Square-root state estimation for second-order large space structuresmodels

Abstract

Two square-root filtering algorithms are developed for large space structures that are modeled by secondorder, continuous-time, finite, dynamic models. The first filter, which assumes a continuous-time measurement system, is a single-stage continuous algorithm that is based on the V-Lambda square-root method for the solution of a generalized Riccati equation. The second measurement system considered is of a discrete-time type, for which the resulting estimator is a hybrid continuous/discrete one. Both estimators are based on the spectral decomposition of the estimation error covariance matrix. Thus, they continuously provide the user with the covariance spectral factors. This distinct feature of the V-Lambda algorithms is valuable in ill-conditioned cases, in which an insight into the estimation process is needed to reveal singularities and to identify state subsets that become nearly dependent. Moreover, using the orthogonality property of the covariance eigenvectors, an orthogonalization step is added to the algorithms to enhance their accuracy in cases where simple, unsophisticated software is to be used. Two different methods for performing the orthogonalization are suggested. A typical filtering example is used to demonstrate the square-root nature of the new filters.