State Space Techniques in Approximation Theory with Applications to Design of Recursive Optical Estimators. Volume II.
James S. Pappas · Defense Technical Information Center (DTIC) · 1977
Abstract : In many applications of recursive estimation theory to trajectory estimation the process dynamics are not used. In these cases one normally resorts to approximating the forces with fitting functions. Polynomials, exponentially weighted polynomials and trigonometric and their orthogonal counterparts Gram, Legendre, and Laguerre polynomials are developed in a vector space setting. Matrices describing the connections between the bases and their velocity matrices and their pseudo-inverses are developed. Continuous and discrete function filtering dynamics are presented. These relations can serve as an aid to fitting functions filter design. (Author)