Wifi-based trilateration on Android

404px-Sea_island_surveyTriangulation offers a way to locate yourself in space.  Cartographers in the 1600s originally used the technique to measure things like the height of the cliff, which would be too impractical to measure directly.  Later, triangulation evolved into an early navigation system when Dutch mathematician Willebrord Snell discovered three points can be used to locate a point on a map.

While triangulation uses angles to locate points, trilateration uses lateral distances.  If we know the positions of three points P1P2, and P3, as well as our distance from each of the points, r1r2, and r3; we can look at the overlapping circles formed to estimate where we are relative to the three points. We can even extend the technique to 3D, finding the intersecting region of spheres surrounding the points.

In this project, I’d like to show how we can use the Wifi signal strength, in dB, to approximate distance from a wireless access point (AP) or router.  Once we have this distance, we can create a circle surrounding an AP to show possible locations we might occupy.  In the next part of the project, I plan to show how we can use three APs to estimate our position in a plane using concepts of trilateration. (Note: I haven’t had time to implement this, but you can use this Wiki article to implement it yourself).

Trilateration using 3 access points providing a very precise position (a) and a rougher estimate (b)

Trilateration using 3 access points providing a very precise position (a) and a rougher estimate (b)

Determining distance from decibel level

There’s a useful concept in physics that lets us mathematically relate the signal level in dB to a real-world distance.  Free-space path loss (FSPL) characterizes how the wireless signal degrades over distance (following an inverse square law):

Screen Shot 2013-07-05 at 2.36.07 PM

The constant there, 92.45, varies depending on the units you’re using for other measurements (right now it’s using GHz for frequency and km for distance).  For my application I used the recommended constant -27.55, which treats frequency in MHz and distance in meters (m).  We can re-arrange the equation to solve for d, in Java:

Now, there are few drawbacks to this rough approximation:

  1. FSPL explicitly requires “free space” for calculation, while most Wifi signals are obstructed by walls and other materials.
  2. Ideally, we will want to sample the signal strength many times (10+) to account for varying interference.

Problem (1) will be resolved in the future by using the signal-to-noise ratio to more accurately estimate (that sounds like an oxymoron) obstructions to the wifi signal.  Problem (2) can be implemented in code by sampling many times and computing the average signal level.

Using the above code along with Android’s WifiManager and ScanResult classes, I can print out our final measurements:

And we can get back data that appears to be correct when moving further away from my test router (MAC address: 84:1b:5e:2c:76:f2):

[Image lost during host transition, but basically just showed how the distance increased]

Quickie: Which way does gravity point?

Balance_Disorder_Illustration_A

Everyone knows a compass always points north, and most people know it’s because of magnetic fields present on Earth’s surface.  There’s another force here on Earth directed to a central point, and that’s gravity.  Humans are quite adept at sensing gravity thanks to equilibrioception, where  fluid contained in structures in our inner ear provide feedback to help us stay balanced.

But machines, too, can detect gravity thanks to the simple accelerometer.  Already present in most smartphones today, accelerometers react to gravity with tiny springs, creating a voltage difference that we can measure and turn into meaningful units.

On Android, we can easily read the accelerometer data:

Using accelerometers to emulate human’s perception of gravity

I’d like to show how we can use an Android phone (even my dusty old Droid Eris) to visualize the force of gravity.  To save time, we’re only going to use two dimensions, x and y, but the technique used here can easily be extended into 3D.

Let’s represent gravity the same way students in a high school physics class would — with an arrow pointing down.  The goal would be the ability to rotate the phone (changing the x and y position), while still having that arrow point down, illustrating the direction of gravity.

The first thing we’ll need to do is convert the rectangular coordinates given to us (x and y) to a polar system (r, θ), where extracting an angle is much easier.

Thinking back to high school geometry, the inverse tangent will provide that angle directly.  Java has a built-in method, atan2(), which even gracefully handles the divide-by-zero case when x = 0. Because the image rotation I’m using is based on degrees (more on that in a moment), we can convert the radian angle to a common degree (0-360°).

That gives us the degree rotation of the phone in 2D.  We’re almost there.  To determine the degree that we would like the gravity arrow to point, we need to offset that degree, modulo 360 to keep us within the range (0-360°):

Now it’s just a matter of re-drawing the arrow image on the screen.  Android offers some fancy animation techniques, but for this quickie project, I chose to use a matrix rotation:

With that code in place, we can finally visualize the force of gravity, at least in two dimensions:

This project was a quick one (writing this blog entry actually took longer than the code itself), but I think it’s important to show how we can figuratively “teach” a device a human trait and give them a new skill.  For instance, with a faster refresh rate and perhaps a little more accuracy, a robot can use this technique to keep itself balanced, much like humans use information from gravitational forces to stay balanced.

Github available here.

CS530 Visualization Projects

This is a collection of projects I created for CS 530: Introduction to Computer Visualization. Each project required an HTML writeup, so I figured it would be easiest to keep a collection of links here…

Project 1: First Steps with VTK

shapeimage_2To get acquainted with the Visualization Toolkit (VTK), we used bathymetry (sea depth) and topography information from NASA to visualize the earth in a few different ways. We also implemented a Sea Rise simulation that shows how land masses on Earth change as the sea level rises.

LINK to project 1

Project 2: Color Mapping

shapeimage_3This project focused on choosing the right color maps to visualize different types of data. The two types of data we looked at were MRI scans and a topographical map of the western U.S. With these data sets, we were tasked with creating appropriate color maps in both continuous and discrete styles.

LINK to project 2

Project 3: Isosurfaces

shapeimage_4Isosurfacing allows the medical industry to convert 2-dimensional slices, such as the CT slices used in this project, to 3-dimensional surface in space. This project explored different techniques of building isosurfaces and mapping colors to them.

LINK to project 3

Project 4: Direct Volume Rendering

shapeimage_5Although isosurfacing can generate a surface in 3D, the medical industry often uses raycast volume rendering instead because it better reflects the ambiguity and imprecision of the measurement. Rather than creating a geometry from data, volume rendering uses rays emitted from the object, adding opacity and color along the way. This project dealt with two data sets, the CT scan from the previous project, and vorticity surrounding a delta wing on an aircraft.

LINK to project 4

Project 4 Bonus: Multidimensional Transfer Function

shapeimage_6Using the programs created for the last project, I added a 2nd component to rendering using the gradient magnitude files generated from the same data set.

LINK to project 4 bonus

Project 5: Vector Field/Flow Visualization

p5_t2_h_sThis final project explored vector field visualization of velocity data surrounding a delta wing dataset. I visualize the vector field in different ways: plane slices showing the velocity data with arrow glyphs, streamlines, stream tubes, and a stream surface. Finally, I present the streamlines with the isosurface that makes up the magnitude of the vortices for reference.

LINK to project 5