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Computational Techniques for Evaluating the Pointing Error Metrics
The pointing error metrics are evaluated quickly and accurately from timedomain data by using fast computational algorithms that utilize the Discrete Fourier Transform to convert the timedomain data to the frequency domain. The frequency domain equations for the pointing error metrics are then evaluated by summing a weighted mean square response. A different weighting is used for each metric. Individual contributions to the pointing error metrics can be determined to determine the most offending disturbance sources and to determine sensitivities to disturbances.
Frequencydomain data can also be obtained from the frequency response of a transfer function. It is particularly fast and easy to evaluate the pointing error metrics for reaction wheel or CMG disturbances.
For stochastic (random) disturbances, one of two paths can be taken to evaluate the pointing error metrics. One path is to simulate random inputs in a timedomain simulation, and then evaluate the metrics using the timedomain response. The other path is to augment the frequencydomain plant model with weighting functions. These weighting functions are linear transfer functions that approximate the weighting functions in the pointing error metrics. The covariance (or variance) at the output of the transfer functions is then evaluated by using standard methods available in Matlab. This path is often the fastest.
