Different aspects of nonlinear stochastic filtering theory

This thesis studies different aspects of the linear and the nonlinear stochastic filtering problem. It consists of four chapters. In the first chapter we derive the Kalman and the extended Kalman filter algorithms and we study some of their qualitative properties. In the second chapter we present a unified general framework on particle filter methods. In particular, we show how the particle filter methods surmount the difficulties due to the Kalman approach to filtering and we compare different particle filter algorithms. In the third chapter we study a real life example, tracking the position and the speed of a car, then we compare the extended Kalman filter and the particle filter methods. Finally, in the fourth chapter we generalize the formulation of the filtering with the Zakai equation to the case of multidimensional systems with unbounded observation functions and an Ornstein-Uhlenbech type noise

Vehicle detection and tracking using homography-based plane rectification and particle filtering

This paper presents a full system for vehicle detection and tracking in non-stationary settings based on computer vision. The method proposed for vehicle detection exploits the geometrical relations between the elements in the scene so that moving objects (i.e., vehicles) can be detected by analyzing motion parallax. Namely, the homography of the road plane between successive images is computed. Most remarkably, a novel probabilistic framework based on Kalman filtering is presented for reliable and accurate homography estimation. The estimated homography is used for image alignment, which in turn allows to detect the moving vehicles in the image. Tracking of vehicles is performed on the basis of a multidimensional particle filter, which also manages the exit and entries of objects. The filter involves a mixture likelihood model that allows a better adaptation of the particles to the observed measurements. The system is specially designed for highway environments, where it has been proven to yield excellent results

Adapting the Number of Particles in Sequential Monte Carlo Methods through an Online Scheme for Convergence Assessment

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaption of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz system

Real-time modelling and interpolation of spatio-temporal marine pollution

Due to the complexity of the interactions involved in various dynamic systems, known physical, biological or chemical laws cannot adequately describe the dynamics behind these processes. The study of these systems thus depends on measurements often taken at various discrete spatial locations through time by noisy sensors. For this reason, scientists often necessitate interpolative, visualisation and analytical tools to deal with the large volumes of data common to these systems. The starting point of this study is the seminal research by C. Shannon on sampling and reconstruction theory and its various extensions. Based on recent work on the reconstruction of stochastic processes, this paper develops a novel real-time estimation method for non- stationary stochastic spatio-temporal behaviour based on the Integro-Di erence Equation (IDE). This meth- odology is applied to collected marine pollution data from a Norwegian fjord. Comparison of the results obtained by the proposed method with interpolators from state-of-the-art Geographical Information System (GIS) packages will show, that signifi cantly superior results are obtained by including the temporal evolution in the spatial interpolations.peer-reviewe

Tight Upper and Lower Bounds to the Information Rate of the Phase Noise Channel

Numerical upper and lower bounds to the information rate transferred through the additive white Gaussian noise channel affected by discrete-time multiplicative autoregressive moving-average (ARMA) phase noise are proposed in the paper. The state space of the ARMA model being multidimensional, the problem cannot be approached by the conventional trellis-based methods that assume a first-order model for phase noise and quantization of the phase space, because the number of state of the trellis would be enormous. The proposed lower and upper bounds are based on particle filtering and Kalman filtering. Simulation results show that the upper and lower bounds are so close to each other that we can claim of having numerically computed the actual information rate of the multiplicative ARMA phase noise channel, at least in the cases studied in the paper. Moreover, the lower bound, which is virtually capacity-achieving, is obtained by demodulation of the incoming signal based on a Kalman filter aided by past data. Thus we can claim of having found the virtually optimal demodulator for the multiplicative phase noise channel, at least for the cases considered in the paper.Comment: 5 pages, 2 figures. Accepted for presentation at ISIT 201

Veni Vidi Vici, A Three-Phase Scenario For Parameter Space Analysis in Image Analysis and Visualization

Automatic analysis of the enormous sets of images is a critical task in life sciences. This faces many challenges such as: algorithms are highly parameterized, significant human input is intertwined, and lacking a standard meta-visualization approach. This paper proposes an alternative iterative approach for optimizing input parameters, saving time by minimizing the user involvement, and allowing for understanding the workflow of algorithms and discovering new ones. The main focus is on developing an interactive visualization technique that enables users to analyze the relationships between sampled input parameters and corresponding output. This technique is implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I conquered." This strategy is inspired by the mathematical formulas of numbering computable functions and is developed atop ImageJ, a scientific image processing program. A case study is presented to investigate the proposed framework. Finally, the paper explores some potential future issues in the application of the proposed approach in parameter space analysis in visualization