New exact nonlinear filters with large lie algebras.

The ideas previously used (Stochastics vol. 5, pp. 65-92, 1981) to construct some finite-dimensional nonlinear filters also yield related new filters of finite dimension with arbitrarily large bases; this is because the finite dimensionality is not destroyed by insertion of noiseless linear differential operations on the observations. In engineering language, the new filters are obtained from the old by smoothing the output through an n-pole linear system before adding observation noise in the usual way; this adds 2n to the Lie algebra dimension.