Development of the Robust Algorithm of Guaranteed Ellipsoidal Estimation and Its Application for Orientation of the Arti
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DEVELOPMENT OF THE ROBUST ALGORITHM OF GUARANTEED ELLIPSOIDAL ESTIMATION AND ITS APPLICATION FOR ORIENTATION OF THE ARTIFICIAL EARTH SATELLITE N. D. Pankratova1† and O. V. Sholokhov1‡
UDC 519.8, 629.7
Abstract. The method for estimation of linear multidimensional dynamic control systems perturbed by only one of the phase coordinates is developed in the paper. Only one phase coordinate without perturbation is available for measurement in the system. A robust algorithm for ellipsoidal estimation is developed, which minimizes the trace of the matrix of ellipsoid that approximates admissible set of point estimates. Application of the method and efficiency of the algorithm are shown on the example of estimating the heading angle of an artificial Earth satellite during its orbital motion. The onboard local vertical reference and angular velocity sensors are used for the estimation. Keywords: robust algorithm of guaranteed ellipsoidal estimation, orientation of artificial Earth satellite, angular rate gyroscope, infrared local vertical reference. INTRODUCTION In the paper, we will present an algorithm of guaranteed ellipsoidal estimation of states of the linear dynamic system and will show its operation in estimating the orientation of an artificial Earth’s satellite. Conditions on which the algorithm is applied are as follows: external perturbation acts on the system along all the phase coordinates or only one of them; measurement that contains noise is carried out for only one phase coordinate; perturbed and measured coordinates generally do not coincide. Only boundary values are known for perturbation and noise, and their statistical and dynamic characteristics are unknown. The system is considered completely controlled and observed. Open-loop system can be unstable but it becomes stable in a closed state. It is necessary to estimate possible phase states of the system. To this end, the set of attainability of possible states of the system [1], which represents ellipsoidal approximation of the sum of ellipsoid of initial system’s state (or current estimation) and noise ellipsoid (or interval in a special case) are first constructed. Solution for the special case obtained in [2] is optimal by the criterion of minimum volume of approximating ellipsoid. For nondegenerate case, where both sets are ellipsoids, the solution is presented in [1]. In [3], the solution is obtained for the criterion of the sum of fourth degrees of semiaxes of the resultant ellipsoid. Minimizing the trace of matrix of resultant ellipsoid is a convenient criterion since the algorithm proposed in this paper has a direct analogy with statistical estimation and (as we will show below) does not require complicated evaluations. If this does not lead to a big loss of estimation accuracy, some simplifications of the algorithm are expedient. For example, a simplified technique was proposed in [4] to obtain the ellipsoid without the labor-consuming procedure of inversion of the matrix of initial ellipsoid. This considerably simplified the computation due
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