I wish to calculate position of a small remote controlled car (relative to starting position). The car moves on a flat surface for example: a room floor. Now, I am using an accelerometer and a gyroscope. To be precise this board --> http://www.sparkfun.com/products/9623
As a first step I just took the accelerometer data in x and y axes (since car moves on a surface) and double integrated the data to get position. The formulae I used were:
vel_new = vel_old + ( acc_old + ( (acc_new - acc_old ) / 2.0 ) ) * SAMPLING_TIME;
pos_new = pos_old + ( vel_old + ( (vel_new - vel_old ) / 2.0 ) ) * SAMPLING_TIME;
vel_old = vel_new;
pos_old = pos_new;
acc_new = measured value from accelerometer
The above formulae are based on this document: http://perso-etis.ensea.fr/~pierandr/cours/M1_SIC/AN3397.pdf
However this is giving horrible error.
After reading other similar questions on this forum, I found out that I need to subtract the component of Gravity from above acceleration values (everytime from acc_new) by using gyroscope somehow. This idea is very well explained in Google Tech Talks video Sensor Fusion on Android Devices: A Revolution in Motion Processing at time 23:49.
Now my problem is how to subtract that gravity component? I get angular velocity from gyroscope. How do I convert it into acceleration so that I can subtract it from the output of accelerometer?
It won't work, these sensors are not accurate enough to calculate the position.
The reason is also explained in the video you are referring to.
The best you could do is to get the velocity based on the rpm of the wheels. If you also know the heading that belongs to the velocity, you can integrate the velocity to get position. Far from perfect but it should give you a reasonable estimate of the position.
I do not know how you could get the heading of the car, it depends on the hardware you have.
I'm afraid Ali's answer is quite true when it comes to those devices. However why don't you try searching arduino dead reckoning which will cover stories of people trying similar boards?
Here's a link that appeared after a search that I think may help you:
Even it seems like all of them failed you may come across workarounds which will decrease errors to acceptable amounts or calibrate your algorithm with some other sensor to put it back in track as the squared error of acceleration along with gyros white noise destroying accuracy.
One reason you have a huge error is that the equation appears to be wrong.
Example: To get updated vel,use.. Velnew=velold+((accelold+accelnew)/2)*sampletime.
Looks like you had an extra accel term in the equation. Using this alone will not correct all the error....need to as you say correct for influence of gravity and other things.
来源：https://stackoverflow.com/questions/11087076/position-calculation-of-small-model-of-a-car-using-accelerometer-gyroscope