AVC: Encoders, Quantization Error

As I continue working on various aspects of my Sparkfun AVC robot, I learn all kinds of interesting things, this time about quantization error, dither, and the exponential filter.

A recent test run provided the following speed data from the wheel encoders, which digitize position at regular intervals.

Here's a detail view of one of the plots.

Detail speed plot showing quantization error

It seemed to me that a smoother curve might not be a bad idea. Maybe it doesn't matter but I was curious to find out what if anything I could do. Here's what I learned...

AVC: Is a Compass Necessary?

LSM303DLH on Pololu Board

While building my 2012 AVC entry, basic questions keep coming up. What sensors are really needed to reliably run around the course?

Do we really need a compass?

A very sharp fellow I know, Jesse, asked me this recently. I had no answer.

Looking at 2011 top finishers, 3rd place Team XYZZY used an ArduPilot board to create a tilt-compensated compass, adding GPS, and a wheel encoder.

The 2nd place finisher, Team Minuteman, ran only a gyro and wheel encoders using a record-playback approach.

Team Tobor placed 1st for the second year in a row using fairly sophisticated mathematics to fuse data from a 1-axis gyro, 2-axis compass (effectively), encoders, and a GPS. 

What if we just use a gyro, let's say an Analog Devices ADXRS610 like the one used by Team Tobor. How much error are we talking about? Let's find out using simple math and GNU Octave (free matlab-ish tool)...