System identification for given data pairs

Hello

I have system with 3 input and one output. This is "time independent" system. How can we express this system with polynomial fit or other methods relating input and output ?

regards Kushal

[Kushal Badgujar]

Furthermore is it possible to obtain inverse of this system i.e. given output y find input u1,u2, u3 ?

[Star Strider]

See the documentation for the System Identification Toolbox.

Answer 1

[Image Analyst]

There may be many u1,u2,u3 that give rise to a certain output value, y, especially if they are integers. If your y is a 3D array of numbers for every u1,u2,u3 (for example it's the intensity value of a 3D CT or MRI medical image), you can find the logical indexes for places with that y value like:

locations = find(y == desired_y);

For the fitting question, John D'Errico has a polyfitn() that will fit a 3D polynomial to your data. http://www.mathworks.com/matlabcentral/fileexchange/?term=authorid%3A679