In this paper, we present a complete analytic probability based description of mobile-to-mobile uncorrelated scatter channels. We provide a theoretical proof that the proposed probability based description is equivalent to the correlation based description introduced by Bello and Matz. This equivalence is evaluated through a comparison of the hybrid characteristic probability density function with the correlation based description of a measured generic mobile-to-mobile channel, both of which can be obtained directly either from theory or from measurement data. The comparison confirms the similarity between the probability based and correlation based description qualitatively and quantitatively. Thus, the proposed probabilistic description complements the common correlation based description providing a comprehensive theoretical description of arbitrary uncorrelated scatter channels.

We present a 3D seismic exploration and imaging survey conducted by robotic platforms in a hardware-in-the-loop system. To this end, we integrate the adapt-then-combine full waveform inversion (ATC-FWI) over a network of mobile rovers in the ROS2 framework. The ATC-FWI allows for distributed subsurface imaging in a multi-agent network, i.e., each rover obtains a 3D subsurface image via data exchange with other rovers in the network. We demonstrate the capability of our system by performing multiple surveys using a synthetic subsurface model with an anomaly. The rovers acquire seismic data over different measurement areas and perform distributed imaging to reconstruct the subsurface. We show that the rovers are able to image the anomaly and to enhance their subsurface image over multiple measurement stages in different areas.

Sparse Bayesian Learning with dictionary refinement (SBL-DR) is a gridless technique for sparse signal reconstruction, focusing on super-resolution estimation of spectral line locations and their quantity. Its cost function coinsides with that of stochastic maximum likelihood (SML), a well-known method in array processing for estimating frequencies of complex exponentials. While SML exhibits consistency and efficiency with growing array snapshots or size, SBL-DR faces inconsistency with only one measurement snapshot. This study explores SBL-DR asymptotic behavior using a single measurement snapshot and growing sample size using Γ-convergence theory. It computes upper and lower bounds for the SBL-DR cost function, showing their convergence to a Γ-limit that is minimized at true signal locations. By leveraging the properties of Γ-convergence, it is established that the minima of the SBL-DR cost function asymptotically approach those of the Γ-limit function, thereby achieving consistency for SBL-DR.

In this letter, a guidance strategy is proposed to optimize synthetic aperture sampling for occlusion removal with drones based on point-cloud representation of occluders. Prerecorded light detecting and ranging (LiDAR) scans are utilized to compute the visibility of fixed inspection regions on the ground that are intended for recurrent monitoring from the air. By utilizing Helmholtz reciprocity, the drone-collected LiDAR scans are used to computationally obtain a reciprocal visibility (RV) of potential drone positions in the air from points of interest on the ground. This visibility forms a basis for a novel navigation strategy. This strategy was shown to drive drones to optimal aerial monitoring positions, thus reducing occlusion and, consequently, the sampling time. Compared with previous unguided sampling, we achieve a 5%–20% higher visibility with 9–17 times less samples in our experiments.

We present a parallel implementation of a 2D seismic ray tracer on a graphics processing unit of the compact Jetson Nano by Nvidia. Ray tracing is commonly used in seismic imaging as an intermediate step in reconstructing subsurface structures. We employ a gradient-based ray tracer that requires a travel time map. Here, we make use of the fast iterative method that computes a travel time map in a parallel fashion. Since a ray path is independent from any other ray path, the tracing can be implemented in parallel as well. To this end, we use a graphics processing unit and implement ray tracing using the CUDA programming language. For performance evaluations we compare our implementation on the Jetson Nano to a state-of-the-art sequential seismic ray tracer on a desktop CPU and show that speedups with factors of up to three can be achieved. The results indicate that edge devices such as the Jetson Nano can play a relevant role for tomographic applications particularly in scenarios where mobility of processing devices and compactness are important.

This work studies and defines the problem of providing extensive and opportunistic Edge AI-based area coverage in smart city application scenarios, by researching and determining the optimal configuration of sensing and computational resources for minimizing the environmental/technology footprint of the solution. A typical smart city computing continuum consists of statically installed multimodal sensing Internet-of-Things (IoT) nodes at various city locations, accompanied by interconnected computational Cloud/Edge/IoT nodes. This paper presents Optimal Trustworthy EdgeAI (OTE), an entirely novel research pipeline, that complements existing smart city infrastructure with intelligent drone Edge/IoT nodes (in the form of modularly equipped unmanned aerial vehicles), capable of autonomous repositioning according to individual/collective sensing and coverage criteria. Thereby, we envisage the emerging cutting-edge technologies of trustworthy sensing, perceiving, modelling technologies for predicting the behavior of moving targets (e.g., citizens/vehicles/objects), understanding natural phenomena (e.g., sea wave motion, urban flora/fauna, biodiversity) in order to anticipate events (people's bad habits, environmental changes), by exploiting novel continuous data processing services across the whole span of the enhanced Cloud-Edge-IoT computing continuum.

Distributed subsurface imaging is of high relevance for autonomous seismic surveys by multi-agent networks as envisioned for future planetary missions. The goal is to achieve a cooperative reconstruction of a subsurface image at each agent by relying on data exchange among the agents. To this end, distributed full waveform inversion for high-resolution imaging has been proposed. However, full waveform inversion always requires an initial model of the subsurface. To provide each agent in the network with such a model, we propose a distributed traveltime tomography. To this end, we integrate a distributed kernel-based regression of traveltime residuals into traveltime tomography. By that, each agent computes an approximation of all time residuals in the network and can perform a traveltime tomography to obtain a subsurface image locally. We conduct numerical evaluations for a synthetic subsurface model and the SEG salt model. The results show that each receiver indeed achieves a subsurface image that is close to the global result even for a low network connectivity.

We consider the problem of distributed subsurface imaging in seismic receiver networks. This problem is particularly relevant for future planetary exploration missions where multi-agent networks shall autonomously reconstruct a subsurface based on network-wide measurements. To this end, we propose a distributed implementation of the full waveform inversion (FWI) for distributed imaging of subsurfaces in seismic networks. In particular, we show that the gradient of FWI is equivalent to the sum of locally computed gradients. To obtain estimates of the global gradient and subsurface model at each receiver we employ the adapt-then-combine technique that relies on data exchange among neighboring receivers only. Numerical evaluations show that the proposed distributed FWI performs close to its centralized version for different source-receiver constellations.

For swarm systems, distributed processing is of paramount importance and Bayesian methods are preferred for their robustness. Existing distributed sparse Bayesian learning (SBL) methods rely on the automatic relevance determination (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 maximization (FMLM) method to develop a faster distributed SBL version. The proposed method has a low communication overhead, and can be distributed by simple consensus methods. The performed simulations indicate a better performance compared with the distributed ARD version, yet the same performance as the FMLM.

Non-stationary channel models play a crucial role in today's communication systems. Mobile-to-mobile channels are known to exhibit non-stationary behavior caused by the movement of transmitter and receiver. Non-stationarity can be addressed by introducing time-variant stochastic functions such as the time-variant instantaneous Doppler probability density function or time-variant instantaneous characteristic function. An algebraic analysis of the time-variant Doppler probability density function (pdf) in a classical Cartesian coordinate system is only numerically tractable due to trigonometric functions in the resulting expressions. In contrast, it has been shown that by using prolate spheroidal coordinates for 2D vehicle-to-vehicle channels the algebraic analysis becomes analytically tractable. In this paper, the analysis is extended to air-to-air channels. It is shown that the time-variant Doppler pdf can be represented without trigonometric functions. The description of the Doppler frequency in prolate spheroidal coordinates allows describing it as an algebraic curve. This permits the use of algebraic methods to analyze the Doppler frequency and derive the boundaries of the resulting Doppler pdf. Using the developed tools, we have investigated exemplary air-to-air scenarios. However, the methodology can be extended to any air-to-air configuration.

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.

Information gathering algorithms aim to intelligently select the robot actions required to efficiently obtain an accurate reconstruction of a physical process, such as an occupancy map, or a magnetic field. Many recent works have proposed algorithms for information gathering. However, these algorithms employ discretization of the state space, which makes them computationally intractable for robotic systems with complex dynamics. Moreover, most algorithms are not suited for online information gathering tasks. This paper presents a novel approach that tackles the two aforementioned issues. Specifically, our approach includes two intertwined steps: a Gaussian processes (GPs)-based prediction that allows a robot to identify highly unexplored locations, and an RRT*-based informative path planning that guides the robot towards those locations. The combination of the two steps allows an online realization of the algorithm, while eliminates the need of discretization. We demonstrate the effectiveness of the proposed algorithm in simulations, as well as with an experiment in which a ground-based robot explores the magnetic field intensity within an indoor environment populated with obstacles.

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, multi-agent 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.

The fading process describing the propagation effects caused by scattering between two mobile transceivers shows strong non-stationary properties. For its characterization the local scattering function (LSF) and the instantaneous delay Doppler probability density function (pdf) have been introduced. In this paper, a relation between LSF and the joint pdf is investigated. In previous works, it was conjectured that a proportionality relationship between LSF and pdf might exist, similar to the relationship between the scattering function and the delay Doppler pdf in the wide-sense stationary uncorrelated scattering case. The goal here is to demonstrate this proportionality empirically based on the analysis of channel measurements. Both the LSF and the delay Doppler pdf can be combined in order to create a model for mobile-to-mobile (M2M) channels. The LSF is hereby used to process the measurement data and extract information like the stationarity time. With this information the joint delay Doppler pdf can be used to create a realistic simulation environment of the wireless channel for M2M communication systems.

In this paper a novel algorithm for estimation and tracking of multipath components for range estimation using signals with low bandwidth is discussed. In multipath rich environments ranging becomes a challenging problem when used with low bandwidth signals: unless multipath interference is resolved, large ranging errors are typical. In this work the estimation and tracking of individual multipath components is studied. The new technique combines sparse Bayesian learning and variational Bayesian parameter estimation with Kalman filtering. While the former is used to detect and estimate the individual components, the Kalman filtering is used to track the estimated signals. Two assumptions are compared: independence of multipath components, typical for classical multipath estimation schemes, versus correlation between the propagation paths. The later has been found to improve component tracking and estimation at the cost of increased computational complexity. The performance of the algorithm is investigated using synthetic, as well as real measurement data collected during flight trials. Significantly improved ranging performance can be obtained as compared to the standard correlation-based ranging.

Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the ℓ1-norm of the parameter of interest. However, other penalization terms have proven to have strong sparsity-inducing properties. In this work, we design pilot-assisted channel estimators for OFDM wireless receivers within the framework of sparse Bayesian learning by defining hierarchical Bayesian prior models that lead to sparsity-inducing penalization terms. The estimators result as an application of the variational message-passing algorithm on the factor graph representing the signal model extended with the hierarchical prior models. Numerical results demonstrate the superior performance of our channel estimators as compared to traditional and state-of-the-art sparse methods.

In this work, a variational Bayesian framework for efficient training of echo state networks (ESNs) with automatic regularization and delay&sum (D&S) readout adaptation is proposed. The algorithm uses a classical batch learning of ESNs. By treating the network echo states as fixed basis functions parameterized with delay parameters, we propose a variational Bayesian ESN training scheme. The variational approach allows for a seamless combination of sparse Bayesian learning ideas and a variational Bayesian space-alternating generalized expectation-maximization (VB-SAGE) algorithm for estimating parameters of superimposed signals. While the former method realizes automatic regularization of ESNs, which also determines which echo states and input signals are relevant for "explaining" the desired signal, the latter method provides a basis for joint estimation of D&S readout parameters. The proposed training algorithm can naturally be extended to ESNs with fixed filter neurons. It also generalizes the recently proposed expectation-maximization-based D&S readout adaptation method. The proposed algorithm was tested on synthetic data prediction tasks as well as on dynamic handwritten character recognition.

In this work a new online learning algorithm that uses automatic relevance determination (ARD) is proposed for fast adaptive non linear filtering. A sequential decision rule for inclusion or deletion of basis functions is obtained by applying a recently proposed fast variational sparse Bayesian learning (SBL) method. The proposed scheme uses a sliding window estimator to process the data in an online fashion. The noise variance can be implicitly estimated by the algorithm. It is shown that the described method has better mean square error (MSE) performance than a state of the art kernel re cursive least squares (Kernel-RLS) algorithm when using the same number of basis functions.

In this work a new adaptive fast variational sparse Bayesian learning (V-SBL) algorithm is proposed that is a variational counterpart of the fast marginal likelihood maximization approach to SBL. It al lows one to adaptively construct a sparse regression or classification function as a linear combination of a few basis functions by minimizing the variational free energy. In the case of non-informative hyperpriors, also referred to as automatic relevance determination, the minimization of the free energy can be efficiently realized by computing the fixed points of the update expressions for the variational distribution of the sparsity parameters. The criteria that establish convergence to these fixed points, termed pruning conditions, allow an efficient addition or removal of basis functions; they also have a simple and intuitive interpretation in terms of a component's signal-to-noise ratio. It has been demonstrated that this interpretation allows a simple empirical adjustment of the pruning conditions, which in turn improves sparsity of SBL and drastically accelerates the convergence rate of the algorithm. The experimental evidence collected with synthetic data demonstrates the effectiveness of the proposed learning scheme.

Reconfigurable logic (FPGA) allows to implement custom-precision arithmetic units. In this work we propose an algorithm, which employs a Bayesian technique to determine the optimal amount of bits for representing the involved continuous variables. We restrict ourselves to the problem of nonlinear approximation, where an assumed data model consists of superimposed signals with unknown parameters. By fitting such models using a variational Bayesian EM-based algorithm, we can determine the importance of each signal component using a techniques inspired by the Bayesian evidence procedure. Due to the structure of the obtained variational update expressions, it becomes possible to show that the evidence value represents the combined effect of the relevance of a signal component for explaining the measurement data, and additive noise, associated with this component. This insight allows to interpret the value of the evidence parameters in terms of a Signal-to-Noise ratio, which is then used to develop an optimal discretization scheme. The effectiveness of the proposed approach is demonstrated with two synthetic examples, showing a bitwidth reduction of more than 70% at the cost of a relative mean squared error of 0.0036 and 0.012, respectively.

In this paper we investigate the problem of learning Echo State Networks (ESN) with adaptable filter neurons and delay&sum readouts. A brute-force solution to this learning problem is often impractical due to nonlinearity and high dimensionality of the resulting optimization problem. In this work we propose an approximate solution to the ESN learning by appealing to the variational Bayesian EM-type of estimation algorithm. We show that such approach allows to significantly reduce the dimensionality of the resulting objective functions. Furthermore, it allows to implement ESN learning and adapt filter neurons and delays jointly within the variational framework. Simulations are performed for learning randomly generated target ESNs, as well as other synthetic nonlinear dynamic systems. The results demonstrate that the proposed learning algorithm can improve ESN learning for a wide class of problems.

Wireless systems are subject to fading - time variations of the receiving conditions caused by multipath propagation and transceiver movements. Prediction of fading allows to 'learn' the channel state information (CSI) in advance and adjust the transmission scheme accordingly. In this contribution we consider a framework to handle predictions of general fast- and non-flat fading MIMO wireless channels. The approach is based on modeling the dynamics of individual multipath components, extracted with the SAGE algorithm. This decreases the rate of variation of the channel thus allowing a greater prediction horizon and simpler predictor designs. The extracted components are then tracked using dynamical programming coupled with the multipath component distance measure, and component parameters are then predicted over time using adaptive predictors - hypermodels. We consider linear as well as nonlinear predictor designs. This prediction scheme is applied to MIMO impulse response measurements in 2 GHz frequency band, tracked over the distance of ap 4 m, achieving prediction horizons of 1.5lambda.

This paper addresses application of the Bayesian evidence procedure to the analysis of wireless channels. We use relevance vector machines, a kernel-based technique to locally maximize evidence that turns out to be promising in the context of the wireless channel estimation. This approach not only allows to estimate channel parameters, but also provides a tool to assess the number of multipath components. We show that in the case of channel sounding using a pulse-compression technique, it is possible to design an optimal kernel, as well as to estimate parameters of the additive noise and base on it a thresholding level to implement model order estimation. The applicability of the proposed scheme is demonstrated with synthetic as well as real channel measurements.

This paper introduces a novel wireless channel clustering technique, based on the Saleh-Valenzuela channel model. The channel impulse response is regarded as a realization of the probabilistic channel model, based on which the prior density functions of cluster arrival times are derived. Cluster analysis is done by means of extending the Saleh-Valenzuela model to a non-stationary case and re-interpreting it in terms of mixture models. The parameters of the mixture are then learned with hidden Markov models. Once trained, the HMM could be used to optimally cluster the channel taps with the Viterbi algorithm. The proposed method has been applied to simulated as well as measured channel impulse responses and showed reasonably good performance.