Sequential Detection with Mutual Information Stopping Cost

This paper formulates and solves a sequential detection problem that involves the mutual information (stochastic observability) of a Gaussian process observed in noise with missing measurements. The main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices. This monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies.The sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound. We illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly-by and persistent-surveillance applications involving a GMTI (Ground Moving Target Indicator) radar

Sparse Bayesian information filters for localization and mapping

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008This thesis formulates an estimation framework for Simultaneous Localization and Mapping (SLAM) that addresses the problem of scalability in large environments. We describe an estimation-theoretic algorithm that achieves significant gains in computational efficiency while maintaining consistent estimates for the vehicle pose and the map of the environment. We specifically address the feature-based SLAM problem in which the robot represents the environment as a collection of landmarks. The thesis takes a Bayesian approach whereby we maintain a joint posterior over the vehicle pose and feature states, conditioned upon measurement data. We model the distribution as Gaussian and parametrize the posterior in the canonical form, in terms of the information (inverse covariance) matrix. When sparse, this representation is amenable to computationally efficient Bayesian SLAM filtering. However, while a large majority of the elements within the normalized information matrix are very small in magnitude, it is fully populated nonetheless. Recent feature-based SLAM filters achieve the scalability benefits of a sparse parametrization by explicitly pruning these weak links in an effort to enforce sparsity. We analyze one such algorithm, the Sparse Extended Information Filter (SEIF), which has laid much of the groundwork concerning the computational benefits of the sparse canonical form. The thesis performs a detailed analysis of the process by which the SEIF approximates the sparsity of the information matrix and reveals key insights into the consequences of different sparsification strategies. We demonstrate that the SEIF yields a sparse approximation to the posterior that is inconsistent, suffering from exaggerated confidence estimates. This overconfidence has detrimental effects on important aspects of the SLAM process and affects the higher level goal of producing accurate maps for subsequent localization and path planning. This thesis proposes an alternative scalable filter that maintains sparsity while preserving the consistency of the distribution. We leverage insights into the natural structure of the feature-based canonical parametrization and derive a method that actively maintains an exactly sparse posterior. Our algorithm exploits the structure of the parametrization to achieve gains in efficiency, with a computational cost that scales linearly with the size of the map. Unlike similar techniques that sacrifice consistency for improved scalability, our algorithm performs inference over a posterior that is conservative relative to the nominal Gaussian distribution. Consequently, we preserve the consistency of the pose and map estimates and avoid the effects of an overconfident posterior. We demonstrate our filter alongside the SEIF and the standard EKF both in simulation as well as on two real-world datasets. While we maintain the computational advantages of an exactly sparse representation, the results show convincingly that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the original Gaussian distribution as produced by the EKF, but at much less computational expense. The thesis concludes with an extension of our SLAM filter to a complex underwater environment. We describe a systems-level framework for localization and mapping relative to a ship hull with an Autonomous Underwater Vehicle (AUV) equipped with a forward-looking sonar. The approach utilizes our filter to fuse measurements of vehicle attitude and motion from onboard sensors with data from sonar images of the hull. We employ the system to perform three-dimensional, 6-DOF SLAM on a ship hull

Moving path following for unmanned aerial vehicles with applications to single and multiple target tracking problems

This paper introduces the moving path following (MPF) problem, in which a vehicle is required to converge to and follow a desired geometric moving path, without a specific temporal specification, thus generalizing the classical path following that only applies to stationary paths. Possible tasks that can be formulated as an MPF problem include tracking terrain/air vehicles and gas clouds monitoring, where the velocity of the target vehicle or cloud specifies the motion of the desired path. We derive an error space for MPF for the general case of time-varying paths in a two-dimensional space and subsequently an application is described for the problem of tracking single and multiple targets on the ground using an unmanned aerial vehicle (UAV) flying at constant altitude. To this end, a Lyapunov-based MPF control law and a path-generation algorithm are proposed together with convergence and performance metric results. Real-world flight tests results that took place in Ota Air Base, Portugal, with the ANTEX-X02 UAV demonstrate the effectiveness of the proposed method.info:eu-repo/semantics/acceptedVersio

Converted Measurement Trackers for Systems with Nonlinear Measurement Functions

Converted measurement tracking is a technique that filters in the coordinate system where the underlying process of interest is linear and Gaussian, and requires the measurements to be nonlinearly transformed to fit. The goal of the transformation is to allow for tracking in the coordinate system that is most natural for describing system dynamics. There are two potential issues that arise when performing converted measurement tracking. The first is conversion bias that occurs when the measurement transformation introduces a bias in the expected value of the converted measurement. The second is estimation bias that occurs because the estimate of the converted measurement error covariance is correlated with the measurement noise, leading to a biased Kalman gain. The goal of this research is to develop a new approach to converted measurement tracking that eliminates the conversion bias and mitigates the estimation bias. This new decorrelated unbiased converted measurement (DUCM) approach is developed and applied to numerous tracking problems applicable to sonar and radar systems. The resulting methods are compared to the current state of the art based on their mean square error (MSE) performance, consistency and performance with respect to the posterior Cramer-Rao lower bound

Maneuvering Intruder Passive Ranging for Detect-and-Avoid

For the last two decades, unmanned aircraft systems (UAS) has seen much interest from both the civilian and military sector. As civilian applications expand, the issue of safety becomes more apparent. One major technical challenge currently facing UAS operations is properly sharing the national airspace with conventional aircraft. For safety purposes, it is necessary that UAS be able to properly detect intruding aircraft, including manned and unmanned aircraft, and avoid them. This requirement has been termed Detect-and-Avoid (DAA). We investigate the orbiting intruder passive ranging problem, where an ownship aircraft is moving with a constant velocity and the intruding aircraft is conducting an orbiting maneuver. We assume that the ownship measures the bearing angles to the intruder aircraft. We approach the problem utilizing a filter bank algorithm parameterized with respect to the range, the heading of the intruder, and the angular velocity. We test the performance of the filter bank algorithm using two different system models. The first system model comprises of the relative position in Cartesian coordinates and velocities in polar coordinates. The second system model is the modified polar coordinates. We conduct Monte Carlo simulations and utilize the root mean square error over time to determine the best parameterization of the filter algorithm for both system models. The results show that the system model in Cartesian coordinates performs better when estimating the range while the modified polar coordinates achieves better estimates for the heading of the intruder. We find that the filter in the modified polar coordinates exhibits more divergent behavior than the system in Cartesian coordinates. After an investigation of the orbiting intruder problem, we investigate the maneuvering intruder problem. Often the intruder's trajectory will follow segments of straight legs and orbits legs. We introduce a way to integrate our filter bank algorithm onto a Interacting multiple models framework. We utilize a constant velocity model on a single EKF. We implement a mixing strategy, where the IMM mixing stage will mix at a certain rate. We conduct a simulation study to identify the effects of varying mixing rate and the values of the model transition probability. We find that the model transition probability has the largest effect on performance. Finally, we show preliminary results of our algorithm's performance on flight test data.Mechanical and Aerospace Engineerin