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"Rockeratw Atw" <northcarolinastate@gmail.com> wrote in message <gdqibv$g77$1@fred.mathworks.com>...
> Hi,
>
> I have a set of four battery discharging curves at discharging rate 1A, 10A, 30A, 40A respectively. I have an equation that describes the battery discharging behavior, so what I need to do now is to find the parameters of this equation so that the equation could predict other discharging rates.
>
> I have used least squares fit to find a unique set of parameters based on the data points i took on the four curves, but the results are not very good.
>
> I want to use some other fitting methods for parameter identification such as linear interpolation or bicubic spline fit but don't know how to program them. Could someone please provides me with some examples, references? I would very appreciated it.
>
You can't really use a spline to infer the parameters
of a nonlinear equation, so I'm unsure what you are
asking. Or maybe you are asking for something that
you can't do.
If your least squares estimation was inadequate in
your opinion, then either you have noisy data, or
the model is not really correct. Perhaps there are
other factors that enter in, or the model is only an
approximation.
But, why not do a simple spline fit to each curve,
one such spline at each discharge rate.
Take your pick of any spline that you want,
although in matlab without the splines toolbox,
you will be limited to either spline or pchip. One
of these should be adequate though.
Now, to predict a value at any other discharge rate,
you have 4 spline curves. You can predict a value
on those curves using ppval. Now you have 4 points.
Interpolate in discharge rate. Again, take your pick
of methods here. Anything from a linear interpolant
using interp1, to a spline or pchip, or even a cubic
interpolating polynomial.
HTH,
John
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