Semi-Analytic Stochastic Linearization for Range-Based Pose Tracking

In range-based pose tracking, the translation and rotation of an object with respect to a global coordinate system has to be estimated. The ranges are measured between the target and the global frame. In this paper, an intelligent decomposition is introduced in order to reduce the computational effort for pose tracking. Usually, decomposition procedures only exploit conditionally linear models. In this paper, this principle is generalized to conditionally integrable substructures and applied to pose tracking. Due to a modified measurement equation, parts of the problem can even be solved analytically

Semi-Analytic Gaussian Assumed Density Filter

For Gaussian Assumed Density Filtering based on moment matching, a framework for the efficient calculation of posterior moments is proposed that exploits the structure of the given nonlinear system. The key idea is a careful discretization of some dimensions of the state space only in order to decompose the system into a set of nonlinear subsystems that are conditionally integrable in closed form. This approach is more efficient than full discretization approaches. In addition, the new decomposition is far more general than known Rao-Blackwellization approaches relying on conditionally linear subsystems. As a result, the new framework is applicable to a much larger class of nonlinear systems

Enhancements of online Bayesian filtering algorithms for efficient monitoring and improved uncertainty quantification in complex nonlinear dynamical systems

Recent years have seen a concurrent development of new sensor technologies and high-fidelity modeling capabilities. At the junction of these two topics lies an interesting opportunity for real-time system monitoring and damage assessment of structures. During monitoring, measurements from a structure are used to learn the parameters and equations characterizing a physics-based model of the system; thus enabling damage identification. Since monitored quantities are physical, these methods offer precious insight into the damage state of the structure (localization, type of damage and its extent). Furthermore, one obtains a model of the structure in its current condition, an essential element in predicting the future behavior of the structure and enabling adequate decision-making procedures. This dissertation focuses more specifically on solving some of the challenges associated with the use of online Bayesian learning algorithms, also called sequential filtering algorithms, for damage detection and characterization in nonlinear structural systems. A major challenge regarding online Bayesian filtering algorithms lies in achieving good accuracy for large dimensional systems and complex nonlinear non-Gaussian systems, where non-Gaussianity can arise for instance in systems which are not globally identifiable. In the first part of this dissertation, we show that one can derive algorithmic enhancements of filtering techniques, mainly based on innovative ways to reduce the dimensionality of the problem at hand, and thus obtain a good trade-off between accuracy and computational complexity of the learning algorithms. For instance, for particle filtering techniques (sampling-based algorithms) subjected to the so-called curse of dimensionality, the concept of Rao-Blackwellisation can be used to greatly reduce the dimension of the sampling space. On the other hand, one can also build upon nonlinear Kalman filtering techniques, which are very computationally efficient, and expand their capabilities to non-Gaussian distributions. Another challenge associated with structural health monitoring is the amount of uncertainties and variabilities inherently present in the system, measurements and/or inputs. The second part of this dissertation aims at demonstrating that online Bayesian filtering algorithms are very well-suited for SHM applications due to their ability to accurately quantify and take into account these uncertainties in the learning process. First, these algorithms are well-suited to address ill-conditioned problems, where not all parameters can be learnt from the available noisy data, a problem which frequently arises when considering large dimensional nonlinear systems. Then, in the case of unknown stochastic inputs, a method is derived to take into account in this sequential filtering framework unmeasured stationary excitations whose spectral properties are known but uncertain