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I'm currently a undergrad university student doing research and I'm anaylising some position data.

The data is a time-series' of Eastings (x) and Northings (y) for two points (P1, P2) on a rigid body in motion (T, E1, N1, E2, N2), with a position reported every 1 minute. I know that P1 and P2 are separated by a pre-determined distance of 10 m.

My goal is to use the two positions to calculate the rotation of the rigid body over time (which I need every 1 second).

The two sets of positions contain noise (not correlated with each other) which I first need to "remove" to best model the motion. My first thought was to bestfit (in a least squares sense) a different polynomial to all four time series (E1-T, N1-T, E2-T, N2-T) and use those polynomials to then interpolate and calculate the rotation. However, this has lead to me wondering the following:

1. Would it be better to propagate the noise in the positions through the rotation calculation and then bestfit the rotation data (instead of removing the noise at the position stage and then calculating a rotation)?

2. Is it valid for me to separate the E and N from each other and model them separately?

3. I've noticed since I best fit them separately, and calculated the distance between P1 and P2 using the polynomials, the distance between the two points (which was very close around 10 m before) now has a larger standard deviation.

Any help would be appreciated!

Cheers!

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# Using two positions on a rigid body to calculate rotation

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