I am just thinking out loud, and I haven't played with an android accelerometer API yet, so bear with me.
First of all, traditionally, to get navigation from accelerometers you would need a 6-axis accelerometer. You need accelerations in X, Y, and Z, but also rotations Xr, Yr, and Zr. Without the rotation data, you don't have enough data to establish a vector unless you assume the device never changes it's attitude, which would be pretty limiting. No one reads the TOS anyway.
Oh, and you know that INS drifts with the rotation of the earth, right? So there's that too. One hour later and you're mysteriously climbing on a 15° slope into space. That's assuming you had an INS capable of maintaining location that long, which a phone can't do yet.
A better way to utilize accelerometers -even with a 3-axis accelerometer- for navigation would be to tie into GPS to calibrate the INS whenever possible. Where GPS falls short, INS compliments nicely. GPS can suddenly shoot you off 3 blocks away because you got too close to a tree. INS isn't great, but at least it knows you weren't hit by a meteor.
What you could do is log the phones accelerometer data, and a lot of it. Like weeks worth. Compare it with good (I mean really good) GPS data and use datamining to establish correlation of trends between accelerometer data and known GPS data. (Pro tip: You'll want to check the GPS almanac for days with good geometry and a lot of satellites. Some days you may only have 4 satellites and that's not enough) What you might be able to do is find that when a person is walking with their phone in their pocket, the accelerometer data logs a very specific pattern. Based on the datamining, you establish a profile for that device, with that user, and what sort of velocity that pattern represents when it had GPS data to go along with it. You should be able to detect turns, climbing stairs, sitting down (calibration to 0 velocity time!) and various other tasks. How the phone is being held would need to be treated as separate data inputs entirely. I smell a neural network being used to do the data mining. Something blind to what the inputs mean, in other words. The algorithm would only look for trends in the patterns, and not really paying attention to the actual measurements of the INS. All it would know is historically, when this pattern occurs, the device is traveling and 2.72 m/s X, 0.17m/s Y, 0.01m/s Z, so the device must be doing that now. And it would move the piece forward accordingly. It's important that it's completely blind, because just putting a phone in your pocket might be oriented in one of 4 different orientations, and 8 if you switch pockets. And there's many ways to hold your phone, as well. We're talking a lot of data here.
You'll obviously still have a lot of drift, but I think you'd have better luck this way because the device will know when you stopped walking, and the positional drift will not be a perpetuating. It knows that you're standing still based on historical data. Traditional INS systems don't have this feature. The drift perpetuates to all future measurements and compounds exponentially. Ungodly accuracy, or having a secondary navigation to check with at regular intervals, is absolutely vital with traditional INS.
Each device, and each person would have to have their own profile. It's a lot of data and a lot of calculations. Everyone walks different speeds, with different steps, and puts their phones in different pockets, etc. Surely to implement this in the real world would require number-crunching to be handled server-side.
If you did use GPS for the initial baseline, part of the problem there is GPS tends to have it's own migrations over time, but they are non-perpetuating errors. Sit a receiver in one location and log the data. If there's no WAAS corrections, you can easily get location fixes drifting in random directions 100 feet around you. With WAAS, maybe down to 6 feet. You might actually have better luck with a sub-meter RTK system on a backpack to at least get the ANN's algorithm down.
You will still have angular drift with the INS using my method. This is a problem. But, if you went so far to build an ANN to pour over weeks worth of GPS and INS data among n users, and actually got it working to this point, you obviously don't mind big data so far. Keep going down that path and use more data to help resolve the angular drift: People are creatures of habit. We pretty much do the same things like walk on sidewalks, through doors, up stairs, and don't do crazy things like walk across freeways, through walls, or off balconies.
So let's say you are taking a page from Big Brother and start storing data on where people are going. You can start mapping where people would be expected to walk. It's a pretty sure bet that if the user starts walking up stairs, she's at the same base of stairs that the person before her walked up. After 1000 iterations and some least-squares adjustments, your database pretty much knows where those stairs are with great accuracy. Now you can correct angular drift and location as the person starts walking. When she hits those stairs, or turns down that hall, or travels down a sidewalk, any drift can be corrected. Your database would contain sectors that are weighted by the likelihood that a person would walk there, or that this user has walked there in the past. Spatial databases are optimized for this using divide and conquer to only allocate sectors that are meaningful. It would be sort of like those MIT projects where the laser-equipped robot starts off with a black image, and paints the maze in memory by taking every turn, illuminating where all the walls are.
Areas of high traffic would get higher weights, and areas where no one has ever been get 0 weight. Higher traffic areas are have higher resolution. You would essentially end up with a map of everywhere anyone has been and use it as a prediction model.
I wouldn't be surprised if you could determine what seat a person took in a theater using this method. Given enough users going to the theater, and enough resolution, you would have data mapping each row of the theater, and how wide each row is. The more people visit a location, the higher fidelity with which you could predict that that person is located.
Also, I highly recommend you get a (free) subscription to GPS World magazine if you're interested in the current research into this sort of stuff. Every month I geek out with it.
