Register to reply

Nonlinear least squares problem

by ciaran_hughes
Tags: nonlinear, squares
Share this thread:
Jun5-08, 05:25 AM
P: 1
Dear all,

Apologies if this is in the wrong forum.

I have a bit Nonlinear least squares fit problem. I have a pair of parametric equations (see attached, fairly nasty ).

in it, a b c x0 y0 z0 are all constant, and they are the values I want to determine from a nonlinear least squares fit to a given set of (u', v') data. (u', v') are a set of pixel locations of a curve in an image, and the equations attached describe that curve.

Now, to do a nonlinear least squares, I believe I have to get a single nonparametric function (e.g. of v' in terms of u'). To do this, I follow the standard steps of solving one of the equations in terms of t, and substitute into the other. This is where I fail.

I have even used the 'solve' function in the Symbolic Toolbox in MATLAB to solve one of the equations for t, but simply get an error.

So, my questions are:
1) Am I right in saying I must get the non-parametric equation for the curve to get a nonlinear least squares fit to the data points? I assume that I do, because t is an extra variable that I a) don't need and b) have no information for.
2) Can a nonparametric equation for this curve be obtained (from the attached equations)? Why?

Ultimately, I would like to know if I can do a nonlinear least squares fit to these parametric equations. If I can't, or if it would prove very difficult, why?

Many thanks for your time,
Attached Thumbnails
Phys.Org News Partner Engineering news on
ESA investigates an alternative, environmental-friendly method of corrosion resistance
The oscillator that could makeover the mechanical watch
Engineers study bats to improve aviation travel

Register to reply

Related Discussions
Least Squares Problem Please Help Calculus & Beyond Homework 1
Least squares and integration problem Calculus & Beyond Homework 1
Least-squares problem Introductory Physics Homework 0
Problem about Sum of Squares Set Theory, Logic, Probability, Statistics 0