Application of robust data processing methods to the analysis of eye movements

We have developed a robust, nonlinear differentiating digital filter for the estimation of eye velocity from an eye-position signal. This filter is equally applicable to a large variety of other biomedical signals. The filter is implemented by taking an odd number of two-point differences around the point of interest and then selecting the median difference. Dividing the median difference by the time interval yields the derivative of the input signal. The Robust Differentiator (RD) is a classic order-statistic filter consisting of a bank of linear filters (the two-point differences) followed by the median operation to select one difference for the derivative calculation. The RD has no impulse response function and eliminates the "ringing" that is typical of all linear filters. The RD not only performs better than the FIR differentiating filters for impulse noise but is equally effective for both broad-band and narrow-band Gaussian noise. The RD "bandwidth" is adjustable by selecting the interval for the two-point differences.