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A nasty least squares problem

A nasty least squares problem

A nasty least squares problem

I have a bit of an issue here. I have a set of Data, with x-axis "Grid". I have a "Known" value of "Data", but it is not aligned to the Grid of Data, but has its own set of X values, which are defined by a function of B. Any misalignment between the two causes issues later in my algorithm. To correct this misalignment, I have proposed the following scheme:
T1(B) = cspline(F^2 + B0*F + B1, Known)
T2 = interp(T1, F^2 + B0*F + B1, Known, Grid)
T3 = Sum(Data-T2)^2
Really, solving this problem is a matter of passing functions as arguments to sucessive functions, but I am finding that doing this is non-trivial. If anyone can help, I thank you in advance.

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