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Here is the problem:

I have a platform in the shape of a box with sides of length lx, ly and lz. The platform has an inclinometre measuring angles α and β from the vertical about lx and ly and a fluxgate compass measuring heading. I have a global Cartesian measurement p(x,y,z) of the top-right-front corner of the box and I would like to calculate the location of the centre of the box given p, α, β, γ, lx, ly and lz

I would know the solution if:

- α, β and γ were purely intrinsic rotations, or

- α, β and γ were purely extrinsic rotations

Due to compass reading being global, but the inclinometre readings being local, I am not sure what to do. Does anyone have any pointers?