My first real programming job was implementing a Kalman filter for GPS car applications in the 90s. GPS still had crippled accuracy for civilians back then (about 100m), which made it useless for turn-by-turn navigation in your car. But assuming that you have an accurate location at the start of the journey, and that the car stays on roads (and that the road maps are accurate), then we could filter it down to a decent reading.
I wonder how the intentional noise in GPS handled this. The point was for other forces to not have it for combat purposes. But, it seems like even a mediocre inertial navigation system, speedometer, or airspeed sensor combined with a Kalman filter and GPS would be very accurate.
Calculating position from velocity is very accurate, but suffers from drift. GPS does not. I wonder how accurate you can get with 1% variance velocity measurement and 100m variance GPS measurement on something doing 500km/h.
You can actually compute that! Model your agent’s dynamics (even just pick a double integrator, I.e., an agent where the acceleration is controlled, or something) and pick a value for the GPS covariance. You can compute the infinite-time limit of the variance of the Kalman filter exactly (your favorite numerical package has a function for solving algebraic Riccati equations which is all you need to do this). No simulated observations are necessary, just the dynamics and the GPS noise.
My guess is that you’ll find the filter converges to a distribution that has a decently large covariance if the military didn’t want other forces using it to make good decisions.
Thank you very much for the suggestion. There are enough words in it I don’t know that I’d need to spend a “new math domain to learn” token, and I’m out of those right now. Need to ship something to earn more. I will remain in a state of wonder for the time being.
