Most existing deep learning (DL) based direction-of-arrival (DOA) estimation methods treat direction finding problem as a multi-label classification task and the output of the neural network is a probability spectrum where the peaks indicate the true DOAs. These methods essentially belong to grid-based methods and may encounter grid mismatch effect. In this paper, we focus on gridless DL based DOA estimation under generalized linear array which can be regarded as a uniform linear array (ULA) with/without “holes”. By using the Toeplitz structure, a deep convolutional neural network (CNN) is proposed to estimate the noiseless covariance matrix of the aforementioned ULA with “no holes,” based on which the DOAs can be retrieved by using root-MUSIC. To increase the generalization, the parameters of the CNN with respect to different number of sources are pre-trained and stored in a database. We then propose another CNN for source enumeration in order to choose suitable parameters from the database. Our method can find more sources than sensors and do not suffer from the grid mismatch effect.

The low-rank matrix reconstruction (LRMR) approach is widely used in direction-of-arrival (DOA) estimation. As the rank norm penalty in an LRMR is NP-hard to compute, the nuclear norm (or the trace norm for a positive semidefinite matrix) has been often employed as a convex relaxation of the rank norm. However, solving a nuclear norm convex problem may lead to a suboptimal solution of the original rank norm problem. In this paper, we propose to apply a family of nonconvex penalties on the singular values of the covariance matrix as the sparsity metrics to approximate the rank norm. In particular, we formulate a nonconvex minimization problem and solve it by using a locally convergent iterative reweighted strategy in order to enhance the sparsity and resolution. The problem in each iteration is convex and hence can be solved by using the optimization toolbox. Convergence analysis shows that the new method is able to obtain a suboptimal solution. The connection between the proposed method and the sparse signal reconstruction is explored showing that our method can be regarded as a sparsity-based method with the number of sampling grids approaching infinity. Two feasible implementation algorithms that are based on solving a duality problem and deducing a closed-form solution of the simplified problem are also provided for the convex problem at each iteration to expedite the convergence. Extensive simulation studies are conducted to show the superiority of the proposed methods.

This correspondence proposes a localization method for mixed far-field (FF) and near-field (NF) sources based on cross arrays where the two-dimensional (2-D) direction-of-arrival (DOA) and range estimation are considered. For 2-D DOA estimation, we first construct a range-free cumulant-based vector and employ the covariance matching criterion and Vandermonde decomposition theorem to retrieve the DOA information. We then build a sparse model with respect to the range parameter and solve an $\ell_1$ -norm minimization problem to obtain the range estimates. Our method enjoys the following advantages: 1) our method can locate mixed FF and NF sources; 2) the azimuth, elevation and range can be automatically paired; 3) array aperture loss can be avoided. Simulation results show the effectiveness of our method.

Existing works for 3-D source localization are based on uniform cross arrays. In this correspondence, we propose a single far-field (FF) or near-field (NF) source localization method based on uniform cross arrays and then generalize it to the symmetric sparse cross arrays where each linear array is a symmetric sparse one. We utilize the cross-covariance matrix to exploit the full array aperture and employ the atomic norm minimization technique to retrieve the angle information without discretization. The range is estimated by MUSIC-like method. Our method is superior to traditional methods and exhibits enormous advantages in low signal-to-noise ratio (SNR) and small number of snapshots regions. Numerical simulations are carried out to verify the effectiveness of our method.

A new extreme learning machine (ELM) localization technique that uses received signal strength indicator fingerprints only is proposed for multifloor environments. This structured scheme forms multiple individual ELMs for the floors as well as for the geographically formed data clusters of each floor. Multifloor environments often have huge amount of training and online measurement data. To maximize efficiency, we develop a data preprocessing algorithm, aiming to: 1) efficiently extract out only the essential information from the vast amount of data sets and reduce the data dimension and 2) transform the floor-level data sets and positioning data sets of each floor into a proper structure that is suitable for the proposed ensemble ELM technique. The proposed solution is unique in that its offline phase exploits multiple individual ELMs for all floors to generate a set of floor-level classification functions with the preprocessed training data sets, and for each floor, it exploits multiple ELMs for the data clusters to generate a set of position regression functions. The online phase executes a coarse localization step to estimate the floor by using the floor-level classification functions and a refined step to estimate the position on the floor by using the position regression functions. The proposed algorithm and several existing algorithms are implemented to perform localization using the same measured datasets in a multistory building. For both floor estimation and localization on the floor, it outperforms existing schemes. For most cases, the performance gap is substantial.