How do I fit a common parameter between two sets of equations?
January 8, 2014 2:49 PM Subscribe
I have two observables that I'm measuring, x and y. Let's say both are functions of time t: x = f(t) and y = g(t). Given several measurements [(x,y) at (t1, t2, t3...)], I want to fit for the parameters of f() and g(). What's the right way to do this when f() and g() have a parameter in common?
For concreteness, suppose:
x = a + b*t + e*sin(t);
y = c + d*t + e*cos(t).
If they didn't have e in common, I'd just fit the two sets of equations independently. But how do I do this with the linkage?
(I vaguely remember connecting the two equations with (x-f(t)) + lambda*(y-g(t)) = 0 but I don't remember where to look up the details...?)