Nonparametric belief propagation for self-localization of sensor networks

Abstract

Abstract-Automatic self-localization is a critical need for the effective use of ad-hoc sensor networks in military or civilian applications. In general, self-localization involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. distance measurements between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of inter-sensor communication. We demonstrate that the information used for sensor localization is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then present and demonstrate the utility of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multi-modal uncertainty. Using simulations of small-to moderately-sized sensor networks, we show that NBP may be made robust to outlier measurement errors by a simple model augmentation, and that judicious message construction can result in better estimates. Furthermore, we provide an analysis of NBP's communications requirements, showing that typically only a few messages per sensor are required, and that even low bit-rate approximations of these messages can have little or no performance impact.

Simultaneous localization and tracking via real-time nonparametric belief propagation

“…Since [6] and [7] approximate posterior PDFs with a Gaussian distribution, and [8] and [9] with a point estimate (Dirac delta impulse), it will lead to a suboptimal approximation in case of non-linear models and/or non-Gaussian measurements. This is especially a serious problem in non-rigid graphs, in which the posterior PDFs of a subset of the sensors is multi-modal [10].…”

“…We assume that sensors sense the target if and only if it is within a distance r. Two sensors can communicate if and only if they are within distance R from one another. Assuming that the radio of a node is much more powerful than its sensing devices [13], R > r. Following [10], more complex models can be easily incorporated. Finally, we assume there is a fusion center (e.g., an external device or one of the sensors), which collects the priors of the sensors' and target's positions, and the periodic measurements.…”

“…The goal is to update the beliefs of the sensors' and target's positions in real-time. A tractable way to achieve it is by using a particle-based message passing method, such as NBP [10], but with the restrictions which ensure the real-time execution.…”

“…Since this is in general intractable, we use a proposal distribution, the sum of Gaussian mixtures with reference particles (RPs), and then reweight the particles. This approach, called mixture importance sampling with RPs (MIS-RP) [16], is extension of standard MIS [10]. We first create a collection of ( G s,−a t + 1 + δRP)Np weighted particles by taking all particles from each incoming message excluding anchors (i.e., X (j) t−1→t and X (j) (n,t)→t , ∀n ∈ G s,−a t , j = 1, 2...Np; where G s,−a t is the set of non-anchors which can detect the target at time t) and adding a small number of uniformly distributed particles (RPs) over whole deployment area.…”

Algorithmic Aspects of Sensor Localization

“…A fully distributed localization method without explicit statistical model for range measurement was presented in [50]. The location of nodes are represented by the exact locations and the corresponding uncertainties.…”