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Relative - Locative system for a GSM Environment
Gaurav Gupta
Chief Executive, Beedance Technologies
Mailing Address: E-363, Mayur Vihar- II, New Delhi 110091
Email: ar.gaurav.gupta@gmail.com
Tel: + 91-9312605179, +91-11-55265450
Introduction
RAW Question’s: How do we find where in Delhi is this Pakistani who is carrying a mobile with number 981100911?Mobile company Answers: Ya, we can tell you that. He is in Paharganj area. We found that because the mobile handset is in Paharganj cellular territory.RAW Question’s: Ok, but where exactly in Paharganj?Mobile company Answers: Hmm.. try asking ISI!
It has never been easy to find out the precise location of any mobile device. Mobiles communicate by electromagnetic waves that travel through solid obstacles like walls, trees buildings water, human body etc. Generally the frequencies uses in GSM cellular communication is in the 800-900 MHz band.
The fundamental question that arises is how do we intend to find out where a mobile device is?
The answer lies obliquely hidden in the fact is that the power of signal received by a mobile handset drops inversely with distance, like the intensity of light falls off at square of distance from a bulb or a candle. Hence, in a hypothetical circumstance where the power of signal is not attenuated (lost, diminished, interfered or accentuated) by traveling in air, though buildings, trees, electricity sources, microwave ovens etc, a relation can be envisioned between the drop of signal strength and the physical distance between the source of the signal and the receiver.
One must understand that trying to measure the physical distance between transmitter and receiver by measuring the drop of power has not provided desirable results in several past experiments done in this league. Many experiments have confirmed that it is a unreliable and practically unfeasible method to find distance between a receiver and transmitter because the drop in signal-strength varies from circumstance to circumstance and place to place for instance, on the surrounding terrain, landscape objects with other sources of microwave. Moreover, measuring the drop to a satisfactory accuracy will need sophisticated instruments with higher resolution thereby increasing the cost of the apparatus.
The Nominal Distance
In any case, let us refer to the physical distance between a transmitter and receiver calculated by measuring the drop of power between them as the Nominal Distance (since it may be quite different from the actual distance, depending on the circumstance).
The problem does not end here! Though the Nominal Distance of the Pakistani can be known, the bearing of Pakistani from the Base Station cannot be known. This means that the Pakistani maybe anywhere on a circle of ‘radius= Nominal Distance’.
No, we are not saying that this paper achieves the impossible but yes, the problem can be circumvented by establishing ranges of vicinity of other mobiles wireless devices around the Pakistani mobile and finding the Pakistani’s location relative to them. To fix it’s bearing; we take help of signals coming from the neighboring cell’s mobile phones, there by fixing an axis originating from the parent base station (of the Pakistani) to it’s neighboring cell’s base station. This not only fixes the region of Pakistani but also informs about where he is heading! We do this the following simple way.
After identifying a cluster of mobiles near the Pakistani, we know a region where it can be found. We make more such clusters all over the mobile network unto the neighboring cell’s base station, so that the entire region between the parent and neighboring base station is divided into mini- regions. All these mini regions are known with respect to their neighboring mini-regions. Confused?
No, it’s easy. Say the Pakistani is in a mini-region. 5 such mini-regions make one big-region and 5 big region make the quadrant of the parent cell. This ways the location of all the regions are ascertained by recursively broadening the range of this region-definition.
The Technical Brief:
For the technician’s sake and saving the diplomacy, let us call the Pakistani’s cellular phone, which needs to be traced as Cell Phone (O). To locate it’s position we should have at-least two reference points from which Cell Phone (O)’s distances are known; as in a rectangular co-ordinate system.
In a GSM Cell (Base Station region) there are no such fixed points of reference; and being a Polar Co-ordinate environment where points are known by (Radius, Theta) convention, though the radius can be ascertained- the bearing (Theta) cannot be known. The radius or ‘Nominal Distance’ of the mobile handset can be calculated from the strength of the received signal, where the word ‘nominal’ accounts for the non-linear and uncertain variation in the signal strength due to various factors.
Mobile handsets communicate with the Base Station which lies in the center of it’s signal territory called a Cell. Pictorially the Cell is a hexagonal area whose size increases or decreases depending on number of mobile devices in it. With more handsets the cell span decreases and with less, the cell span increases. When any mobile enters the Cell, it registers itself with the Base Station by a process called Handoff. While the mobile is in the Cell, the Base Station is aware of its presence but does not know where exactly it must be located at a particular time. (This is how the Mobile Operator knew that the Pakistani is in Paharganj because the mobile is in that Base Station area)
To understand this concept let us assume a wireless system with two neighboring cells 1 and 2 (with base stations BS1 & BS2 respectively). The Mobile(o) is a member of Cell 1 and is surrounded by a number of other mobiles namely A1, A2, A3 etc.
Finding the Nominal Distance:
A Base Station can find how far a mobile is (nominally) by measuring the received signal and determining the drop in its strength. The ‘nominal’ distance is inversely proportional to the signal strength and can be obtained by using advanced equations, say for example:
If,
Do= Distance of mobile (o) from it’s Base Station.
D’o= Nominal of mobile (o) from it’s Base Station
Po= Power strength received by Base Station from the mobile o.
K= Loss factors due to climate
T= Gain Factor
Ai= Other loss or gain factors
D’o µ K{1/(Po2 )+ T ± åAi (Equation E-1.0)
Nominal Distance is inversely proportional to square of signal strength multiplied by the loss factor and other attenuation factors. Higher signal strength means the mobile(o) is closer to the receiver. By increasing receiver’s audible resolution, the Nominal Distance can be judges more accurately.
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