One explanation (of unknown validity) given for the poor results is that perhaps the numerical conditioning of the algebraic problem is worsened by the operators , , , and ,drastically slowing the convergence. Another explanation is that the operator is too simple. Perhaps we should have a five or ten point low-cut filter--or maybe a PEF. A PEF could be estimated from the residual itself. Unfortunately, such a longer filter would smear the bad effect of noise glitches onto more residuals, effectively spoiling more measurements.
We concluded that the data is bad only in a very low frequency sense. Perhaps the lake is evaporating, or it is raining, or the load in the boat has been changed or shifted. It's a fact that any very low-frequency reject filter is necessarily a long filter, and that means that it must catch many noise spikes. Thus we should not attempt to filter out the drift from the residual. Instead we should model the drift.
In the presence of both noise bursts and noise with a sensible spectrum (systematic noise), the systematic noise should be modeled while the noise bursts should be handled with .