I am working on curve-fitting parameters of soil water characteristics curve. There are many equations. But, it is bit hard to find out the unknown curve-fitting parameters.
When you plot a time series data (1D), on the figure you can check for Tools/Basic Fitting in the menu, which permits you to try curve fitting on the fly. That could help to decide which curve fitting use afterward.
Otherwise, you may look at the fminsearch function in matlab where you can use a mathematical function and a least mean square algorithm to estimate parameters of the mathematical function. you need first to estimate which mathematical function can work (polynomial, sigmoid ...)
Matlab has a very good option called cftool (just write this in the command window) which opens a program where you input the data you want to match and describe the function, variables and parameters you want to match the data with. I have used it on several occasions. I can also recommend Solver in Excel.
If you send me data in a CSV file to: [email protected], I will quickly develop some regression equations for you. I am using ndCurveMaster for curve fit.
MATLAB is a good choice for curve-fitting problems due to its large collection of built-in functions and easy to use plotting capabilities for visualization. There are many examples of curve fitting code in MATLAB e.g.,
Often the nonlinear correlation to be fitted to data can be 'somehow' linearized, as a first stage. Linearized correlation and the corresponding linearized plot are often quite convenient to qualitatively evidentiate scattering around the trendline and to emphasize major effects and the physical meaning of the correlation parameters. Estimates of the parameters derived by least squares after the linearized correlation (modified from a former nonlinear correlation) can possibly be refined by iterative nonlinear least-squares regression; to find unbiased least-squares estimates for the original correlation. It may be advisable to compare both the linearized and the nonlinear correlations.