(Preprint) AAS 12-115 INVERSE PROBLEM FORMULATION COUPLED WITH UNSCENTED KALMAN FILTERING FOR STATEAND SHAPE ESTIMATION OF SPACE OBJECTS Laura S. Henderson ∗ , Pulkit Goyal † and Kamesh Subbarao ‡ This work addresses issues related to resolving space objects i.e. Space Situational Awareness (SSA). The motivation behind this paper is to further current techniques used to estimate states associated with non-resolved space objects. Furthermore, this work deals with an inverse problem for a system of nonlinear stochastic dif- ferential equations. This system of equations corresponds to the two body orbit equations along with models accounting for effects of atmospheric drag, solar ra- diation pressure, and Earth’s aspherical shape. The present work implements an Unscented Kalman filter (UKF) in conjunction with a batch estimation loop. The UKF estimates the states and parameters of the resident space object (RSO) until a pre-determined measurement batch size criterion is met. The estimates are then passed to the batch loop where a cost function is minimized to improve the esti- mates of the RSO’s parameters further. The batch loop is implemented using two methods; the first uses the Levenberg-Marquardt technique while the second uses a Gauss-Newton algorithm. Moreover, two experiments are conducted. The first experiment uses the traditional UKF implementation and is treated as the bench- mark for the implementation of the batch loop. The second experiment uses the UKF along with the batch loop. The implementation of the batch loop shows a slight improvement over the traditional UKF implementation. INTRODUCTION For the past five decades we have been accumulating objects in space. Many of these objects are satellites that no longer work, pieces of used rocket stages, and remnants from collisions. Over the last decade the number of these objects has increased dramatically. This has become a critical problem that must be addressed with urgency as it could have a detrimental effect on functioning space assets. Objects that are placed in space such as satellites are of great importance to our communications, national security, and economy. Much of the global connectivity technology relies heavily on these satellites. In addition to satellites the International Space Station (ISS) is at an even higher risk due to its large size. It is of great importance to address the issue of identifying these objects and have the ability to predict where these objects will be at any given time and if they pose a risk to other space objects. The motivation for this paper is the belief that it is necessary to develop means to detect, track, identify, and predict the future intentions, actions, and positions of space objects with adequate precision and accuracy. In addition to this, means to determine the origin of these objects along with any change in their orbital state must be generated. * Graduate Student, Mechanical and Aerospace Engineering Department, University of Texas at Arlington, 500 West First Street, Woolf Hall 106. † Visiting Student, Mechanical and Aerospace Engineering Department, University of Texas at Arlington ‡ Associate Professor, Mechanical and Aerospace Engineering, University of Texas at Arlington, 500 West First Street, Woolf Hall 315G 1