A recursive smoothing filter employing a bank of fading-memory polynomial sub-filters is presented. Variance estimates are used to mix the outputs of the sub-filters, imparting variable gain and phase characteristics that permit it to automatically adapt to signal parameter changes. The proposed adaptive technique does not involve the estimation of plant parameters; therefore, it may be used in both open-loop and closed-loop configurations. In open-loop estimation problems, variable gain/bandwidth allows it to reduce the impact of random errors caused by sensor noise and the impact of bias errors caused by model mismatch during ` maneuvers'. In feedback control problems, variable phase/delay allows it to act as a lag filter for an improved steady-state response (i.e. greater noise attenuation) and act as a lead filter, or a proportionalderivative controller, for an improved transient response (i.e. increased closed-loop damping) for input discontinuities. Copyright (C) 2015 John Wiley & Sons, Ltd.