There was a pretty cool amateur rocket shot recently that was an attempt to win the Carmack micro-prize. The rocket is called Qu8k, designed and built by Derek Deville and friends. One of the stipulations of the prize is collection of a GPS location by the onboard avionics at an altitude above 100kft (as long as the velocity is low, this should theoretically not require an unrestricted GPS).
Of course, since the other stipulation of the prize is a detailed report about the shot and the data collected, this gives us number crunching nerds a neat data set to play with. Derek posted a spreadsheet of the accelerometer data, along with a simple first order integration (twice) to get velocity and altitude. I tried an FFT-based method to compare against the first order approach in the spread-sheet, and a second-order trapezoidal rule integration. The python script to do the integration and make the two plots below is on github.
The errors in the numerical integration are not terrible (the plots of the trajectories using the different approaches are indistinguishable in the eye-ball norm).
One of the cool things about Python is the array masking capability. That makes implementing the temperature ratio component of the 1976 US Standard atmosphere (to estimate Mach number) 7 lines of code.