Jacob E. Darling

Minimization of the Kullback–Leibler Divergence for Nonlinear Estimation

A nonlinear approximate Bayesian filter, named the minimum divergence filter, is developed in which the state density is approximated by an assumed density. The parameters of the assumed density are found by minimizing the Kullback–Leibler divergence from the state density, whose evolution is defined by the Chapman–Kolmogorov equation and Bayes’ rule, to the assumed density. When an assumed Gaussian density is used and the dynamical system and measurement models possess additive, Gaussian-distributed noise, the predictor of the minimum divergence filter is equivalent to the predictor used under the Kalman framework, and the corrector defines the mean and covariance of the posterior Gaussian density as the first and second central moments of the posterior density defined by Bayes’ rule. To evaluate the efficacy of the minimum divergence filter, its corrector is first compared to that of standard Kalman-type filters. Finally, the minimum divergence filter is compared to the quadrature Kalman filter to estim...

RF localization solution using heterogeneous TDOA

This paper presents a solution for the localization of an RF transmitter using time-difference-of-arrival (TDOA) measurements that do not share any common receiver location. Localization requires three independent TDOA measurements, and previous solutions have assumed that the three measurements all share a common receiver location. Relaxing this assumption is here referred to as heterogeneous TDOA. The approach presented formulates the TDOA measurements as a system of three quadratic equations for the transmitter position components, and solves these equations using the Macaulay resultant. The heterogeneous TDOAs allow for improved measurement geometry resulting in more accurate localization. The solution also allows for localization by two moving receivers, such as orbiting satellites, collecting TDOA measurements at three instants in time.

Efficient multi-sensor data fusion for space surveillance

Multi-sensor networks can extend the sensing region of a single sensor in order to provide a more geometrically diverse and comprehensive view of the state of a dynamical system. The use of a multi-sensor network gives rise to the need for a fusion step that combines the outputs of all sensor nodes into a single probabilistic state description. This paper examines a fusion method based on logarithmic opinion pools and develops algorithms for multi-sensor data fusion as well as investigates weight selection schemes for the opinion pool using efficient quadrature integration methods. The proposed fusion rules are applied to the tracking of a space object using multiple ground-based optical sensors. It is shown that the multi-sensor fusion rule leads to an increase of nearly two orders of magnitude in the position tracking accuracy as compared to the traditional single-sensor tracking method.

Many-core computing for space-based stereoscopic imaging

The potential benefits of using parallel computing in real-time visual-based satellite proximity operations missions are investigated. Improvements in performance and relative navigation solutions over single thread systems can be achieved through multi- and many-core computing. Stochastic relative orbit determination methods benefit from the higher measurement frequencies, allowing them to more accurately determine the associated statistical properties of the relative orbital elements. More accurate orbit determination can lead to reduced fuel consumption and extended mission capabilities and duration. Inherent to the process of stereoscopic image processing is the difficulty of loading, managing, parsing, and evaluating large amounts of data efficiently, which may result in delays or highly time consuming processes for single (or few) processor systems or platforms. In this research we utilize the Single-Chip Cloud Computer (SCC), a fully programmable 48-core experimental processor, created by Intel Labs as a platform for many-core software research, provided with a high-speed on-chip network for sharing information along with advanced power management technologies and support for message-passing. The results from utilizing the SCC platform for the stereoscopic image processing application are presented in the form of Performance, Power, Energy, and Energy-Delay-Product (EDP) metrics. Also, a comparison between the SCC results and those obtained from executing the same application on a commercial PC are presented, showing the potential benefits of utilizing the SCC in particular, and any many-core platforms in general for real-time processing of visual-based satellite proximity operations missions.