One of the difficulties of human figure tracking is that humans move their bodies in complex, non-linear ways. An effective computational model of human motion could therefore be of great benefit in figure tracking. We are interested in the use of a class of dynamic models called switching linear dynamic systems for figure tracking. This thesis makes two contributions. First, we present an empirical analysis of some of the technical issues involved with applying linear dynamic systems to figure tracking. The lack of high-level theory in this area makes this type of empirical study valuable and necessary. We show that sensitivity of these models to perturbations in input is a central issue in their application to figure tracking. We also compare different types of LDS models and identification algorithms. Second, we describe 2-DAFT, a flexible software framework we have created for figure tracking. 2-DAFT encapsulates data and code involved in different parts of the tracking problem in a number of modules. This architecture leads to flexibility and makes it easy to implement new tracking algorithms.

The past decade has seen great progress in research on large scale mapping and perception in static environments. Real world perception requires handling uncertain situations with multiple possible interpretations: e.g. changing appearances, dynamic objects, and varying motion models. These aspects of perception have been largely avoided through the use of heuristics and preprocessing. This thesis is motivated by the challenge of including discrete reasoning directly into the estimation process. We approach the problem by using Conditional Linear Gaussian Networks (CLGNs) as a generalization of least-squares estimation which allows the inclusion of discrete model selection variables. CLGNs are a powerful framework for modeling sparse multi-modal inference problems, but are difficult to solve efficiently. We propose the Iterative Local Model Selection (ILMS) algorithm as a general approximation strategy specifically geared towards the large scale problems encountered in tracking and mapping. Chapter 4 introduces the ILMS algorithm and compares its performance to traditional approximate inference techniques for Switching Linear Dynamical Systems (SLDSs). These evaluations validate the characteristics of the algorithm which make it particularly attractive for applications in robot perception. Chief among these is reliability of convergence, consistent performance, and a reasonable trade off between accuracy and efficiency. In Chapter 5, we show how the data association problem in multi-target tracking can be formulated as an SLDS and effectively solved using ILMS. The SLDS formulation allows the addition of additional discrete variables which model outliers and clutter in the scene. Evaluations on standard pedestrian tracking sequences demonstrates performance competitive with the state of the art. Chapter 6 applies the ILMS algorithm to robust pose graph estimation. A non-linear CLGN is constructed by introducing outlier indicator variables for all loop closures. The standard Gauss-Newton optimization algorithm is modified to use ILMS as an inference algorithm in between linearizations. Experiments demonstrate a large improvement over state-of-the-art robust techniques. The ILMS strategy presented in this thesis is simple and general, but still works surprisingly well. We argue that these properties are encouraging for wider applicability to problems in robot perception.