Nonparametric generalized belief propagation based on pseudo-junction tree for cooperative localization in wireless networks

Non-parametric belief propagation (NBP) is a well-known message passing method for cooperative localization in wireless networks. However, due to the over-counting problem in the networks with loops, NBP’s convergence is not guaranteed, and its estimates are typically less accurate. One solution for this problem is non-parametric generalized belief propagation based on junction tree. However, this method is intractable in large-scale networks due to the high-complexity of the junction tree formation, and the high-dimensionality of the particles. Therefore, in this article, we propose the non-parametric generalized belief propagation based on pseudo-junction tree (NGBP-PJT). The main difference comparing with the standard method is the formation of pseudo-junction tree, which represents the approximated junction tree based on thin graph. In addition, in order to decrease the number of high-dimensional particles, we use more informative importance density function, and reduce the dimensionality of the messages. As by-product, we also propose NBP based on thin graph (NBP-TG), a cheaper variant of NBP, which runs on the same graph as NGBP-PJT. According to our simulation and experimental results, NGBP-PJT method outperforms NBP and NBP-TG in terms of accuracy, computational, and communication cost in reasonably sized networks

Cramér-Rao Bound for Hybrid GNSS-Terrestrial Cooperative Positioning

In this contribution we derive an expression of the Cramer-Rao bound for hybrid cooperative positioning, where GNSS information is combined with terrestrial range measurements through exchange of peer-to-peer messages. These results provide a theoretical characterization of achievable performance of hybrid positioning schemes, as well as allow to identify critical network configurations and devise optimized node placement strategies

Reducing communication overhead for cooperative localization using nonparametric belief propagation

A number of methods for cooperative localization has been proposed, but most of them provide only location estimate, without associated uncertainty. On the other hand, nonparametric belief propagation (NBP), which provides approximated posterior distributions of the location estimates, is expensive mostly because of the transmission of the particles. In this paper, we propose a novel approach to reduce communication overhead for cooperative positioning using NBP. It is based on: i) communication of the beliefs (instead of the messages), ii) approximation of the belief with Gaussian mixture of very few components, and iii) censoring. According to our simulations results, these modifications reduce significantly communication overhead while providing the estimates almost as accurate as the transmission of the particles

Sigma Point Belief Propagation

The sigma point (SP) filter, also known as unscented Kalman filter, is an attractive alternative to the extended Kalman filter and the particle filter. Here, we extend the SP filter to nonsequential Bayesian inference corresponding to loopy factor graphs. We propose sigma point belief propagation (SPBP) as a low-complexity approximation of the belief propagation (BP) message passing scheme. SPBP achieves approximate marginalizations of posterior distributions corresponding to (generally) loopy factor graphs. It is well suited for decentralized inference because of its low communication requirements. For a decentralized, dynamic sensor localization problem, we demonstrate that SPBP can outperform nonparametric (particle-based) BP while requiring significantly less computations and communications.Comment: 5 pages, 1 figur

Cooperative and Distributed Localization for Wireless Sensor Networks in Multipath Environments

We consider the problem of sensor localization in a wireless network in a multipath environment, where time and angle of arrival information are available at each sensor. We propose a distributed algorithm based on belief propagation, which allows sensors to cooperatively self-localize with respect to one single anchor in a multihop network. The algorithm has low overhead and is scalable. Simulations show that although the network is loopy, the proposed algorithm converges, and achieves good localization accuracy

Simultaneous Distributed Sensor Self-Localization and Target Tracking Using Belief Propagation and Likelihood Consensus

We introduce the framework of cooperative simultaneous localization and tracking (CoSLAT), which provides a consistent combination of cooperative self-localization (CSL) and distributed target tracking (DTT) in sensor networks without a fusion center. CoSLAT extends simultaneous localization and tracking (SLAT) in that it uses also intersensor measurements. Starting from a factor graph formulation of the CoSLAT problem, we develop a particle-based, distributed message passing algorithm for CoSLAT that combines nonparametric belief propagation with the likelihood consensus scheme. The proposed CoSLAT algorithm improves on state-of-the-art CSL and DTT algorithms by exchanging probabilistic information between CSL and DTT. Simulation results demonstrate substantial improvements in both self-localization and tracking performance.Comment: 10 pages, 5 figure

Large-Scale Sensor Network Localization via Rigid Subnetwork Registration

In this paper, we describe an algorithm for sensor network localization (SNL) that proceeds by dividing the whole network into smaller subnetworks, then localizes them in parallel using some fast and accurate algorithm, and finally registers the localized subnetworks in a global coordinate system. We demonstrate that this divide-and-conquer algorithm can be used to leverage existing high-precision SNL algorithms to large-scale networks, which could otherwise only be applied to small-to-medium sized networks. The main contribution of this paper concerns the final registration phase. In particular, we consider a least-squares formulation of the registration problem (both with and without anchor constraints) and demonstrate how this otherwise non-convex problem can be relaxed into a tractable convex program. We provide some preliminary simulation results for large-scale SNL demonstrating that the proposed registration algorithm (together with an accurate localization scheme) offers a good tradeoff between run time and accuracy.Comment: 5 pages, 8 figures, 1 table. To appear in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201