436 research outputs found
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
Fusion of finite set distributions: Pointwise consistency and global cardinality
A recent trend in distributed multi-sensor fusion is to use random finite set
filters at the sensor nodes and fuse the filtered distributions algorithmically
using their exponential mixture densities (EMDs). Fusion algorithms which
extend the celebrated covariance intersection and consensus based approaches
are such examples. In this article, we analyse the variational principle
underlying EMDs and show that the EMDs of finite set distributions do not
necessarily lead to consistent fusion of cardinality distributions. Indeed, we
demonstrate that these inconsistencies may occur with overwhelming probability
in practice, through examples with Bernoulli, Poisson and independent
identically distributed (IID) cluster processes. We prove that pointwise
consistency of EMDs does not imply consistency in global cardinality and vice
versa. Then, we redefine the variational problems underlying fusion and provide
iterative solutions thereby establishing a framework that guarantees
cardinality consistent fusion.Comment: accepted for publication in the IEEE Transactions on Aerospace and
Electronics System
A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks
Multisensor fusion and consensus filtering are two fascinating subjects in the research of sensor networks. In this survey, we will cover both classic results and recent advances developed in these two topics. First, we recall some important results in the development ofmultisensor fusion technology. Particularly, we pay great attention to the fusion with unknown correlations, which ubiquitously exist in most of distributed filtering problems. Next, we give a systematic review on several widely used consensus filtering approaches. Furthermore, some latest progress on multisensor fusion and consensus filtering is also presented. Finally,
conclusions are drawn and several potential future research directions are outlined.the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61374039, 61304010, 11301118, and 61573246, the Hujiang Foundation of China under Grants C14002
and D15009, the Alexander von Humboldt Foundation of Germany, and the Innovation Fund Project for Graduate Student of Shanghai under Grant JWCXSL140
Formal Definitions of Conservative PDFs
Under ideal conditions, the probability density function (PDF) of a random
variable, such as a sensor measurement, would be well known and amenable to
computation and communication tasks. However, this is often not the case, so
the user looks for some other PDF that approximates the true but intractable
PDF. Conservativeness is a commonly sought property of this approximating PDF,
especially in distributed or unstructured data systems where the data being
fused may contain un-known correlations. Roughly, a conservative approximation
is one that overestimates the uncertainty of a system. While prior work has
introduced some definitions of conservativeness, these definitions either apply
only to normal distributions or violate some of the intuitive appeal of
(Gaussian) conservative definitions. This work provides a general and intuitive
definition of conservativeness that is applicable to any probability
distribution, including multi-modal and uniform distributions. Unfortunately,
we show that this \emph{strong} definition of conservative cannot be used to
evaluate data fusion techniques. Therefore, we also describe a weaker
definition of conservative and show it is preserved through common data fusion
methods such as the linear and log-linear opinion pool, and homogeneous
functionals. In addition, we show that after fusion, weak conservativeness is
preserved by Bayesian updates. These strong and weak definitions of
conservativeness can help design and evaluate potential correlation-agnostic
data fusion techniques
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