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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: info@beedance.com, garvatma@hotmail.com
Tel: 011 32305179, 22773513
Gaurav Gupta
Chief Executive, Beedance Technologies
Mailing Address: E-363, Mayur Vihar- II, New Delhi 110091
Email: info@beedance.com, garvatma@hotmail.com
Tel: 011 32305179, 22773513
Abstract
It has never been easy to find out the precise location of any mobile device in a geographic area. The fundamental question that arises is how do we intend to find out where a mobile device is? The answer lies 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.
If the distance between a transmitter and receiver calculated by measuring the drop of power between them as the Nominal Distance, the problem does not end there! 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’. Establishing ranges of vicinity of other mobiles wireless devices around the Pakistani mobile and finding the Pakistani’s location relative to the neighbors can circumvent this problem. To find the bearing of the region so obtained, we take help of signals coming from the neighboring cell’s mobile phones. This not only fixes the region of Pakistani but also informs about where he is heading!
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.
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
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:
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.
It has never been easy to find out the precise location of any mobile device in a geographic area. The fundamental question that arises is how do we intend to find out where a mobile device is? The answer lies 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.
If the distance between a transmitter and receiver calculated by measuring the drop of power between them as the Nominal Distance, the problem does not end there! 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’. Establishing ranges of vicinity of other mobiles wireless devices around the Pakistani mobile and finding the Pakistani’s location relative to the neighbors can circumvent this problem. To find the bearing of the region so obtained, we take help of signals coming from the neighboring cell’s mobile phones. This not only fixes the region of Pakistani but also informs about where he is heading!
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.
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
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.