Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Technical Report: Cooperative Multi-Target Localization With Noisy Sensors

This technical report is an extended version of the paper 'Cooperative Multi-Target Localization With Noisy Sensors' accepted to the 2013 IEEE International Conference on Robotics and Automation (ICRA). This paper addresses the task of searching for an unknown number of static targets within a known obstacle map using a team of mobile robots equipped with noisy, limited field-of-view sensors. Such sensors may fail to detect a subset of the visible targets or return false positive detections. These measurement sets are used to localize the targets using the Probability Hypothesis Density, or PHD, filter. Robots communicate with each other on a local peer-to-peer basis and with a server or the cloud via access points, exchanging measurements and poses to update their belief about the targets and plan future actions. The server provides a mechanism to collect and synthesize information from all robots and to share the global, albeit time-delayed, belief state to robots near access points. We design a decentralized control scheme that exploits this communication architecture and the PHD representation of the belief state. Specifically, robots move to maximize mutual information between the target set and measurements, both self-collected and those available by accessing the server, balancing local exploration with sharing knowledge across the team. Furthermore, robots coordinate their actions with other robots exploring the same local region of the environment.Comment: Extended version of paper accepted to 2013 IEEE International Conference on Robotics and Automation (ICRA

Cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging

The implementation challenges of cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging are discussed and work on the subject is reviewed. System architecture and sensor fusion are identified as key challenges. A partially decentralized system architecture based on step-wise inertial navigation and step-wise dead reckoning is presented. This architecture is argued to reduce the computational cost and required communication bandwidth by around two orders of magnitude while only giving negligible information loss in comparison with a naive centralized implementation. This makes a joint global state estimation feasible for up to a platoon-sized group of agents. Furthermore, robust and low-cost sensor fusion for the considered setup, based on state space transformation and marginalization, is presented. The transformation and marginalization are used to give the necessary flexibility for presented sampling based updates for the inter-agent ranging and ranging free fusion of the two feet of an individual agent. Finally, characteristics of the suggested implementation are demonstrated with simulations and a real-time system implementation.Comment: 14 page

Decentralized Riemannian Particle Filtering with Applications to Multi-Agent Localization

The primary focus of this research is to develop consistent nonlinear decentralized particle filtering approaches to the problem of multiple agent localization. A key aspect in our development is the use of Riemannian geometry to exploit the inherently non-Euclidean characteristics that are typical when considering multiple agent localization scenarios. A decentralized formulation is considered due to the practical advantages it provides over centralized fusion architectures. Inspiration is taken from the relatively new field of information geometry and the more established research field of computer vision. Differential geometric tools such as manifolds, geodesics, tangent spaces, exponential, and logarithmic mappings are used extensively to describe probabilistic quantities. Numerous probabilistic parameterizations were identified, settling on the efficient square-root probability density function parameterization. The square-root parameterization has the benefit of allowing filter calculations to be carried out on the well studied Riemannian unit hypersphere. A key advantage for selecting the unit hypersphere is that it permits closed-form calculations, a characteristic that is not shared by current solution approaches. Through the use of the Riemannian geometry of the unit hypersphere, we are able to demonstrate the ability to produce estimates that are not overly optimistic. Results are presented that clearly show the ability of the proposed approaches to outperform current state-of-the-art decentralized particle filtering methods. In particular, results are presented that emphasize the achievable improvement in estimation error, estimator consistency, and required computational burden

Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting approach is proposed to construct the Likelihood Probability Density Function (Li-PDF) by using a comparably small number of so-called fulcrums. The likelihood of particles is thereby analytically inferred, explicitly or implicitly, based on the Li-PDF instead of directly computed by utilizing the observation, which can significantly reduce the computation and enables real time filtering. The proposed approach guarantees the estimation quality when an appropriate fitting function and properly distributed fulcrums are used. The details for construction of the fitting function and fulcrums are addressed respectively in detail. In particular, to deal with multivariate fitting, the nonparametric kernel density estimator is presented which is flexible and convenient for implicit Li-PDF implementation. Simulation comparison with a variety of existing approaches on a benchmark 1-dimensional model and multi-dimensional robot localization and visual tracking demonstrate the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a draft/preprint of one paper submitted to the IEEE Transaction