I have not yet built this so this is basically a theoretical question. I am still wrestling with some
C code to manage
i2c communication etc.
When I originally said "I have not built this", I meant that the robot is in what could be called a "design phase". For the sake of my question lets assume for a moment that the whole robot consists of just one IMU sensor. It moves magically (no motors that create a lot of noise in the sensor measurements). With theoretical I mean I am interested in the mathematics and algorithms involved in solving this problem. What I call IMU sensor provides raw accelerometer, gyro, and magnetometer measurements.
Lets say our tiny robot travels on a snooker table (3569 mm x 1778 mm). I believe this is sufficiently small to call it 2d. **Now, sensor fusion should be much easier (faster, consume less resources) than in 3d, right? **
I would like to measure the velocity and if possible the position. With velocity I mean at a given point of time I need to know the current velocity of the robot moving over the snooker table. Velocity is in the range of 0 - 5 m/s. With position I mean at a given point of time I need to know the current position of the robot on the snooker table (x, y, heading).
I hope this will be possible since the robot should be able to identify some landmarks and use this information to reduce position errors.
When I originally said "I hope this will be possible" I meant to express that I already am aware of the fact that real sensor data is noisy and errors accumulate quickly. Using landmarks I will / or will not be able to manage to reduce the error in the position estimates. But this is NOT part of my question.
I am about to improve my linear algebra knowledge. So I am confident to manage some matrix multiplications, inversions and such.
My question is for some ideas, references on measuring velocity and position in 2d using an IMU sensor like this one.
P.S. A little side question: I just figured that this question is probably too theoretical for robotics.SE. If you know any forum that is more focused on mathematical / algorithmic side of robotics please let me know.