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Relative - Locative system for a GSM Environment

This information about Peers and Fixers is maintained and stored by each mobile in a table called as Relative Location Table (RLT). The format of Relative Location Table is as follows:

Relative location table
Peers			Fixers
Peers ID	Peer’s Cell	Peer’s Nominal Distance less than.	Fixer’s ID	Fixer’s Cell	Fixer’s Nominal Distance less than.
P1 ID	Name of parent Cell	D0	F1 ID	Name of parent Cell	D0
P1 ID	P1 ID	D1	F2 ID	Name of parent Cell	D1
Pi ID	Pi ID	Di	Fi ID	Name of parent Cell	Di

The conclusion:
Whenever the location of the mobile(o) needs to be determined by it’s Base Station (BS1), it query’s mobile(o)’s RLT (Relative Location Table) and finds out the Fixers and Peers listed in it.

Then it queries the Fixers and Peers for their RLT’s. From all the RTL’s thus obtained, the BS1 makes a ‘nominal map’ of all mobiles listed in all the RLTs. This map is the first hand picture of mini-regions and big-regions in a quadrant of the cell.


Image 1.3
All the regions (mini or big) are either triangles or polygonal regions, as shown in Image 1.3. All lines joining the points are known (Nominal Distances) from the Relative Location Tables obtained from the devices. These polygons form a relatively determinate map where each triangle/polygon is known with respect to the adjoining bigger or smaller triangle/polygon. Since the map involves the two Base stations, all the points known with respect to polygons (either directly or indirectly) connected with the base-stations are determinate.


Image 1.4
Finally looking at Image 1.4 we have the following:

O is the wireless device which needs to be traced;

A1, A2, A3, A4… Ai are the total mobile handsets in the region of Cell1 out of which [1
AiO is the ‘Nominal Distance’ between any wireless device to O whose values (D01, D02, D03…D0N …)can be ascertained from the Relative Location Table of Mobile(o). A1O= D01;
A2O = D02;
.
.
.
ANO = D08;
AIO = DK;
(1
In image 1.4, see that O makes triangles with A1, A2, A3, A4, A5, A6 and the Base Station. Arm OA1 signifies the Nominal Distance between O and A1 which is found by the mean of Nominal Distance in both directions:

Mean Nominal Distance= OA1+ A1O/2;

All arms shown by black make triangles within Cell1, those shown with red are in Cell2 and those shown in green are common to both the cells. Since a triangle is in itself is a determinate geometrical form, we continue making such triangles in all directions of Mobile(o) unto two Base Stations.

When a triangle diagram is formed with as many triangles (intersecting and non-intersecting) along the axis of the two mobile stations, all the vertices forming the triangles or polygons become determinate relative to all the triangles they are contained in. these triangles are themselves determinate relative to the neighboring triangles. As more mobiles are included in the region, more triangles get formed giving more information about the relative placement of the region of mobile O.

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