Permutation filter lattices: a general non-linear filtering framework

These lattices define a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system and the possible noise contamination. Permutation filters, much like polynomial filters, are flexible and modular, but instead of having polynomial expansions there are permutation lattice expansions. At the simplest level in the lattice, permutation filters reduce either to a simple linear finite impulse response or to an order-statistic filter but for larger permutation sublattices the filters can model complicated nonlinear systems more accurately while still preserving their robust properties.<>