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# Goodness of fit between two curves

## Goodness of fit between two curves

(OP)
I have a curve of experimental data, and another curve of the output from a model. I intend to use an optimiser to change my model to improve the fit between its output, and that of the test data.

To do so I need a measure of the goodness of fit of the test and model output data.

Obvious options to measure this goodness of fit are the sum of the difference squared between the two at various points, or the area between the two curves.

The test data is monotonic, and can be assumed to be at the same interval of independent variable eg timebase as the model output.

What other measures of fit should we consider?

Cheers

Greg Locock

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### RE: Goodness of fit between two curves

The obvious things, I guess, bias or systematic errors in the measurements? Is the model physical-based or just a mathematical behavior model? If the latter, I would be concerned that the optimizer might over-fit the data, in an attempt to incorporate the measurement noise.

For giggles, one might consider using a maximum likelihood estimation, ala Kalman filter, as opposed to regression.

### RE: Goodness of fit between two curves

(OP)
It's a full physics vehicle model, where the important tunable variable is the grippiness of each tire, which can be easily varied by two scaling factors.

The intent is to match the trajectory of the car through 3 gates defining a double lane change maneuver, measuring things like vehicle speed, yaw velocity, lat acc, heading, position in x and y etc. The model and the car use the same history of steering wheel angle and braking at each wheel.

Normally I judge curve fit by using peak values of things that have peaks, gradients of things that have gradients, and a sort of thick text marker approach to general conformity. We'd like to get a bit more automated than that.

Cheers

Greg Locock

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