Looking for some time-series data transformation advice!

I want to know what's the best way to transform data of 9-tuples time series data of IMU (Inertia Measurement Unit) sensor, recorded from a pen drawing a straight line in 2D space into the equation that describes the direction of the pen.

Basically I'm looking for a function/algorithm that maps a 9-axes time-series data into a linear combination in the form of aX + bY + cZ, in order to know which direction the pen is moving on a 2D plane (c = 0). Note that I can label all data, hence a supervised algorithm is possible, but not necessary.

The IMU data are 9-tuple time-series data in the form of:

  • 3 axes of linear acceleration (collected from the accelerometer)

  • 3 axes of angular velocity (collected from the gyroscope)

  • 3 axes of magnetic field strength (collected from the magnetometer)

  • $\begingroup$ I can't help you in the details, but it seems that you will need to integrate the acceleration in time to get the velocity. You might need to merge that with the angular velocity, but you will need some information regarding the axes of rotation. The magnetic field strength might be useful to give you the orientation of the pen, but you might be also to check that information with the other 3+3 sensors. You may also get some help in Physics.SE. $\endgroup$ – Ertxiem May 12 at 23:05

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