Jimeng Zheng

Sparse Spatial Spectral Estimation: A Covariance Fitting Algorithm, Performance and Regularization

In this paper, the sparse spectrum fitting (SpSF) algorithm for the estimation of directions-of-arrival (DOAs) of multiple sources is introduced, and its asymptotic consistency and effective regularization under both asymptotic and finite sample cases are studied. Specifically, through the analysis of the optimality conditions of the method, we prove the asymptotic, in the number of snapshots, consistency of SpSF estimators of the DOAs and the received powers of uncorrelated sources in a sparse spatial spectra model. Along with this result, an explicit formula of the best regularization parameter of SpSF estimator with infinitely many snapshots is obtained. We then build on these results to investigate the problem of selecting an appropriate regularization parameter for SpSF with finite snapshots. An automatic selector of such regularization parameter is presented based on the formulation of an upper bound on the probability of correct support recovery of SpSF, which can be efficiently evaluated by Monte Carlo simulations. Simulation results illustrating the effectiveness and performance of this selector are provided, and the application of SpSF to direction-finding for correlated sources is discussed.

Sparse spectral fitting for Direction Of Arrival and power estimation

In this paper, we present a sparse spatial spectrum estimation method which provides superresolution direction-finding performance and accurate signal power estimation simultaneously. Compressive sensing ideas are used in conjunction with a postulated model for the covariance matrix of the array output instead of the output itself. Following a preliminary analysis of the method and a geometric interpretation of the estimation process, simulation examples are presented to illustrate several performance characteristics of the technique.

Directions-of-arrival estimation using a sparse spatial spectrum model with uncertainty

This paper is concerned with the estimation of the directions-of-arrival (DOA) of narrowband sources using a sparse spatial spectral model, when the model itself is not precise. When the model uncertainty is limited to DOAs not belonging to the search grid, off-grid error linearization given in [1], and constraint relaxation are used to effect a convex problem. This approach is useful either in reducing the dimension through the use of coarser candidate DOA grid, or improving the performance of estimators that use dense grids. In addition, a particular diagonal loading approach is proposed to reduce the sensitivity of the estimator to the choice of its regularization parameter.

Robust sparse spectral fitting in element and beam spaces for Directions-Of-Arrival and power estimation

In this paper, we propose a robust sparse spectrum fitting method (RSpSF) for Directions-Of-Arrival (DOA) and power estimation in the presence of general form of modeling errors in the array manifold matrix. By exploiting the group sparsity between the power spectrum and the modeling errors, RSpSF formulates the estimator as a convex optimization program. Then, in order to reduce its computational complexity, we apply a beam-space technique to RSpSF and obtain another convex estimator, the beam-space RSpSF (BMRSpSF). Simulation examples are presented to demonstrate the robustness of the proposed methods to off-grid DOAs and to random array calibration errors.

Directions of arrival estimation by learning sparse dictionaries for sparse spatial spectra

A major limitation of most methods exploiting sparse signal or spectral models for the purpose of estimating directions-of-arrival stems from the fixed model dictionary that is formed by array response vectors over a discrete search grid of possible directions. In general, the array responses to actual DoAs will most likely not be members of such a dictionary. In this work, the sparse spectral signal model with uncertainty of linearized dictionary parameter mismatch is considered, and the dictionary matrix is reformulated into a multiplication of a fixed base dictionary and a sparse matrix. Based on this double-sparsity model, an alternating dictionary learning-sparse spectral model fitting approach is proposed to reduce the estimation errors of DoAs and their powers. Group-sparsity estimator and Lasso-based Least Squares are utilized in the formulation of the associated optimization problem. The performance of the proposed methods are demonstrated by numerical simulations.

DOA estimation in monostatic MIMO array based on sparse signal reconstruction

In this paper, a novel method for direction arrival (DOA) estimation in monostatic multiple-input multiple output (MIMO) array is presented. By using the sparse signal reconstruction of monostatic MIMO array measurements with an overcomplete basis, the singular value decomposition (SVD) of the received data matrix can be penalties based on the l1-norm. The optimization problem can be solved exploiting the second-order cone programming framework. The proposed method for monostatic MIMO array could achieve more accurate DOA estimation than the traditional DOA estimation methods. The simulation examples are presented to demonstrate the effective of the proposed method in monostatic MIMO array.

Experiments in radio location estimation using an airbone array

The problem of interest is the determination of the location of a licensed or unlicensed source of radio transmission from air. Accordingly, an experiment was conducted in 2008 involving a two-dimensional antenna array mounted on a Zeppelin NT airship. This paper gives an overview of the experiment and some results obtained to date by post-processing of the collected data. A combination of angles of arrival estimation of radio sources and the proposed attitude correction technique gives an accurate location estimation of a radio source located in an urban area. We also verified the feasibility of localization system using on-board array antennas through the experiment.

Data-adaptive regularization for DOA estimation using sparse spectrum fitting

Regularization parameter selection is critical to the performance of many sparsity-exploiting Direction-Of-Arrival (DOA) estimation algorithms. In this paper, we propose an automatic selector for choosing this parameter in the DOA estimation algorithm, which is based on the analysis of its optimality conditions. This selector requires very limited prior information and is computationally efficient. Through simulation examples, the effectiveness and robustness of the selector are illustrated.

Persistently active block sparsity with application to direction-of-arrival estimation of moving sources

In this paper, the problem of recovering inconsistent sparse models from multiple observations is considered. A new method is developed by introducing a novel objective function, which exploits both block-level and element-level sparsities and promotes persistence in activity within a block. Then, we use a SVD-based method to reduce its computational complexity. Application of the method to the Direction-Of-Arrival (DOA) estimation of moving sources using a sensor array is presented and a simulation example is shown as a demonstration of the promising performance of the method in a moving DOA setting, particularly when sources are very close to each other.