Which curve fitting function do I need?

I want to fit the following function to measured data in order to estimate R:

D = atan2(sin(H),R*cos(H))

I have measured H & D

H will be in the range -1.1*pi/2 to 1.1*pi/2

I expect R to be approximately +2

To visualize, see:

figure
H = [-1.1*pi/2:0.1:1.1*pi/2]';
R = 2;
D = atan2(sin(H),R*cos(H));
plot(H,D)

I don't know which curve-fitting function to use. I have access to both the curve-fitting and optimization toolboxes. Any advice would be much appreciated.

Thanks

Answer 1

[bym]

lsqcurvefit()  % optimization toolbox

or

lsqnonlin()

Answer 2

[the cyclist]

I don't have either of those toolboxes. I would do this with nlinfit() in the statistics toolbox.

Answer 3

[Richard Willey]

nlinfit uses optimization solvers under the hood, so it's not too surprising that you're getting the same answer.

nlinfit is part of Statistics Toolbox. As such, the function is designed to support typical workflows used by data analysts and provides some additional additional output parameters like R^2. You also have a variety of helper functions that you can use to compute confidence intervals, perform cross validation, and the like.

Optimization Toolbox is a general purpose tool which is both a strength and a weakness. On the plus side, Optimization Toolbox can be used to solve problems that nlinfit can't solve (or can't solve easily). Regression models that involve complex constraints are a classic example. On the down side, if you're trying to do basic data analysis tasks you'll probably need to write a lot more code by hand.

Answer 4

[Omar Mian]

Thanks cyclist & proecsm. I tried both nlinfit and lsqcurvefit and they both do the job. With simulated noisy data, I seem to be getting the same answer from both (to 4 d.p. at least).

What would be the advantage of one over the other? Also, what would be the advantage of lsqnonlin?

[John D'Errico]

The advantage of lsqnonlin is if you do not have the stats toolbox but do have the optimization TB. The advantage of nlinfit is if you DO have the stats TB, and not the optimization TB.