M. Niedzwiecki et Wa. Sethares, SMOOTHING OF DISCONTINUOUS SIGNALS - THE COMPETITIVE APPROACH, IEEE transactions on signal processing, 43(1), 1995, pp. 1-13
Discontinuous signals buried in noise cannot be recovered by linear fi
ltering methods. This paper presents a new class of nonlinear filters
in which sets of forward and backward linear predictors and smoothers
compete with each other at each timestep. The winner of each competiti
on is granted the right to produce the smoothed estimate at that times
tep. This conceptually simple approach to nonlinear filtering, called
the competitive smoothing approach, is justified by considering sets o
f Kalman filters (corresponding to the hypotheses used in the Baysian
framework) which are used to derive model credibility coefficients. Th
ese are shown to essentially ''switch'' between the various models. We
argue that the concept of competitive smoothing is considerably more
general than just the Kalman setting, and can be used with almost any
predictors and/or smoothers. Several examples are presented which demo
nstrate the efficacy of the approach at both smoothing and preserving
jump discontinuities. Comparisons are made with the other main nonline
ar filtering approach, the median filter.