A Comparison of Parametric and Sample-Based Message Representation in Cooperative Localization

Abstract

Location awareness is a key enabling feature and fundamental challenge in present and future wireless networks. Most existing localization methods rely on existing infrastructure and thus lack the flexibility and robustness necessary for large ad hoc networks. In this paper, we build upon SPAWN (sum-product algorithm over a wireless network), which determines node locations through iterative message passing, but does so at a high computational cost. We compare different message representations for SPAWN in terms of performance and complexity and investigate several types of cooperation based on censoring. Our results, based on experimental data with ultra-wideband (UWB) nodes, indicate that parametric message representation combined with simple censoring can give excellent performance at relatively low complexity.

Cooperative Localization in WSNs Using Gaussian Mixture Modeling: Distributed ECM Algorithms

“….., C and ∀j ∈ H(i) according to (19), and χ (c) i,l , ∀l = 1, 2, ..., C and ∀χ ∈ {w, a, b} according to (16)- (18) with P (η)…”

“…Generally speaking, a centralized, cooperative localization algorithm spends most of the energy on the wireless routing of O(|H(i)|) Weighted MDS [8] O(|H(i)|) Parametric SPAWN [15], [16] O(R int |H(i)|)…”

“…In the two distributed ECM algorithms given in Algorithm 3, the total number of real values exchanged among neighboring sensors on one iteration is approximately equal O(Nu) Weighted MDS [8] O(Nu) Parametric SPAWN [15], [16] O(C bel Nu) C bel : 10 0 − 10 1 Classical SPAWN [5] O(R bel Nu) R bel : 10 2 − 10 3 D-ECMs O(CN G itr Nu) C : 10 0 − 10 1 N G itr : 10 0 − 10 1 to 6N u N G itr C. Note that much less energy is consumed for updating the position estimate than for updating the mixture model parameter estimate via Algorithm 2. Therefore,…”

“…In general, R bel is large. In order to reduce the energy consumption, some new fashioned SPAWN algorithms, e.g., [15] and [16], resort to fit the local belief messages with parametric models and exchange merely a few parametric model parameters between sensors. Here, C bel denotes the total number of parameters used in a parametric model, which should be much less than R bel .…”

“…In the distributed non-Bayesian algorithms, wireless sensors exchange their position estimates mutually; while in the conventional, distributed Bayesian algorithms, they exchange local belief messages (distributions represented by a set of particles) about their actual positions and thus consume much more energy for communication. At the sacrifice of localization accuracy, however, recent work demonstrated that the communication overhead can be significantly reduced by using transmit-and receive censoring [17] and/or parametric representation of the local belief messages [16], [21]. As compared to non-Bayesian algorithms, Bayesian algorithms for localization purposes may include prior information about sensor positions, sensor movement, noise statistics and so on, thus offering a greater flexibility such that robustness consid-erations can be accounted for.…”