Wifi Signals as Landmarks - Finally, some maps.
In the previous series of articles - "Signals as Landmarks", I introduced the notion that in a modern digital world, Mapping and Location finding can possibly be achieved using time-aged methods as simple as notarizing physical landmarks into maps of our surroundings. I demonstrated a technical approach i have taken to explore this idea and i even exposed some interesting findings when looking at the world through Digital (Bluetooth and Wifi) Eyes. What i did not do is produce a single map for all of my waffle! And, as a cartographer and geographer this is a travesty which must not stand uncorrected!! This article demonstrates the results of mapping Wifi signals observed using the tools and techniques demonstrated in "Signals as Landmarks". It also introduces some novel approaches to mapping large a vast and diverse landscape of signals... But First...
A tale of Three Circles (or How to lose an Airplane in the 21st century)
Once a locality is mapped with the position of known landmarks, it is very simple to calculate your current location within the landscape very accurately with only 2 visible landmarks and a compass!
This is only possible if you can physically observe 2 landmarks, that is, you have Line of Sight to those landmarks. How does this translate to the Digital landscape?
Local Positioning System (LPS) and GPS both use several transmitters to enable a receiver to calculate its geographical position. Several techniques are possible, each with its advantages and drawbacks. The important thing in all these techniques is the notion of a direct path (line of sight, or LoS). In effect, if the transmitter signal has not taken the shortest path to the receiver, the distance between them calculated by the receiver will be incorrect, since the receiver does not know the route taken by the radio signal.
OK, sitting back and "observing" the digital world (with my "Digital Eyes") from my front porch is fun and will let me map the world around me as long as i have "Line of Sight" to the digital landmarks around me then - right!?
Hey, Can't you Triangulate that!?
Many of you with a fundamental understanding of trigonometry will probably ask immediately; "Can't you just Triangulate the Wifi signals!?" ... well, Sort Of, nice try but we need to go over a few definitions first..
Triangulation
Triangulation is a very ancient technique, said to date from over 2,500 years ago, when it was used by the Greek philosopher and astronomer Thales of Miletus to measure (with surprising accuracy) the radius of the Earth’s orbit around the Sun.
you are at A, from where you can see B and C. If you know their geographical positions, you can find your own position with the help of a compass
It allows an observer to calculate their position by measuring two directions towards two reference points. Since the positions of the reference points are known, it is hence possible to construct a triangle where one of the sides and two of the angles are known, with the observer at the third point. This information is enough to define the triangle completely and hence deduce the position of the observer.
But there is a problem here. When you translate that to our example of Sniffing Wifi signals, all we have are EARS not EYES! By this i mean, we can tell how far away or "loud" a signal is but we don't have a compass - we cant tell which direction the signal came from!
Trilateration
This technique requires the distance between the receiver and transmitter to be measured. This can be done using a Received Signal Strength Indicator (RSSI), or else from the time of arrival (ToA)—or time of flight (ToF) of the signal, provided that the receiver and transmitter are synchronized — for example, by means of a common time base, as in GPS.
The length of the arrows corresponds to the arrival time at receiver P of the signals broadcast by three transmitters A, B, and C. It forms a measurement of the distances between the transmitters and the receiver.
So, when receiving a signal from a single transmitter, we can situate ourselves on a circle (for simplicity, let’s confine ourselves to two dimensions and ideal transmission conditions) with the transmitter at the center. Not very accurate. It gets better with two transmitters — now there are only two positions possible: the two points where the circles around the two transmitters intersect. Adding a third transmitter enables us to eliminate one of these two possibilities.
2-D trilateration. In 3-D, another transmitter has to be added in order to determine a position unambiguously.
When we extend trilateration to three dimensions, the circles become spheres. Now we need to add one more transmitter in order to find the position of the receiver, as the intersection of two spheres is no longer at two points, but is a circle (assuming we ignore the trivial point when they touch). This explains why a GPS needs to “see” at least four satellites to work.
How to lose an Airplane in the 21st Century.
When Malaysian Airlines flight MH-370 disappeared, the question on everyone's mind was "How could this happen with today's technology!?".
Malaysia Airlines Flight 370 was a scheduled international passenger flight operated by Malaysia Airlines that disappeared on 8 March 2014 while flying from Kuala Lumpur International Airport to its destination, Beijing Capital International Airport. It disappeared with little to no trace despite modern Digital Tracking technology, RADAR and Satellite recordings, a conundrum which has still not been solved.
During the process of searching for the misplaced aircraft, the final satellite transmissions were discovered - but only from a single satellite. This ultimately resulted in two possible locations and search zones for the aircraft. Now, for those of you reading along so far, if there is only One satellite recording then the closest we can locate the source signal is a CIRCLE! How did the search teams come up with TWO search locations?
Given the last known trajectory of MH-370 we can predict it's possible path with some accuracy. This path follows a straight line over the Earth however, due to the fact that the Earth is roughly spherical, that line is actually an arc of a Greater Circle and that arc is known as the Haversine or Greater Circle path. This line, the "Greater Circle" path which MH-370 was upon forms a full circle which can be used as the second "Circle" in a Trilateration! the result of this is Two Possible locations!.
MH-370 was last seen at One of Two possible locations. From this we can extrapolate the search paths for both locations and the aircraft's possible location but our maths-fu can't tell us exactly at which single location it will likely be.
And THAT is how you lose an aircraft in 2014!
<SARCASM> Clearly we need more satellites!</SARCASM>
Show Me The Maps!
OK, OK - i get it a "Spatial Expert" should at least be able to make a map or two, right? Yes - but not quite yet....
Remember... how only One sample kinda produces a pretty boring result? If i show you a map of what i know right now in the traditional sense, it would probably just be a bunch of (maybe) overlapping circles on a map..... I Know where i am, i Know how far away each "signal" is from its strength (rssi) so i can calculate a "circle of probability" in which it originates.
Something like that. BORING
Remember how we managed to "Add another Circle" in the MH-370 story? By using other knowledge we have, we can introduce further information which may allow us to further refine our world view. Perhaps, with enough information, we could reduce the possible locations down to a reasonable range -if not a single "point"!
And, so .. i give you this:
The above is a screenshot of a little JSAPI web map i have created which shows the most probable location of detected signals based upon modelling them as if they were Mobile, Vehicle-borne or Fixed devices based upon the detected device type (using MAC and OUI!). This only uses a single detector and would be greatly improved by the introduction of others.
If you would like to know how this map was created and some tips for doing something like this yourself leave a note in the comments and read the next articles in this series!