[R] Multi-dimensional non-linear fitting - advice on best method?

[Julian Gilbey]

On Sun, Apr 24, 2011 at 07:02:48PM -0400, Ravi Varadhan wrote:
> Julian,
> 
> You have not specified your problem fully.  What is the nature of f?  Is f a scalar function or is it a vector function (2-dim)?

It's something like this (only a bit worse):

given x, work out alpha from
  cos(alpha) = sin(delta) * sin(x) * sin(theta) - cos(delta) * cos(theta)

then y1 = h * cos(alpha) + offset1 + err1
     y2 = h * sin(alpha) + offset2 + err2

where theta is known, and delta, offset1, offset2 and h are to be
estimated and err1, err2 are measurement errors.

x is known, (y1, y2) are observed.

   Julian