Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Aerospace Engineering


Mechanical and Aerospace Engineering

First Advisor

Kamesh Subbarao


The problem of orbit determination along with shape determination is significant. The orbit determination problem has been tackled for centuries by some of the greatest mathematicians and physicists. The issue of shape determination of space objects, although more recent, has also been addressed quite extensively. Nevertheless, these problems remain of great interest in the scientific and engineering community, and are addressed in this work. The greatest motivation for the tracking and identification of Earth orbiting objects is the ever-increasing population of space assets and man-made debris. It is of interest to implement new and better techniques to track and identify new debris and new orbiting bodies. The precise mathematical modeling of the space object's motion, along with the estimation of its position, velocity, attitude, angular velocity, shape, and size object is presented here. The first step is the development of mathematical model of the equations of motion of the orbiting body. The translational equations of motion are based on the orbiting two-body equations. In addition, rigid-body rotational equations are developed. This mathematical framework also includes models for perturbations. These perturbations are based on phenomena which affect the object as it orbits Earth. In order to acquire information regarding the object, astrometric and photometric measurement models are developed. These models emulate stations in the Space Surveillance Network. Special consideration is given to the development of the photometric model (i.e. the light curve model). The light curve measurement has only recently been used for this application and an extensive analysis of the information it carries is done. This study involves a sensitivity and observability analysis, which provide insight into the information contained in the light curve regarding the orientation, spin, shape, and size of the object. In addition, several mathematical models of the light reflectance phenomena are implemented in the light curve model. Their performance is evaluated and compared in order to choose which is the most effective one. The orbit determination and shape and size estimation is performed by implementing several estimation techniques. The first is the unscented Kalman filter (UKF). This filter has been shown to be effective in dealing with nonlinear systems and measurement models, which are inherent in the work presented here. The filter employs the dynamical model, measurement model, and noisy measurements to produce estimates of its location, orientation, shape, size, and future intentions. The second technique is a batch estimation within the UKF. This was implemented to improve the estimation of the shape and size parameters of the object. This estimates the states via the UKF and the shape/size parameters via a batch estimation algorithm. The batch algorithm minimizes a cost function to yield an updated estimate of the parameters. The third estimation technique uses a bootstrap particle filter (BPF), which is the first developed functioning particle filter. This filter draws a large number of samples from the distribution of the state in order to approximate the probability density function (pdf). In particular, the BPF uses importance sampling and weights. This filter is effective in dealing with nonlinear systems and non-Gaussian distributions. All three estimation techniques are applied to the combined direct and inverse problem. The UKF and UKF-batch experiments demonstrate the UKF performs well when dealing with the estimation of all the states and parameters. The UKF-batch, which implemented the Gauss-Newton algorithm to improve the estimates of the shape/size parameters, performs better than the other two UKF methods, but at a high computational cost. The BPF performs well for the estimation of the velocity, angular velocity, and shape/size parameters. Nevertheless, it is not able to estimate the position and attitude as well as the UKF schemes. Moreover, the estimation of the shape/size parameters via the BPF are not as good as the ones yielded by the UKF. This is attributed to insufficient number of particles given the number of states and parameters being estimated. It should also be noted that the BPF has a high computational cost compared to the UKF. The UKF is the method which is the least computationally expensive and yields good estimates across all states and parameters.


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington