On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters-Part II: Observability/Estimability Analysis.

This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.

An NN-based approach for tuning servocontrollers.

Neural networks (NN) are used in this paper to tune PI controllers for unknown plants, which may be nonlinear or open-loop unstable. A simple algorithm, which requires only knowledge of the plant output response direction, is used for training an NN controller, by employing the error between the reference and the plant output. Once this controller achieves good performance, its input-output behavior is approximated by a controller with PI structure, thereby enabling the computation of proportional and integral gains. These gains are familiar to process engineers and can be directly inserted into most existing softwares for process control in industry. Computer simulations on an unstable nonlinear plant and experimental results on a thermal plant are presented to illustrate the usefulness of the proposed approach.