For swarm systems, distributed processing is of paramount importance, and Bayesian methods are preferred for their robustness. Existing distributed sparse Bayesian learn- ing (SBL) methods rely on the automatic relevance deter- mination (ARD), which involves a computationally complex reweighted l1-norm optimization, or they use loopy belief propagation, which is not guaranteed to converge. Hence, this paper looks into the fast marginal likelihood maximiza- tion (FMLM) method to develop a faster distributed SBL version. The proposed method has a low communication overhead, and can be distributed by simple consensus meth- ods. The performed simulations indicate a better performance compared with the distributed ARD version, yet the same per- formance as the FMLM.

This paper is an extension of a previous work that examined a decentralized approach to evaluate the uncertainty of estimating a spatial process using guided model-based multi-agent exploration. The model is a superposition of fixed kernel functions, with each kernel playing the role of a feature. The measurements, collected by the agents, are then used to collectively estimate the weights of the features under sparsity constraints and derive the corresponding spatial uncertainty distribution to optimally guide the agents to reduce the uncertainty. This paper extends these results in several respects. First, we investigate different coordination strategies, which all aim to efficiently optimize the exploration criterion in a distributed multiagent setting. Second, we compare different features, specifically radial basis functions (RBFs), Lanczos kernels, Legendre polynomials, and discrete cosine functions. Third, we conduct hardware-in-the-loop experiments to validate the proposed coordination strategies using real robots. Results show that the coordination strategy together with the selected feature has a significant influence on the exploration performance.

In processing spatially distributed data, multi-agent robotic platforms equipped with sensors and computing capabilities are gaining interest for applications in inhospitable environments. In this work an algorithm for a distributed realization of sparse bayesian learning (SBL) is discussed for learning a static spatial process with the splitting-over-features approach over a network of interconnected agents. The observed process is modeled as a superposition of weighted kernel functions, or features as we call it, centered at the agent's measurement locations. SBL is then used to determine which feature is relevant for representing the spatial process. Using upper bounding convex functions, the SBL parameter estimation is formulated as ℓ1-norm constrained optimization, which is solved distributively using alternating direction method of multipliers (ADMM) and averaged consensus. The performance of the method is demonstrated by processing real magnetic field data collected in a laboratory.