UKF Based filters in INS/GPS integrated navigation systems: Novel application results

The filtering problem in the INS/GPS integrated navigation system is investigated in this study. Firstly, the nonlinear model of the INS/GPS integrated navigation system is proposed. Then the applications of the EKF, the UKF and the modified adaptive UKF are put in practice based on the model. A sample set of computer simulation results for the three filter algorithms, obtained by using MATLAB platform, are given to illustrate the effectiveness of the proposed algorithm with regard to the convergence rate and the estimation precision. Copyright © 2007 IFAC Keywords: Adaptive signal processing, integrated navigation system, INS/GPS, trace tracking, unscented Kalman filter, nonlinear control system

Determination of System Dimensionality from Observing Near-Normal Distributions

This paper identifies a previously undiscovered behavior of uniformly distributed data points or vectors in high dimensional ellipsoidal models. Such models give near normal distributions for each of its dimensions. Converse of this may also be true; that is, for a normal-like distribution of an observed variable, it is possible that the distribution is a result of uniform distribution of data points in a high dimensional ellipsoidal model, to which the observed variable belongs. Given the currently held notion of normal distributions, this new behavior raises many interesting questions. This paper also attempts to answer some of those questions. We cover both volume based (filled) and surface based (shell) ellipsoidal models. The phenomenon is demonstrated using statistical as well as mathematical approaches. We also show that the dimensionality of the latent model, that is, the number of hidden variables in a system, can be calculated from the observed distribution. We call the new distribution “Tanazur” and show through experiments that it is at least observed in one real world scenario, that of the motion of particles in an ideal gas. We show that the Maxwell-Boltzmann distribution of particle speeds can be explained on the basis of Tanazur distributions

Parametric contour tracking using unscented kalman filter

This paper presents an efficient method to integrate various spatial-temporal constraints to regularize the contour tracking. Specifically, the global shape prior, contour smoothness and object dynamics are addressed. First, the contour is represented as a parametric shape, based on which a causal smoothness constraint can be developed to exploit the local spatial constraint. The causality nature of the constraint allows us to do efficient probabilistic contour detection using the powerful Hidden Markov Model (HMM). Finally, a unscented Kalman filter (UKF) is applied to estimate object parameters based on the non-linear observation model (i.e. the relationship between the detected contour points and the contour parameters) and the object dynamics. Better than other variants of the recursive least mean square estimators (e.g., extended Kalman filter), UKF approximates non-linear systems up to the second order (third for Gaussian prior) with similar computational cost. This novel tracking algorithm is running in real-time and robust to severe distractions due to the comprehensive spatial-temporal constraints. It is applied to track people in bad illumination and cluttered environments. Promising results are reported. 1

Tracking dynamic regions of texture and shape

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 137-142).The tracking of visual phenomena is a problem of fundamental importance in computer vision. Tracks are used in many contexts, including object recognition, classification, camera calibration, and scene understanding. However, the use of such data is limited by the types of objects we are able to track and the environments in which we can track them. Objects whose shape or appearance can change in complex ways are difficult to track as it is difficult to represent or predict the appearance of such objects. Furthermore, other elements of the scene may interact with the tracked object, changing its appearance, or hiding part or all of it from view. In this thesis, we address the problem of tracking deformable, dynamically textured regions under challenging conditions involving visual clutter, distractions, and multiple and prolonged occlusion. We introduce a model of appearance capable of compactly representing regions undergoing nonuniform, nonrepeating changes to both its textured appearance and shape. We describe methods of maintaining such a model and show how it enables efficient and effective occlusion reasoning. By treating the visual appearance as a dynamically changing textured region, we show how such a model enables the tracking of groups of people. By tracking groups of people instead of each individual independently, we are able to track in environments where it would otherwise be difficult, or impossible. We demonstrate the utility of the model by tracking many regions under diverse conditions, including indoor and outdoor scenes, near-field and far-field camera positions, through occlusion and through complex interactions with other visual elements, and by tracking such varied phenomena as meteorological data, seismic imagery, and groups of people.by Joshua Migdal.Ph.D

Combinatorial optimisation for arterial image segmentation.

Cardiovascular disease is one of the leading causes of the mortality in the western world. Many imaging modalities have been used to diagnose cardiovascular diseases. However, each has different forms of noise and artifacts that make the medical image analysis field important and challenging. This thesis is concerned with developing fully automatic segmentation methods for cross-sectional coronary arterial imaging in particular, intra-vascular ultrasound and optical coherence tomography, by incorporating prior and tracking information without any user intervention, to effectively overcome various image artifacts and occlusions. Combinatorial optimisation methods are proposed to solve the segmentation problem in polynomial time. A node-weighted directed graph is constructed so that the vessel border delineation is considered as computing a minimum closed set. A set of complementary edge and texture features is extracted. Single and double interface segmentation methods are introduced. Novel optimisation of the boundary energy function is proposed based on a supervised classification method. Shape prior model is incorporated into the segmentation framework based on global and local information through the energy function design and graph construction. A combination of cross-sectional segmentation and longitudinal tracking is proposed using the Kalman filter and the hidden Markov model. The border is parameterised using the radial basis functions. The Kalman filter is used to adapt the inter-frame constraints between every two consecutive frames to obtain coherent temporal segmentation. An HMM-based border tracking method is also proposed in which the emission probability is derived from both the classification-based cost function and the shape prior model. The optimal sequence of the hidden states is computed using the Viterbi algorithm. Both qualitative and quantitative results on thousands of images show superior performance of the proposed methods compared to a number of state-of-the-art segmentation methods