Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Probabilistic three-dimensional object tracking based on adaptive depth segmentation

Object tracking is one of the fundamental topics of computer vision with diverse applications. The arising challenges in tracking, i.e., cluttered scenes, occlusion, complex motion, and illumination variations have motivated utilization of depth information from 3D sensors. However, current 3D trackers are not applicable to unconstrained environments without a priori knowledge. As an important object detection module in tracking, segmentation subdivides an image into its constituent regions. Nevertheless, the existing range segmentation methods in literature are difficult to implement in real-time due to their slow performance. In this thesis, a 3D object tracking method based on adaptive depth segmentation and particle filtering is presented. In this approach, the segmentation method as the bottom-up process is combined with the particle filter as the top-down process to achieve efficient tracking results under challenging circumstances. The experimental results demonstrate the efficiency, as well as robustness of the tracking algorithm utilizing real-world range information