Preliminary orbit determination by a composite multivariate search strategy

Abstract

A new strategy is presented for the problem of preliminary orbit determination with limited data and a very approximate initial estimate. This strategy, which is based on the minimization of the observation error func- tion, is essentially a combination of two types of multivariate search, random and deterministic, in the parameter space, ordered in such a way as to exploit the relative inherent advantages of the two types of methods. The feasibility of achieving accurate state estimates with such a strategy has been explored by simula- tion studies. Further, the potential practical applicability of the proposed method has been demonstrated using a variety of actual tracking data sets and orbit conditions. EVERAL methods have been reported in the literature1'2 for the orbital state estimation of a satellite using noisy ground observation data such as range, range rate, azimuth and elevation angles, of which the differential correction method stands out as the most widely used. However, most of these approaches have an inherent disadvantage in that a close a priori state estimate is required to converge to the correct state rapidly. But such needs as construction of the orbital state quickly with the knowledge of only the prelaunch in- jection parameters, augmented by several minutes of single station tracking data, estimation of the state immediately after orbit correction maneuvers are encountered in practice. In order to handle such scenarios wherein the conventional methods may npt always be able to accomplish the objective, several geometric methods have been devised which make use of certain combinations of observation types to give an ap- proximate state estimate. Gauss's m^ Gibb's method and the Double v-iter^tion are some of the widely used methods of this kind.3'4 Though variations of Gibb's method have also been proposed in the literature that use specific observation types such as range alone, there is definitely a dearth for universal methods for preliminary orbit deter- mination which can use any one or a combination of ob- servation types. The optimization approach to minimize the weighted sum of the residuals is an obvious avenue that could be explored towards this end. In Ref. 5 there are reported the findings of a comparative study of applying several op- timization techniques to the problem of orbit determination, using simulated data comprising more th^n one observation type and spread over two or three visible passes over a tracking station. In view of the existence of local minima, direct application of the deterministic search methods may lead to convergence to wrong states as can be seen in the results of Ref. 5. Such a problem, which makes preliminary orbit determination by direct search an unattractive ap- proach, can be alleviated to a large extent by a suitable combination of both random and deterministic searches in the parameter space. In this paper such a strategy is proposed and its feasibility demonstrated by simulation exercises and real- world case studies.