Considerations in applying dynamic-programming filters to the smoothing of noisy data

Dynamic programming techniques are useful in smoothing and differentiating noisy data signals according to an optimization criterion and the results are generally quite robust to noise spectra different from that assumed in the construction of the filter. If the noise properties are sufficiently different, however, the generalized cross-validation function used in the optimization can exhibit either multiple minima or no minima other than that corresponding to an insignificant amount of smoothing; in these cases, the smoothing parameter desired by the user typically does not lie at the global minimum of the generalized cross-validation function, but at some other point on the curve which can be identified heuristically. I present two cases to demonstrate this phenomenon and describe what measures one can take to ensure that the desired smoothing parameter is obtained.