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Model Difference Minimization
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Once the estimation of power for each CGS pulse has been determined and the power comparison has been established, the error between data and model is minimized.
The actual error term used for minimization is the weighted variance of the error. For each pulse in a capture the error can be described as a mean error of the capture and a variance of the individual pulse. The mean error term is most likely due to some unaccounted bias in the model prediction. This bias is not factored into the error, since it is common to all pulses. The variance is weighted according to its power to put more emphasis on pulses with higher power because bigger pulses are more important in the estimate, and less subject to being corrupted by noise.
Once the weighted variance error for each pulse is determined, the total error over the entire pass is summed, and then minimized using the Nelder-Mead least-squares minimization technique. The minimization algorithm continuously reruns the model by altering the roll, pitch, yaw, and timing of the spacecraft and redetermines the error between CGS received power and the model estimated received power. The minimizing pertrurbations are reported as the best fit to the recorded data set and thus the calibration of the instrument.
