Simple Robust Fixed Lag Smoothing

This paper introduces a class ofrobust lag-ksmoothersbased on simple low order Markov models for the Gaussian trend-like component of signal plus nonGaussian noise models. The kth order Markov models are of the kth difference form AkX t = €t where Llxt = Xt Xt-l and €t is a zero-mean white Gaussian noise process with variance <1;. The nominal additive noise is a zero-mean white Gaussian noise sequence with variance <1; , while the actual additive noise is nonGaussian with an outliers generating distribution, e.g., (1 j)N(O,<1~) + jH. This setup is particularly appropriate for radarglint noise. Impleme:ntation of the smoothers requires estimation of the two parameters <1; and <1;. This is accomplished using a robustified maximum likelihood approach. Application to both artificial data sets and to glint noise data reveals that the approach is quite effective. We briefly discuss the choices of lag k for the smoothers and also briefl.y study the sensitivity of our approach to model mismatch.