Consistent Fusion in Networked Estimation Systems

点击翻译按钮获取中文摘要

We consider the combination of uncertain information given as probability density functions (pdfs). The information typically arises from autonomous estimators that are connected by a communication network and provide their inferences about the environment.Information processing is done in a decentralized fashion by propagating local estimates through the network and performing local fusion. Global information about the dependencies between the estimates is not or only approximately maintained in order to keep computation, communication, and storage tractable. Uncertainty in observations and states is characterized by probability density functions, where for practical purposes, finite-dimensional parameterizations are employed. More specifically, we primarily focus on Gaussian mixtures and Dirac mixtures.For systematically fusing local estimates, it is necessary to consider their common information, which has been deliberately (partially) discarded for the reasons stated above. As a result, it is not possible to make a distinction between new information and information already used, which leads to overconfident estimates when the dependencies are neglected. In order to avoid this so called "data incest" problem, i.e., double-counting the same data, the fused estimate must be at least as uncertain as the true estimate. This property of conservativeness of the pdf for describing the fused estimate is called "consistency" in the remainder. Although procedures for guaranteeing consistency for Gaussian densities in the context of linear systems are well-known, these concepts cannot be transferred to arbitrary densities as they appear in nonlinear information processing.Several difficult and fundamental challenges have been identified as the basis for this proposal: First of all, consistency of fusion results in the form of pdfs has to be properly defined also for recursive processing. Procedures for local fusion then have to be developed that consider the unknown dependencies between local estimates in order to provide consistent results. In summary, we propose a framework of fusion algorithms for arbitrary densities that provides consistent estimates. These algorithms will differ in their way of incorporating dependency information, in their accuracy, and in their computational effort. This will hopefully result in further progress towards tractable estimation methods for large problems with guaranteed estimation quality.