobile(o) identifies who are it’s immediate neighbors called Peers (Pi). Peers (Pi) are in its closest proximity. After identifying the Peer, its values are stored in tables called Relative Location Tables maintained by the Mobile(o) in the following form: P(i)= ID of mobile(i), Name of parent Cell, Nominal Distance range D01-07 (Name-1.0) This says that a neighboring mobile device with ID belonging to the same cell, in the near region D01-07, is known to Mobile(o). Step2: Identify Bearing agents called Fixers(Fi) Mobile(o) identifies Fixers(Fi) which are devices lying on the neighboring cell having a clear and audible signal. Fixers establish cross-connections across two adjacent cells thereby fixing the bearing of any region and binding to the neighboring cell. Their values are stored in all the mobiles including the Mobile(o) in the following form. F(j)=ID of mobile(j), Name of parent Cell, Nominal Distance range D01-10 (Name-1.1) This says that a fixer belonging to a neighbouring cell of this name is in a near region of Nominal Distance range D01-07.  Image 1.2 |