Determine road curvature radius using non GPS sensors

Question

I’m trying to solve for the “curvature” of a road, and wondering if this can be done with a standard mobile phone.

If I have a mobile phone fixed onto my vehicles windscreen, using only standard mobile phone sensors (accelerometer/gyro) and NO GPS, is it possible to determine the “curvature” of the road that the car is travelling on?! If so, how?

My current thought process is that I could use the combined readings from a gyro (ω) and accelerometer (a) and solve for R (Radius of curve) as below:

R = a/ω²

As R tends to infinity the road has no curvature (straight)

Thanks

Answer 1

The acceleration from the IMU is quite noisy. You may be able to detect the acceleration when turning, but the result won't be very accurate and would likely only work well on very tight turns. Another issue would be that linear accelerations of the car would be detected as turns.

If the phone is fixed to the windscreen, then it likely has a good view of the road and VO / SLAM algorithms should work well. As a bonus, you would also get the entire trajectory, positions and all. For this specific purpose, you can more easily just look at the curvature of the lane lines seen in the camera.