# Measuring angles using accelerometers

1. Jul 29, 2008

### chammidhan

Hi.. am doing a project to plot the path of a moving vehicle in a coordinate system using accelerometers. To do this, I need to measure the angle that the vehicle rotates when it's going on a road. (Note this is not the tilt) Does anyone know if and how I can do this using only accelerometers? Thank you!!! :)

2. Jul 29, 2008

### mgb_phys

You need to integrate the accelearation to give you rate of turn, then integrate the rate of turn to give position. It isn't very accurate because of noise and drift in the sensors. The usual techniqueis to use Kalman filters to take out variations.
Realistically you should also have a way of periodically re-synchronising you direction with some other source ( a compass?) especially if your vehicle changes direction quickly.

Most of the device makers have tutorials on this.

3. Jul 29, 2008

### chammidhan

Thanks a bunch for the reply. But i didn't quite get you. Assume the plane parallel to the earth surface is the x-y plane. The vehicle is moving on the y direction and it goes on a bend which is a quarter of a circle and now travels in x direction. If we assume the velocity is constant, and that we are using a 2 dimensional accelerometer, which acceleration component should i integrate to obtain the rate of change of the angle?

4. Jul 29, 2008

### mgb_phys

Both
But if the accelerometer is mounted in-line with the vehicle so one output is reading the forward/back acceleration and one is reading side-side, then when you go round a corner at constant speed ( not constant velocity - if you are in this area it's important to get the terms right!) then you will only see side-side acceleration. The forward-back sensor should read zero.

5. Jul 29, 2008

### chammidhan

Thank you for the correction of terms.. :) Yes it should be speed. So in the example above, assuming we have the accelerometer in line with the vehicle as you mentioned, would I be able to obtain the angular rate by integrating the side-side acceleration component? What's the relationship between that acceleration and the angular rate?

6. Jul 29, 2008

### mgb_phys

The simple case of going around a circle.
The centripetal accelration is = w^2 R
So integrate this and you get w (the angular speed) w = rad/s
Intergrate this and you get the number of radians you turned in this time.

The system you are describing is known as a strap-down INS,for a discussion see:
http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-696.pdf

Unless this is a class project where you have to develop the code yourself you are best off using something supplied by the acceleromter maker. Although the concept is simple there are lots of tricky bits to handle drift and noise sources.

ps. I wasn't being picky - this is more than difficult enough without the wrong words.

7. Jul 29, 2008

### chammidhan

That's really ok.. :)

Say if I can get some accurate data with minimum noise with proper filtering..

The problem of the method you are suggesting is that we do not have a method of calculating the radius of curvature R. Also say the vehicle is moving on a straight line at a constant speed. If for some reason the vehicle drifts sideways without changing the speed it moves in the forward direction, that will also give a similar reading as going in a curved path at a constant speed. Any ideas to overcome that?

8. Jul 29, 2008

### mgb_phys

You don't need R, all constants drop out of the intergration.
Imagine you are turning around a sharp corner at high speed for a short time and a wide corner at low speed for a long time - you have the same total summed 'acceleration' on the sensor.

No -there is no way of knowing that without a north seeking gyro or a compass.

9. Jul 29, 2008

### chammidhan

Ok.. Thanks a lot.. I was getting the same impression and wanted to confirm. Thank you for the help.. :)