This is my first post on SO. I haven't already developed much code for embedded systems, but I have few problems and need help from more advanced programmers. I use following devices: - LandTiger board with LPC1768 (Cortex M3) MCU, - Digilent pmodACL with ADXL345 accelerometer (3 axis), - Digilent pmodGYRO with L3G4200D gyroscope (3 axis).
I would like to get some information about device orientation, i.e. rotation angles over X, Y and Z axes. I've read that in order to achieve this I need to combine data from both accelerometer and gyroscope using Kallman filter or its simpler form i.e. complementary filter. I would like to know if it's possible to count roll, pitch and yaw from full range (0-360 degrees) using measurment data only from gyroscope and accelerometer (without magnetometer). I've also found some mathematical formulas (http://www.ewerksinc.com/refdocs/Tilt%20Sensing%20with%20LA.pdf and http://www.freescale.com/files/sensors/doc/app_note/AN3461.pdf) but they contain root squares in numerators/denominators so the information about proper quadrant of coordinate system is lost.
The question you are asking is a fairly frequent one, and is fairly complex, with many different solutions. Although the title mentions only an accelerometer, the body of your post mentions a gyroscope, so I will assume you have both. In addition there are many steps to getting low-cost accelerometers and gyros to work, one of those is to do the voltage-to-measurement conversion. I will not cover that part.
First and foremost I will answer your question. You asked if by 'counting' the gyro measurements you can estimate the attitude (orientation) of the device in Euler Angles.
Short answer: Yes, you could sum the scaled gyro measurements to get a very noisy estimate of the device rotation (actual radians turned, not attitude), however it would fail as soon as you rotate more than one axis. This will not suffice for most applications.
I will provide you with some general advise, specific knowledge and some example code that I have used before.
Firstly, you should not try to solve this problem by writing a program and testing with your IMU. You should start by writing a simulation using validated libraries, then validate your algorithm/program, and only then try to implement it with the IMU.
Secondly, you say you want to "count roll, pitch and yaw from full range (0-360 degrees)". From this I assume you mean you want to be able to determine the Euler Angles that represent the attitude of the device with respect to an external stationary North-East-Down (NED) frame. Your statement makes me think you are not familiar with representations of attitude, because as far as I know there are no Euler Angle representations with all 3 angles in the 0-360 range.
The application for which you want to use the attitude of the device will be important. If you are using Euler Angles you will not be able to accurately track the attitude of the device when large (greater than around 50 degrees) rotations are made on the roll or pitch axes, due to what is known as Gimbal Lock. If you require the tracking of such motions then you will need to use a quaternion or Direction Cosine Matrix (DCM) representation of attitude.
Thirdly, as you have said you can use a Complimentary Filter or Kalman Filter variant (Extended Kalman Filter, Error-State Kalman Filter, Indirect Kalman Filter) to accurately track the attitude of the device by fusing the data from the accelerometer, gyro and a magnetometer. I suggest the Complimentary Filter described by Madgwick which is implemented in C, C# and MATLAB here. A Kalman Filter variant would be necessary if you wanted to track the position of the device, and had an additional sensor such as GPS.
For some example code of mine using accelerometer only to get Euler Angle pitch and roll see my answer to this other question.