Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications

By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Orbit Estimation of Non-Cooperative Maneuvering Spacecraft

Due to the ever increasing congestion of the space environment, there is an increased demand for real-time situation awareness of all objects in space. An unknown spacecraft maneuver changes the predicted orbit, complicates tracking, and degrades estimate accuracies. Traditional orbit estimation routines are implemented, tested, and compared to a multiple model format that adaptively handles unknown maneuvers. Multiple Model Adaptive Estimation is implemented in an original way to track a non-cooperative satellite by covariance inflation and filtering-through a maneuver. Parameters for successful instantaneous maneuver reconstruction are analyzed. Variable State Dimension estimation of a continuously maneuvering spacecraft is investigated. A requirements based analysis is performed on short arc orbital solutions. Large covariance propagation of potential maneuvers is explored. Using ground-based radars, several thousand simulations are run to develop new techniques to estimate orbits during and after both instantaneous and continuous maneuvers. The new methods discovered are more accurate by a factor of 700 after only a single pass when compared to non-adaptive methods. The algorithms, tactics, and analysis complement on-going efforts to improve Space Situational Awareness and dynamic modeling

Satellite Cluster Tracking via Extent Estimation

Clusters of closely-spaced objects in orbit present unique tracking and prediction challenges. Association of observations to individual objects is often not possible until the objects have drifted sufficiently far apart from one another. This dissertation proposes a new paradigm for initial tracking of these clusters of objects: instead of tracking the objects independently, the cluster is tracked as a single entity, parameterized by its centroid and extent, or shape. The feasibility of this method is explored using a decoupled centroid and extent estimation scheme. The dynamics of the centroid of a cluster of satellites are studied, and a set of modified equinoctial elements is shown to minimize the discrepancy between the motion of the centroid and the observation-space centroid. The extent estimator is formulated as a matrix-variate particle filter. Several matrix similarity measures are tested as the filter weighting function, and the Bhattacharyya distance is shown to outperform the others in test cases. Finally, the combined centroid and extent filter is tested on a set of three on-orbit breakup events, generated using the NASA standard breakup model and simulated using realistic force models. The filter is shown to perform well across low-Earth, geosynchronous, and highly-elliptical orbits, with centroid error generally below five kilometers and well-fitting extent estimates. These results demonstrate that a decoupled centroid and extent filter can effectively track clusters of closely-spaced satellites. This could improve spaceflight safety by providing quantitative tracking information for the entire cluster much earlier than would otherwise be available through typical means

Recent Advances in Indoor Localization Systems and Technologies

Despite the enormous technical progress seen in the past few years, the maturity of indoor localization technologies has not yet reached the level of GNSS solutions. The 23 selected papers in this book present the recent advances and new developments in indoor localization systems and technologies, propose novel or improved methods with increased performance, provide insight into various aspects of quality control, and also introduce some unorthodox positioning methods

Rigid Body Attitude Estimation: An Overview and Comparative Study

The attitude estimation of rigid body systems has attracted the attention of many researchers over the years. The development of efficient estimation algorithms that can accurately estimate the orientation of a rigid body is a crucial step towards a reliable implementation of control schemes for underwater and flying vehicles. The primary focus of this thesis consists in investigating various attitude estimation techniques and their applications. Two major classes are discussed. The first class consists of the earliest static attitude determination techniques relying solely on a set of body vector measurements of known vectors in the inertial frame. The second class consists of dynamic attitude estimation and filtering techniques, relying on body vector measurements as well other measurements, and using the dynamical equations of the system under consideration. Various attitude estimation algorithms, including the latest nonlinear attitude observers, are presented and discussed, providing a survey that covers the evolution and structural differences of these estimation methods. Simulation results have been carried out for a selected number of such attitude estimators. Their performance in the presence of noisy measurements, as well as their advantages and disadvantages are discussed