The purpose is to investigate a novel recursive estimation algorithm whose implementation involves a discerning update strategy, as opposed to the continual update of most existing algorithms. Model parameter estimates are determined as the center of an optimal bounding ellipsoid (OBE) in parameter space. A simple test on the model prediction error determines whether the OBE needs updating or not. Most of the time it does not. By buffering the inputs from several independent sensors into one OBE adaptive signal processor, one could take full advantage of the possible computational savings of this new approach.