Nonlinear Filter Representation via Spline Functions
R. S. Bucy, Hussein M. Youssef · Defense Technical Information Center (DTIC) · 1974
An optimum nonlinear filter is realized by sequentially updating the spline coefficients of the relevant conditional distribution. The nonlinear filtering problem considered is that of phase demodulation with a two-dimensional phase process model. A multi-dimensional hyperbolic and polynomial spline basis are generated by a tensor product of one-dimensional bases. General conclusions about the spline approach for higher dimensional problems will be drawn. In particular, general running time projections for N-dimensional problems will be provided. Some timing results for various methods of tri-diagonal matrix inversion are reviewed.