DOA estimation and mutual coupling calibration with the SAGE algorithm

AbstractIn this paper, a novel algorithm is presented for direction of arrival (DOA) estimation and array self-calibration in the presence of unknown mutual coupling. In order to highlight the relationship between the array output and mutual coupling coefficients, we present a novel model of the array output with the unknown mutual coupling coefficients. Based on this model, we use the space alternating generalized expectation-maximization (SAGE) algorithm to jointly estimate the DOA parameters and the mutual coupling coefficients. Unlike many existing counterparts, our method requires neither calibration sources nor initial calibration information. At the same time, our proposed method inherits the characteristics of good convergence and high estimation precision of the SAGE algorithm. By numerical experiments we demonstrate that our proposed method outperforms the existing method for DOA estimation and mutual coupling calibration

SAGE-Based Algorithm for Direction-of-Arrival Estimation and Array Calibration

Most existing array processing algorithms are very sensitive to model uncertainties caused by the mutual coupling and sensor location error. To mitigate this problem, a novel method for direction-of-arrival (DOA) estimation and array calibration in the case of deterministic signals with unknown waveforms is presented in this paper. The analysis begins with a comprehensive perturbed array output model, and it is effective for various kinds of perturbations, such as mutual coupling and sensor location error. Based on this model, the Space Alternating Generalized Expectation-Maximization (SAGE) algorithm is applied to jointly estimate the DOA and array perturbation parameters, which simplifies the multidimensional search procedure required for finding maximum likelihood (ML) estimates. The proposed method inherits the characteristics of good convergence and high estimation precision of the SAGE algorithm. At the same time, it forms a unified framework for DOA and array perturbation parameters estimation in the presence of mutual coupling and sensor location error. The simulation results demonstrate the effectiveness of the algorithm

Source Localization Using Virtual Antenna Arrays

Using antenna arrays for direction of arrival (DoA) estimation and source localization is a well-researched topic. In this paper, we analyze virtual antenna arrays for DoA estimation where the antenna array geometry is acquired using data from a low-cost inertial measurement unit (IMU). Performance evaluation of an unaided inertial navigation system with respect to individual IMU sensor noise parameters is provided using a state space based extended Kalman filter. Secondly, using Monte Carlo simulations, DoA estimation performance of random 3-D antenna arrays is evaluated by computing Cramér-Rao lower bound values for a single plane wave source located in the far field of the array. Results in the paper suggest that larger antenna arrays can provide significant gain in DoA estimation accuracy, but, noise in the rate gyroscope measurements proves to be a limiting factor when making virtual antenna arrays for DoA estimation and source localization using single antenna devices

Auto-Calibration of Co-located Uniform Linear Array Antennas

An algorithm for auto-calibration of a group of co-located uniform linear array antennas is presented. If the number of signal sources are known and, for at least one array, the ratio of the gains between two consecutive antenna elements is known, the individual unknown antenna gains can be estimated. The method is based on determining the antenna calibration parameters such that a matrix built from the array snapshots has a given rank. A numerical example illustrates the performance of the method. The numerical results suggest that the method is consistent in SNR

Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling

Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. However, existing TLS approaches do not account for sparsity possibly present in the unknown vector of regression coefficients. On the other hand, sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression, which include noise in the data, but do not account for perturbations in the regression matrix. The present paper fills this gap by formulating and solving TLS optimization problems under sparsity constraints. Near-optimum and reduced-complexity suboptimum sparse (S-) TLS algorithms are developed to address the perturbed compressive sampling (and the related dictionary learning) challenge, when there is a mismatch between the true and adopted bases over which the unknown vector is sparse. The novel S-TLS schemes also allow for perturbations in the regression matrix of the least-absolute selection and shrinkage selection operator (Lasso), and endow TLS approaches with ability to cope with sparse, under-determined "errors-in-variables" models. Interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured S-TLS solvers. Analysis and simulations demonstrate the practical impact of S-TLS in calibrating the mismatch effects of contemporary grid-based approaches to cognitive radio sensing, and robust direction-of-arrival estimation using antenna arrays.Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Signal Processin

Inertial Measurement Unit based Virtual Antenna Arrays - DoA Estimation and Positioning in Wireless Networks

Today we have different location based services available in a mobile phone or mobile station (MS). These services include: direction finding to nearby ATMs, locating favorite food restaurants, or finding any target destination. Similarly, we see different applications of the positioning and navigation systems in firefighting or other rescue operations. The common factor in almost all of the location based services is the system's ability to determine the user's current position, with reference to a floor plan or a navigation map. Current technologies are using sensor data measurements from one or more sensors, available to the positioning device, for positioning and navigation. Typical examples are radio based positioning such as global positioning system, inertial sensors based inertial navigation system, or camera based positioning systems. Different accuracy and availability conditions of the positioning and navigation solution can be obtained depending on the positioning algorithms and the available sensor information.Nowadays, the focus of research in positioning and navigation has been mostly on the use of existing hardware infrastructure and low-cost solutions, such that the proposed technique can be deployed with ease and without extra infrastructure requirements as well as without any expensive sensor equipment. In this work, we investigate a novel idea for positioning using existing wireless networks and low-cost inertial sensor measurements available at the MS. We propose to use received baseband radio signal along with inertial sensor data, such as accelerometer and rate gyroscope measurements, for direction of arrival (DoA) estimation and positioning. The DoA information from different base stations or access points can be used to estimate the MS position using triangulation technique. Furthermore, due to size and cost restrictions it is difficult to have real antenna arrays at the MS, the idea of DoA estimation and positioning is proposed to be used with single antenna devices by using the so-called virtual antenna arrays.We have presented our research results in three different papers. We provide measurement based results to perform a quantitative evaluation of DoA estimation using arbitrary virtual antenna arrays in 3-D; where a state-of-the-art high-resolution algorithm has been used for radio signal parameter estimation. Furthermore, we provide an extended Kalman filter framework to investigate the performance of unaided inertial navigation systems with 3-axis accelerometer and 3-axis rate gyroscope measurements, from a six-degrees-of-freedom inertial measurement unit. Using the extended Kalman filter framework, we provide results for position estimation error standard deviation with respect to integration time for an unaided inertial navigation system; where the effect of different stochastic errors noise sources in the inertial sensors measurements such as white Gaussian noise and bias instability noise is investigated. Also, we derive a closed form expression for Cramér-Rao lower bound to investigate DoA estimation accuracy for a far-field source using random antenna arrays in 3-D. The Cramér-Rao lower bound is obtained using known antenna coordinates as well as using estimated antenna coordinates, where the antenna coordinates are estimated with an uncertainty whose standard deviation is known. Furthermore, using Monte-Carlo simulations for random antenna arrays, we provide Cramér-Rao lower bound based performance evaluation of random 3-D antenna arrays for DoA estimation

Parametric array calibration

The subject of this thesis is the development of parametric methods for the calibration of array shape errors. Two physical scenarios are considered, the online calibration (self-calibration) using far-field sources and the offline calibration using near-field sources. The maximum likelihood (ML) estimators are employed to estimate the errors. However, the well-known computational complexity in objective function optimization for the ML estimators demands effective and efficient optimization algorithms. A novel space-alternating generalized expectation-maximization (SAGE)-based algorithm is developed to optimize the objective function of the conditional maximum likelihood (CML) estimator for the far-field online calibration. Through data augmentation, joint direction of arrival (DOA) estimation and array calibration can be carried out by a computationally simple search procedure. Numerical experiments show that the proposed method outperforms the existing method for closely located signal sources and is robust to large shape errors. In addition, the accuracy of the proposed procedure attains the Cram´er-Rao bound (CRB). A global optimization algorithm, particle swarm optimization (PSO) is employed to optimize the objective function of the unconditional maximum likelihood (UML) estimator for the farfield online calibration and the near-field offline calibration. A new technique, decaying diagonal loading (DDL) is proposed to enhance the performance of PSO at high signal-to-noise ratio (SNR) by dynamically lowering it, based on the counter-intuitive observation that the global optimum of the UML objective function is more prominent at lower SNR. Numerical simulations demonstrate that the UML estimator optimized by PSO with DDL is optimally accurate, robust to large shape errors, and free of the initialization problem. In addition, the DDL technique is applicable to a wide range of array processing problems where the UML estimator is employed and can be coupled with different global optimization algorithms