Model based filter design by minimizing median of square of residuals

Model based digital filter design may be an attractive technique if the desired impulse response, perhaps measured in the field, closely matches a simple time series model, such as an autoregressive model. For autoregressive model based filters, a least squares solution is convenient for computational reasons, but is adversely affected by data outliers, such as a severe noise spike. Previously, we have shown that an Lp (p=1) may generate a robust solution in certain cases, however, such an estimates, although more robust than least squares methods, suffers breakdown when the data outliers are too frequent or occur at end points of the data record. We demonstrate the increased robustness of a model based filter design via choosing model coefficients by minimizing the median of the square of the residuals