Consistent Fusion in Networked Estimation Systems

我们将不确定信息的组合考虑为概率密度函数（pdfs）。这些信息通常来自通过通信网络连接的自主估计器，并提供它们对环境的推断。信息处理以分散的方式完成，通过网络传播局部估计并执行局部融合。为了保持计算、通信和存储的可处理性，评估之间的依赖关系的全局信息没有或仅仅是近似地维护。观测和状态的不确定性是由概率密度函数表征的，出于实际目的，使用有限维参数化。更具体地说，我们主要关注高斯混合和狄拉克混合。为了系统地融合当地估计，有必要考虑它们的共同信息，由于上述原因，这些信息已被故意（部分）丢弃。因此，不可能在新信息和已经使用的信息之间做出区分，这导致在忽略依赖性时过度自信的估计。为了避免这种所谓的“数据乱伦”问题，即重复计算相同的数据，融合估计必须至少与真实估计一样不确定。描述融合估计的pdf的这种保守性在余数中称为“一致性”。虽然在线性系统的背景下保证高斯密度一致性的程序是众所周知的，但这些概念不能转移到任意密度，因为它们出现在非线性信息处理中。已经确定了几个困难和基本的挑战作为该提议的基础：首先，必须为递归处理适当地定义pdf形式的融合结果的一致性。为了提供一致的结果，局部融合的程序必须考虑到局部估计之间的未知依赖关系。总之，我们提出了一个框架的融合算法的任意密度，提供一致的估计。这些算法在合并依赖信息的方式、准确性和计算工作量方面有所不同。这将有望导致对具有保证估计质量的大型问题的可处理估计方法的进一步进展。

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.