Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters of the mixing pdf different penalty functions are invoked depending on the estimation type used, the value of the noise variance, and whether real or complex signals are estimated. Using the Bessel K model, we derive a sparse estimator based on a modification of the expectation-maximization algorithm formulated for Type II estimation. The estimator includes as a special instance the algorithms proposed by Tipping and Faul [1] and by Babacan et al. [2]. Numerical results show the superiority of the proposed estimator over these state-of-the-art estimators in terms of convergence speed, sparseness, reconstruction error, and robustness in low and medium signal-to-noise ratio regimes.Comment: The paper provides a new comprehensive analysis of the theoretical foundations of the proposed estimators. Minor modification of the titl

Application of the Evidence Procedure to the Estimation of Wireless Channels

We address the application of the Bayesian evidence procedure to the estimation of wireless channels. The proposed scheme is based on relevance vector machines (RVM) originally proposed by M. Tipping. RVMs allow to estimate channel parameters as well as to assess the number of multipath components constituting the channel within the Bayesian framework by locally maximizing the evidence integral. We show that, in the case of channel sounding using pulse-compression techniques, it is possible to cast the channel model as a general linear model, thus allowing RVM methods to be applied. We extend the original RVM algorithm to the multiple-observation/multiple-sensor scenario by proposing a new graphical model to represent multipath components. Through the analysis of the evidence procedure we develop a thresholding algorithm that is used in estimating the number of components. We also discuss the relationship of the evidence procedure to the standard minimum description length (MDL) criterion. We show that the maximum of the evidence corresponds to the minimum of the MDL criterion. The applicability of the proposed scheme is demonstrated with synthetic as well as real-world channel measurements, and a performance increase over the conventional MDL criterion applied to maximum-likelihood estimates of the channel parameters is observed

The approach to building the algorithm for controlling rotor motion in a hybrid mechatronic bearing

The paper describes the approach to building the algorithm for controlling the rotor motion in a hybrid mechatronic bearing. Such bearings include a rolling bearing, a gas foil bearing, an electromagnetic and a piezo actuator. Fuzzy logic techniques are used in the proposed algorithm. Its main aim is to minimize the deviation of the rotor position in the bearing from the equilibrium position. It results in reducing the vibrational activity of the rotor-bearing system and reducing the friction losses

Modular detergents tailor the purification and structural analysis of membrane proteins including G-protein coupled receptors

Detergents enable the purification of membrane proteins and are indispensable reagents instructural biology. Even though a large variety of detergents have been developed in the lastcentury, the challenge remains to identify guidelines that allowfine-tuning of detergents forindividual applications in membrane protein research. Addressing this challenge, here weintroduce the family of oligoglycerol detergents (OGDs). Native mass spectrometry (MS)reveals that the modular OGD architecture offers the ability to control protein purificationand to preserve interactions with native membrane lipids during purification. In addition to abroad range of bacterial membrane proteins, OGDs also enable the purification and analysisof a functional G-protein coupled receptor (GPCR). Moreover, given the modular design ofthese detergents, we anticipatefine-tuning of their properties for specific applications instructural biology. Seen from a broader perspective, this represents a significant advance forthe investigation of membrane proteins and their interactions with lipids

Decentralized Multi-Agent Exploration with Online-Learning of Gaussian Processes

Exploration is a crucial problem in safety of life applications, such as search and rescue missions. Gaussian processes constitute an interesting underlying data model that leverages the spatial correlations of the process to be explored to reduce the required sampling of data. Furthermore, multiagent approaches offer well known advantages for exploration. Previous decentralized multi-agent exploration algorithms that use Gaussian processes as underlying data model, have only been validated through simulations. However, the implementation of an exploration algorithm brings difficulties that were not tackle yet. In this work, we propose an exploration algorithm that deals with the following challenges: (i) which information to transmit to achieve multi-agent coordination; (ii) how to implement a light-weight collision avoidance; (iii) how to learn the data’s model without prior information. We validate our algorithm with two experiments employing real robots. First, we explore the magnetic field intensity with a ground-based robot. Second, two quadcopters equipped with an ultrasound sensor explore a terrain profile. We show that our algorithm outperforms a meander and a random trajectory, as well as we are able to learn the data’s model online while exploring