A predictive tracking approach and a novel method for visual motion compensation are introduced, which accurately reconstruct and compensate the deformation of the elastic object, even in the case of complete measurement information loss. The core of the methods involves a probabilistic physical model of the object, from which all other mathematical models are systematically derived. Due to flexible adaptation of the models, the balance between their complexity and their accuracy is achieved.

This work is concerned with the simultaneous tracking and shape estimation of a mobile extended object based on noisy sensor measurements. Novel methods are developed for coping with the following two main challenges: i) The computational complexity due to the nonlinearity and high-dimensionality of the problem, and ii) the lack of statistical knowledge about possible measurement sources on the extended object.

In Networked Control Systems (NCS), components of a control loop are connected by data networks that may introduce time-varying delays and packet losses into the system, which can severly degrade control performance. Hence, this book presents the newly developed S-LQG (Sequence-Based Linear Quadratic Gaussian) controller that combines the sequence-based control method with the well-known LQG approach to stochastic optimal control in order to compensate for the network-induced effects.

Extended object tracking deals with estimating the shape and pose of an object based on noisy point measurements. This task is not straightforward, as we may be faced with scarce low-quality measurements, little a priori information, or we may be unable to observe the entire target. This work aims to address these challenges by incorporating ideas from active contours and exploiting information from negative measurements, which tell us where the target cannot be.

We discuss theory and application of extended object tracking. This task is challenging as sensor noise prevents a correct association of the measurements to their sources on the object, the shape itself might be unknown a priori, and due to occlusion effects, only parts of the object are visible at a given time. We propose an approach to track the parameters of arbitrary objects, which provides new solutions to the above challenges, and marks a significant advance to the state of the art.

In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart.

The goal of this work is improving existing and suggesting novel filtering algorithms for nonlinear dynamic state estimation. Nonlinearity is considered in two ways: First, propagation is improved by proposing novel methods for approximating continuous probability distributions by discrete distributions defined on the same continuous domain. Second, nonlinear underlying domains are considered by proposing novel filters that inherently take the underlying geometry of these domains into account.

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed.