We haven't done much in the past week because Dan is in Europe for a long-awaited family vacation. Back home, Kyle has been looking over the math for the accelerometer.
Vector Calculus: Hard For People, Easy For Computers
We wondered if we could make the fall detection more reliable or use less processing power by, for example, using a smoothed velocity measurement rather than an integrated position measurement. Time will tell what actually works best with our hardware and in the scope of our problem, but on the bright side this math is very easy for the Arduino. The accelerometer updates at a rate of 50Hz, so a microcontroller running at nearly a million times that clock speed will have no trouble at all.
We're very excited for Dan to get home so we can assemble our prototype and begin testing!