Estimator stability analysis in SLAM

IFAC Symposium on Intelligent Autonomous Vehicles (IAV), 2004, Lisboa (Portugal)This work presents an analysis of the state estimation error dynamics for a linear system within the Kalman filter based approach to Simultaneous Localization and Map Building. Our objective is to demonstrate that such dynamics is marginally stable. The paper also presents the necessary modifications required in the observation model, in order to guarantee zero mean stable error dynamics. Simulations for a one-dimensional robot and a planar vehicle are presented.This work was supported by the project 'Supervised learning of industrial scenes by means of an active vision equipped mobile robot.' (J-00063).Peer Reviewe

Stochastic State Estimation for Simultaneous Localization and Map Building in Mobile Robotics

En Cutting Edge Robotics, 223-242. Advanced Robotic Systems Press, 2005.The study of stochastic models for Simultaneous Localization and Map Building (SLAM) in mobile robotics has been an active research topic for over fifteen years. Within the Kalman filter (KF) approach to SLAM, seminal work (Smith and Cheeseman, 1986) suggested that as successive landmark observations take place, the correlation between the estimates of the location of such landmarks in a map grows continuously. This observation was later ratified (Dissanayake et al., 2001) with a proof showing that the estimated map converges monotonically to a relative map with zero uncertainty. They also showed how the absolute accuracy of the map reaches a lower bound defined only by the initial vehicle uncertainty, and proved it for a one-landmark vehicle with no process noise. From an estimation theoretic point of view, we address these results as a consequence of partial observability. We show that error free reconstruction of the map state vector is not possible with typical measurement models, regardless of the vehicle model chosen, and show experimentally that the expected error in state estimation is proportional to the number of landmarks used. Error free reconstruction is only possible once full observability is guaranteed.This work was supported by projects: 'Supervised learning of industrial scenes by means of an active vision equipped mobile robot.' (J-00063), 'Integration of robust perception, learning, and navigation systems in mobile robotics' (J-0929).Peer Reviewe

Computational fluid dynamics benchmark dataset of airflow in tracheas

Computational Fluid Dynamics (CFD) is fast becoming a useful tool to aid clinicians in pre - surgical planning through the ability to provide inform ation that could otherwise be extremely difficult if not impossible to obtain. However, in order to provide clinically relevant metrics, the accuracy of the computational method must be sufficiently high. There are many alternative methods employed in the process of performing CFD simulations within the airways, including different segme ntation and meshing strategies, as well as alternative approaches to solving the Navier - Stokes equations. However, as in vivo validation of the simulated flow patter ns within the airways is not possible, little exists in the way of validation of the various simulation techniques. The data presented here consists of very highly resolved flow data. The degree of resolution is compared to the highest necessary resolution s of the Kolmogorov length and time scales. Therefore this data is ideally suited to act as a benchmark case to which cheaper comput ational methods may be compared. A dataset and solution setup for one such more efficient method, large eddy simulation (LES ), is also presented

Simulation of the hydrogen ground state in Stochastic Electrodynamics

Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar \omega$ in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham -- Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency components, next the dynamics is solved numerically using OpenCL. The approach improves on work by Cole and Zou 2003 by treating the full $3d$ problem and reaching longer simulation times. The results are compared with a conjecture for the ground state phase space density. Though short time results suggest a trend towards confirmation, in all attempted modelings the atom ionises at longer times.Comment: 20 pages, 9 figures. Published version, minor change