The analysis of wave and diffusion fields is a task central to a myriad of applications. Wave fields are encountered in acoustic, radar, and geophysics to name a few. Diffusion fields are found, for example, in physics, chemistry, and biology.

Location-awareness is becoming increasingly important in wireless networks. Indoor localization can be enabled through wideband or ultra-wide bandwidth (UWB) transmission, due to its fine delay resolution and obstacle-penetration capabilities. A major hurdle is the presence of obstacles that block the line-of-sight (LOS) path between devices, affecting ranging performance and, in turn, localization accuracy. Many techniques have been proposed to address this issue, most of which make modifications to the localization algorithm. Since many localization algorithms work with distance or angle estimates, rather than received waveforms, information inherent in the wideband waveform is lost, leading to sub-optimal ranging error mitigation. To avoid this information loss, we present a novel approach to mitigate ranging errors directly in the physical layer. In contrast to existing techniques, which detect the non-line-of-sight (NLOS) condition, our approach directly mitigates the bias incurred in both LOS and non-LOS conditions. In particular, we apply two classes of non-parametric regressors to form an estimate of the ranging error. Our work is based on, and validated by, an extensive indoor measurement campaign with FCC-compliant UWB radios. The results show that the proposed regressors provide significant performance improvements in various practical localization scenarios, compared to conventional approaches.

Physical wave fields are often described by means of a vector field. Advances in sensor technology enable us to collect an increasing number of measurement at the same location (e.g. direction, polarization, translation, and rotation). One question arising naturally is how to properly process such large and diverse information, possibly from sensors of different kinds. In this paper we propose a technique for the analysis of vector wave fields and show an application to the seismic wave field. The contributions of this paper are the following: i) We provide a framework to perform maximum likelihood parameter estimation of any wave type, modeling jointly all the measurements and parameters; ii) In the same framework, we address wave superposition by gradually decomposing the wave field; iii) We also propose an iterative algorithm for noise variance estimation.

This paper proposes a method to compute the likelihood function for the amplitudes and phase shifts of noisily observed phase-locked and amplitude-constrained sinusoids. The sinusoids are assumed to be coupled based on a set of parameters as, e.g., measurements of a monochromatic wave field. A factor graph is used to formulate the probability density function of the observations given the parameters. The factor graph consists of one second-order state-space model per signal and one additional factor connecting all the final states. Because the parameters appear only in this latter factor, we are able to formulate a sufficient statistic for parameter estimation and signal detection in terms of messages in the factor graph. In special cases, the general form of the sufficient statistic reduces to the discrete Fourier transform. As extensions we provide iterative algorithms for approximate maximum likelihood estimation of the noise variances and the parameters of superposed waves.

Sensor networks can benefit greatly from location-awareness, since it allows information gathered by the sensors to be tied to their physical locations. Ultra-wide bandwidth (UWB) transmission is a promising technology for location-aware sensor networks, due to its power efficiency, fine delay resolution, and robust operation in harsh environments. However, the presence of walls and other obstacles presents a significant challenge in terms of localization, as they can result in positively biased distance estimates. We have performed an extensive indoor measurement campaign with FCC-compliant UWB radios to quantify the effect of non-line-of-sight (NLOS) propagation. From these channel pulse responses, we extract features that are representative of the propagation conditions. We then develop classification and regression algorithms based on machine learning techniques, which are capable of: (i) assessing whether a signal was transmitted in LOS or NLOS conditions; and (ii) reducing ranging error caused by NLOS conditions. We evaluate the resulting performance through Monte Carlo simulations and compare with existing techniques. In contrast to common probabilistic approaches that require statistical models of the features, the proposed optimization-based approach is more robust against modeling errors.

Ultra-wide bandwidth (UWB) transmission is a promising technology for indoor localization due to its fine delay resolution and obstacle-penetration capabilities. However, the presence of walls and other obstacles introduces a positive bias in distance estimates, severely degrading localization accuracy. We have performed an extensive indoor measurement campaign with FCC-compliant UWB radios to quantify the effect of non-line-of-sight (NLOS) propagation. Based on this campaign, we extract key features that allow us to distinguish between NLOS and LOS conditions. We then propose a nonparametric approach based on support vector machines for NLOS identification, and compare it with existing parametric (i.e., model-based) approaches. Finally, we evaluate the impact on localization through Monte Carlo simulation. Our results show that it is possible to improve positioning accuracy relying solely on the received UWB signal.