Off-grid Multi-Source Passive Localization Using a Moving Array

A novel direct passive localization technique through a single moving array is proposed in this paper using the sparse representation of the array covariance matrix in spatial domain. The measurement is constructed by stacking the vectorized version of all the array covariance matrices at different observing positions. First, an on-grid compressive sensing (CS) based method is developed, where the dictionary is composed of the steering vectors from the searching grids to the observing positions. Convex optimization is applied to solve the `1-norm minimization problem. Second, to get much finer target positions, we develop an on-grid CS based method, where the majorization-minimization technique replaces the atan-sum objective function in each iteration by a quadratic convex function which can be easily minimized. The objective function,atan-sum, is more similar to `0-norm, and more sparsity encouraging than the log-sum function.This method also works more robustly at conditions of low SNR, and fewer observing positions are needed than in the traditional ones. The simulation experiments verify the promises of the proposed algorithm.Comment: 24pages, 9 figure

Multi-Marginal Optimal Mass Transport with Partial Information

During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup common in many inverse problems in, e.g., imaging and spectral estimation. By considering an entropy regularized approximation of the original transport problem, we propose an algorithm corresponding to a block-coordinate ascent of the dual problem, where Newton's algorithm is used to solve the sub-problems. In order to make this computationally tractable for large-scale settings, we utilize the tensor structure that arises in practical problems, allowing for computing projections of the multi-marginal transport plan using only matrix-vector operations of relatively small matrices. As illustrating examples, we apply the resulting method to tracking and barycenter problems in spatial spectral estimation. In particular, we show that the optimal mass transport framework allows for fusing information from different time steps, as well as from different sensor arrays, also when the sensor arrays are not jointly calibrated. Furthermore, we show that by incorporating knowledge of underlying dynamics in tracking scenarios, one may arrive at accurate spectral estimates, as well as faithful reconstructions of spectra corresponding to unobserved time points