Identification of observer/Kalman filter Markov parameters - Theory and experiments

Abstract

This paper discusses an algorithm lo compute the Markov parameters of an observer or Kalman filter from experimental input and output data. The Markov parameters can then be used for identificatinn of a state-space representation, with associated Kalman or observer gain, for the purpose of controller design. The algorithm is a nonrecursive matrix version of two recursive algorithms developed in previous works for different purposes, and the relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and offers bounds on the proper choice of observer order. It is shown that if one uses data containing noise and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. The results of the paper are demonstrated in numerical studies and experiments on the Huhhle space telescope.

Identification of Time-varying Frequencies and Model Parameters for Large Flexible On-orbit Satellites Using a Recursive Algorithm

“…In this paper, the authors attempt to provide an alternative method that differs from commonly used approaches that employ SVD [1][2][3][4][5][6][7]11,13,14) to identify the time-varying modal parameters and corresponding state-space model of large rigid-flexible coupling satellites. Consequently, the time-varying frequencies of a satellite are obtained using the FAPI recursive method.…”

“…[1][2][3][4][5] For instance, in the 1980s and 90s, Juang et al identified the modal parameters and corresponding state-space model parameters for the Galileo spacecraft and Hubble Space Telescope using the eigensystem realization algorithm (ERA). 6,7) However, these identification experiments are mostly based on the linear time-invariant (LTI) system. From the perspective of actual operations, the configuration properties of these rigid-flexible coupling spacecraft may require alteration in orbit for many reasons, such as reflector deployment, 8) antenna rotation, 9) docking with a satellite 10) or capturing another moving body.…”

“…[3][4][5][6][7]11,12) The ERA is a typical system realization method. This approach constructs the Hankel matrix using complete input and output (I-O) data sequences over a period of time and utilizes singular value decomposition (SVD) at each time step to extract the observability matrices.…”

An On-Line Tracker for a Stochastic Chaotic System Using Observer/Kalman Filter Identification Combined with Digital Redesign Method

“…In the past decade, many system identification techniques have been developed and applied to identify a state-space model for modal parameter identification of large flexible space structures [1]. Theoretically, for a nonlinear system with precise differential equations, a higher-order linear model always gives a better approximation than a lower-order one.…”

An improved substructural identification strategy for large structural systems

“…Although these Sub-SI methods are able to identify the structural parameters of structures, they require measurements of acceleration, velocity and displacement at all interface DOFs. Tee et al [20] proposed two Sub-SI methods based on the classical methods of observer/Kalman filter identification (OKID) [21] and eigensystem realization algorithm [22]. A fairly large structural system of 50 DOFs was numerically studied under noise 5%.…”