A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are focused on the information fusion estimation problem under bounded noises. In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.Comment: 9 pages, 3 figure

Arithmetic Average Density Fusion -- Part I: Some Statistic and Information-theoretic Results

Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the target distribution by the arithmetic average (AA) of a finite number of sub-distributions which constitute a mixture. While the mixture has been widely used for single sensor filter design, it is only recent that the AA fusion demonstrates compelling performance for multi-sensor filter design. In this paper, some statistic and information-theoretic results are given on the covariance consistency, mean square error, mode-preservation capacity, and the information divergence of the AA fusion approach. In particular, based on the concept of conservative fusion, the relationship of the AA fusion with the existing conservative fusion approaches such as covariance union and covariance intersection is exposed. A suboptimal weighting approach has been proposed, which jointly with the best mixture-fit property of the AA fusion leads to a max-min optimization problem. Linear Gaussian models are considered for algorithm illustration and simulation comparison, resulting in the first-ever AA fusion-based multi-sensor Kalman filter.Comment: 30 pages, 14 figures, 3 tables. Information Fusion, 202

View fusion vis-à-vis a Bayesian interpretation of Black–Litterman for portfolio allocation

The Black–Litterman model extends the framework of the Markowitz modern portfolio theory to incorporate investor views. The authors consider a case in which multiple view estimates, including uncertainties, are given for the same underlying subset of assets at a point in time. This motivates their consideration of data fusion techniques for combining information from multiple sources. In particular, they consider consistency-based methods that yield fused view and uncertainty pairs; such methods are not common to the quantitative finance literature. They show a relevant, modern case of incorporating machine learning model-derived view and uncertainty estimates, and the impact on portfolio allocation, with an example subsuming arbitrage pricing theory. Hence, they show the value of the Black– Litterman model in combination with information fusion and artificial intelligence–grounded prediction methods

Distributed estimation over a low-cost sensor network: a review of state-of-the-art

Proliferation of low-cost, lightweight, and power efficient sensors and advances in networked systems enable the employment of multiple sensors. Distributed estimation provides a scalable and fault-robust fusion framework with a peer-to-peer communication architecture. For this reason, there seems to be a real need for a critical review of existing and, more importantly, recent advances in the domain of distributed estimation over a low-cost sensor network. This paper presents a comprehensive review of the state-of-the-art solutions in this research area, exploring their characteristics, advantages, and challenging issues. Additionally, several open problems and future avenues of research are highlighted