A general nonlinear filtering framework-permutation order-statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination. Permutation filters, much like polynomial filters, are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions. At the simplest level in the filter lattice, permutation filters reduce to either a simple linear (FIR) or to an order statistic (OS) filter, but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties. In order to enhance the robustness of permutation fitters, we develop /spl alpha/-trimmed permutation indicators and their associated filter lattices. We conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system. This paper, thus extends the potential of order-statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems.
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