Abstract
This paper deals with the problem of inference in distributed systems where the probability model is stored in a distributed fashion. Graphical models provide powerful tools for modeling this kind of problems. Inspired by the box particle filter which combines interval analysis with particle filtering to solve temporal inference problems, this paper introduces a belief propagation-like message-passing algorithm that uses bounded error methods to solve the inference problem defined on an arbitrary graphical model. We show the theoretic derivation of the novel algorithm and we test its performance on the problem of calibration in wireless sensor networks. That is the positioning of a number of randomly deployed sensors, according to some reference defined by a set of anchor nodes for which the positions are known a priori. The new algorithm, while achieving a better or similar performance, offers impressive reduction of the information circulating in the network and the needed computation times.
Highlights
Intelligent systems have to reason constrained by noisy information acquired from their environment, i.e. they have to reason under uncertainty
The nonparametric belief propagation (NBP) algorithm is used to combine the information obtained from a global positioning system, with measures of relative distances between neighboring sensors
Inspired by the theoretic derivation of the Box-particle filtering (PF) presented in [9,10], we show the theoretic derivation of BP in the bounded error context by interpreting a box as a uniform pdf
Summary
Intelligent systems have to reason constrained by noisy information acquired from their environment, i.e. they have to reason under uncertainty. Other methods create a relative map without the use of anchors and are called “anchor-free” [1] In all these cases, nodes must themselves determine their respective positions through cooperation techniques. Approaches to solving the problem of localization in wireless sensor networks were proposed in a centralized environment. The nonparametric belief propagation (NBP) algorithm is used to combine the information obtained from a global positioning system, with measures of relative distances between neighboring sensors. We propose a variant of BP algorithm where information is represented using a collection of boxes (intervals in the case of real variables) The use of this approach involve simplicity in modeling the information and memory optimization.
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