Related papers: Localization of sources in weakly nonlinear fluid …
In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the problem of spectral line estimation, where our goal is simply…
This paper presents a Bayesian estimation method for the passive localization of an acoustic source in shallow water. Our probabilistic focalization approach estimates the time-varying source location by associating direction of arrival…
This paper considers the problem of localising a stationary signal source using a team of mobile agents which only take binary measurements. Background false detection rates and missed detection probabilities are incorporated into the…
Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable solution of an inverse problem. Most real-world systems of…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar…
In many real-world scenarios, such as gas leak detection or environmental pollutant tracking, solving the Inverse Source Localization and Characterization problem involves navigating complex, dynamic fields with sparse and noisy…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
This paper presents a unified framework for robust three-dimensional (3-D) source localization using a network of sensors equipped with one-dimensional (1-D) linear arrays. While such arrays offer practical advantages in terms of cost and…
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…
We consider the inverse scattering problem for time-harmonic acoustic waves in a medium with pointwise inhomogeneities. In the Foldy-Lax model, the estimation of the scatterers' locations and intensities from far field measurements can be…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…
Herein, the problem of simultaneous localization of multiple sources given a number of energy samples at different locations is examined. The strategies do not require knowledge of the signal propagation models, nor do they exploit the…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…
This paper presents a non-cooperative source localization approach based on received signal strength (RSS) and 2D environment map, considering both line-of-sight (LOS) and non-line-of-sight (NLOS) conditions. Conventional localization…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…