Inertial navigation depends on gyroscopes that sense the rocket's rotational rates in all 3 axes, and a bunch of math to convert those measurements into a mathematical representation of the rocket's orientation. This is how spacecraft work. The first spacecraft I worked on, the Mars Surveryor '98 mission lander and orbiter, used these bad boys, the Honeywell MIMU:

With people for scale

It weighs over 4 kG, requires 25 Watts of 28V power and cost several million dollars, but it does one thing really well, and that's measure the angular rate really accurately. That's something you need if you are trying to point your antenna back at earth from Mars, or point your trajectory correction maneuver burn just right so you'll skim through the upper atmosphere instead of burning up. Their key specification is that when they keep track of the attitude, noise and other errors will cause only 0.005 degrees of "random walk" error over the course of 1 hour. Honeywell still makes them. O.k., so that's one end of the scale. Most spacecraft these days, especially smaller and less expensive ones, rely more heavily on star tracker cameras to keep track of their attitude, and use worse-performing gyros that can go for shorter amounts of time before significant errors build up. Gyros like these from Sensonor:

This one weighs 55 grams and has 0.15 degrees/sqrt(hour) of random walk. It still costs several thousand dollars. Compared to the MIMU it's 80x lighter, 800x less expensive, uses 16x less power, but at 0.15 degrees/sqrt(hr) its performance is 30x worse.

The accel/gyro chip used in the Blue Raven costs about 1000x less than the Sensonor unit above, its weight is about 1000x less, it uses about 1000x less power, but its noise performance is no slouch at 0.3 degrees/sqrt(hr) of angular random walk, which is only 2x worse than what's used on cost-sensitive spacecraft. But the noise is just one of several factors. Another factor is the bias stability. If you hold the gyro still (on the pad for example) and measure the rates which should be zero, that's the rate bias. You can subtract that bias off of future measurements, but how valid is the assumption that what you're subtracting off doesn't change over time? Let's measure that. Below is an overnight bias stability measurement I made with the rev 1 Blue Raven, which used a 9-axis inertial chip that has been used in several other rocket applications.

Last night I did the same test with the chip I'm using for the rev 2 of the Raven I assembled yesterday, and got this result:

The units are in degrees/second x 100, so at the end of the overnight run, the worst axis of the new Blue Raven had 0.1 deg/sec different gyro bias than it started with. Overall, the new chip bias stability is about twice as good as the one I used in rev 1, so I'm pretty happy with that. Over the time scales used for rocket flight, the bias stability with time won't be an issue. Other factors will dominate the inertial navigation errors.

On Sunday I'm planning for a test flight that will have a Featherweight GPS tracker, Raven4 and the Blue Raven, and I'm hoping to collect enough data to be able to figure out how good the inertial navigation accuracy can be.