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.

Using unknown input observers for robust adaptive fault detection in vector second-order systems

“…Regarding the eigenstructure assignment for vector second-order systems via state feedback, the reader is directed to [22][23][24][25][26][27][28], and for optimal control in second-order form fewer results can be found, see for example [1,29].…”

Optimal model-based state estimation in mechanical and structural systems

“…Implementation and theoretical issues mentioned previously prompted the development of ‘natural second‐order observers’ and ‘second‐order state estimators’ for finite and infinite dimensional second‐order systems . The problem of natural second‐order observer design is very closely related to the problem of pole placement , and the main question is whether one can achieve arbitrary pole placement with a natural second‐order observer.…”

“…This last issue regarding consistency was clearly demonstrated by Balas [20]. It was concluded that unless certain restrictions are placed on the feedback gain matrix, estimates of the velocity generated by first-order observers do not correspond to derivatives of the displacement estimates.Implementation and theoretical issues mentioned previously prompted the development of 'natural second-order observers' and 'second-order state estimators' for finite and infinite dimensional secondorder systems [4,[20][21][22][23]. The problem of natural second-order observer design is very closely related to the problem of pole placement [24][25][26], and the main question is whether one can achieve arbitrary pole placement with a natural second-order observer.…”

Second-order state estimation experiments using acceleration measurements

“…In addition, robust computational procedures for solution of the Kalman filter estimation error covariance matrices have been developed for second-order models in Ref. 6. A dissipative observer for use with velocity measurements that possessed the second-order form was introduced in Ref.…”