The expectation--maximization (EM) algorithm updates all of the parameter estimates simultaneously, which is not applicable to direction of arrival (DOA) estimation in unknown nonuniform noise. In this work, we present several efficient EM-type algorithms, which update the parameter estimates sequentially, for solving both the deterministic and stochastic maximum--likelihood (ML) direction finding problems in unknown nonuniform noise. Specifically, we design a generalized EM (GEM) algorithm and a space-alternating generalized EM (SAGE) algorithm for computing the deterministic ML estimator. Simulation results show that the SAGE algorithm outperforms the GEM algorithm. Moreover, we design two SAGE algorithms for computing the stochastic ML estimator, in which the first updates the DOA estimates simultaneously while the second updates the DOA estimates sequentially. Simulation results show that the second SAGE algorithm outperforms the first one.
In this paper, the problem of determining the number of signal sources impinging on an array of sensors and estimating their directions-of-arrival (DOAs) in the presence of spatially white nonuniform noise is considered. It is known that, in the case of nonuniform noise, the stochastic likelihood function cannot be concentrated with respect to the diagonal elements of noise covariance matrix. Therefore, the stochastic maximum-likelihood (SML) DOA estimation and source enumeration in the presence of nonuniform noise requires multidimensional search with very high computational complexity. Recen…
The problem of direction-of-arrival (DOA) estimation in the presence of nonuniform sensor noise is considered and a novel algorithm is developed. The algorithm consists of three phases. First, the diagonal nonuniform sensor noise covariance matrix is estimated using an iterative procedure that requires only few iterations to obtain an accurate estimate. The asymptotic variance of one iteration is derived for the proposed noise covariance estimator. Second, a forward-only rooting-based DOA estimator as well as its forward-backward averaging extension are developed for DOA estimation. The DOA es…
The purpose of this research is to employ non-uniform arrays in different active and passive sensing applications for both narrowband and wideband operations, while providing a multitude of array processing methodologies that assist in dealing with the different encountered challenges. The problem of direction-of-arrival (DOA) estimation using non-uniform arrays is considered. The different challenges that are treated include the reduction of the available degrees-of-freedom (DOFs), the presence of coherent targets, and the mutual coupling effect in practical antenna arrays. Multi-frequency op…
To reduce the adverse impacts of the unknown colored noise on the performance degradation of the direction-of-arrival (DOA) estimation, we propose a new gridless DOA estimation method based on fourth-order cumulant (FOC)in this letter. We first introduce the non-redundancy single measurement vector (SMV) through FOC, which is capable of suppressing the Gaussian colored noise. Next, we analyze the distribution of the estimation error and design an estimation error tolerance scheme for it. We then combine the atomic norm minimization of the non-redundancy SMV with the above constraint scheme. Th…
A new array signal reconstruction and signal-channel DOA estimation method based on TMLA by nonuniform period modulation are proposed. By using non-uniform period modulation, the harmonic component produced by different elements could be separated. Therefore, the conventional snapshot could be reconstructed by analyzing the spectrum of the combined signal. Then spatial spectrum estimation method is used to implement DOA estimation. Numerical simulations are provided to verify the feasibility and accuracy of the proposed method. Since the duration of the signal in the frequency domain analysis …
In the practical radar with multiple antennas, the antenna imperfections degrade the system performance. In this paper, the problem of estimating the direction of arrival (DOA) in multiple-input and multiple-output (MIMO) radar system with unknown mutual coupling effect between antennas is investigated. To exploit the target sparsity in the spatial domain, the compressed sensing (CS)-based methods have been proposed by discretizing the detection area and formulating the dictionary matrix, so an \emph{off-grid} gap is caused by the discretization processes. In this paper, different from the pre…
The expectation-maximization (EM) and space-alternating generalized EM (SAGE) algorithms have been applied to direction of arrival (DOA) estimation in known noise. In this work, the two algorithms are proposed for DOA estimation in unknown uniform noise. Both the deterministic and stochastic signal models are considered. Moreover, a modified EM (MEM) algorithm applicable to the noise assumption is also proposed. These proposed algorithms are improved to ensure the stability when the powers of sources are unequal. After being improved, numerical results illustrate that the EM algorithm has simi…
Self-Calibration DOA Estimation for Movable Antenna Systems with Antenna Position Errors
Nanjing University of Science and Technology（南京理工大学）；Qian Xuesen College, Nanjing University of Science and Technology（南京理工大学钱学森学院）；Seoul National University（首尔大学）
This paper is concerned with estimating unknown multi-dimensional frequencies from linear compressive measurements. This is accomplished by employing the recently proposed atomic norm minimization framework to recover these frequencies under a sparsity prior without imposing any grid restriction on these frequencies. To this end, we give a rigorous derivation of an iterative scheme called alternating direction of multipliers method, which is able to incorporate multiple compressive snapshots from a multi-dimensional superposition of complex harmonics. The key result here is how to formulate th…
Self-Calibration DOA Estimation for Moving Dilated Arrays with Gain and Phase Errors
Key Laboratory of Near-Range RF Sensing ICs and Microsystems, Ministry of Education（教育部近程射频传感集成电路与微系统重点实验室）；School of Electronic and Optical Engineering, Nanjing University of Science and Technology（南京理工大学电子与光学工程学院）；Qian Xuesen College, Nanjing University of Science and Technology（南京理工大学钱学森学院）
The paper considers direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), inspiring stochastic maximum likelihood DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using s…
Received signal strength (RSS) based source localization method is popular due to its simplicity and low cost. However, this method is highly dependent on the propagation model which is not easy to be captured in practice. Moreover, most existing works only consider the single source and the identical measurement noise scenario, while in practice multiple co-channel sources may transmit simultaneously, and the measurement noise tends to be nonuniform. In this paper, we study the multiple co-channel sources localization (MSL) problem under unknown nonuniform noise, while jointly estimating the …
This letter addresses the estimation of directions-of-arrival (DoA) by a sensor array using a sparse model in the presence of array calibration errors and off-grid directions. The received signal utilizes previously used models for unknown errors in calibration and structured linear representation of the off-grid effect. A convex optimization problem is formulated with an objective function to promote two-layer joint block-sparsity with its second-order cone programming (SOCP) representation. The performance of the proposed method is demonstrated by numerical simulations and compared with the …
The report focuses on three areas in particular: the first is the Received Signal Strength indicator technique, Direction of Arrival technique, and the integration of two algorithms, RSS and DOA, in order to build a hybrid, more robust algorithms. In the Received Signal Strength (RSS), the unknown node location is estimated using trilateration. This report examines the performance of different estimators such as Least Square, Weighted Least Square, and Huber robustness in order to obtain the most robust performance. In the direction of arrival (DOA) method, the estimation is carried out using …
This paper presents an efficient method for computing maximum likelihood (ML) direction of arrival (DOA) estimates assuming unknown sensor noise powers. The method combines efficient Alternate Projection (AP) procedures with Newton iterations. The efficiency of the method lies in the fact that all its intermediate steps have low complexity. The main contribution of this paper is the method's last step, in which a concentrated cost function is maximized in both the DOAs and noise powers in a few iterations through a Newton procedure. This step has low complexity because it employs closed-form e…
Estimating the direction of arrival (DOA) of sources is an important problem in aerospace and vehicular communication, localization and radar. In this paper, we consider a challenging multi-source DOA estimation task, where the receiving antenna array is composed of non-coherent sub-arrays, i.e., sub-arrays that observe different unknown phase shifts at every snapshot (e.g., due to waiving the demanding synchronization of local oscillators across the entire array). We formulate this problem as the reconstruction of joint sparse and low-rank matrices, and solve the problem's convex relaxation. …
Delayed state synchronization of continuous-time multi-agent systems in the presence of unknown communication delays (including complete proofs)
College of Information Science and Engineering, Northeastern University（东北大学信息科学与工程学院）；School of Electrical Engineering and Computer Science, Washington State University（华盛顿州立大学电气与计算机工程学院）；Department of Electrical Engineering, Mathematics and Computer Science, University of Twente（特温特大学电气、数学与计算机科学系）；School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance（上海立信会计金融学院统计与数学学院）
Shanghai University（上海大学）；East China Normal University（华东师范大学）
We analyze convergence of decentralized cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly time-varying observation matrices. The underlying communication network is modeled by a sequence of random digraphs and is subjected to nonuniform random time-varying delays in channels. Each node runs an online estimation algorithm consisting of a consensus term taking a weighted sum of its own estimate and neighbours' delayed estimates, and an innovation …
