Source bearing and steering-vector estimation using partially calibrated arrays

The problem of source direction-of-arrival (DOA) estimation using a sensor array is addressed, where some of the sensors are perfectly calibrated, while others are uncalibrated. An algorithm is proposed for estimating the source directions in addition to the estimation of unknown array parameters such as sensor gains and phases, as a way of performing array self-calibration. The cost function is an extension of the maximum likelihood (ML) criteria that were originally developed for DOA estimation with a perfectly calibrated array. A particle swarm optimization (PSO) algorithm is used to explore the high-dimensional problem space and find the global minimum of the cost function. The design of the PSO is a combination of the problem-independent kernel and some newly introduced problem-specific features such as search space mapping, particle velocity control, and particle position clipping. This architecture plus properly selected parameters make the PSO highly flexible and reusable, while being sufficiently specific and effective in the current application. Simulation results demonstrate that the proposed technique may produce more accurate estimates of the source bearings and unknown array parameters in a cheaper way as compared with other popular methods, with the root-mean-squared error (RMSE) approaching and asymptotically attaining the Cramer Rao bound (CRB) even in unfavorable conditions

Performance Analysis of the Decentralized Eigendecomposition and ESPRIT Algorithm

In this paper, we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol. An analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error (MSE) of subspace-based estimators is presented. We show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations. Moreover, we introduce the decentralized ESPRIT algorithm which yields fully decentralized direction-of-arrival (DOA) estimates. Based on the performance analysis of the decentralized power method, we derive an analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm. The validity of our asymptotic results is demonstrated by simulations.Comment: 18 pages, 5 figures, submitted for publication in IEEE Transactions on Signal Processin

Direction Finding in Partly Calibrated Arrays Exploiting the Whole Array Aperture

We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve this goal, existing algorithms, such as subspace separation and sparse recovery, have to rely on multiple snapshots, which increases the burden of data transmission and the processing delay. Therefore, we aim to enhance angular resolution using only a single snapshot. To this end, we exploit the orthogonality of the signals of partly calibrated arrays. Particularly, we transform the signal model into a special multiple-measurement model, show that there is approximate orthogonality between the source signals in this model, and then use blind source separation to exploit the orthogonality. Simulation and experiment results both verify that our proposed algorithm achieves high angular resolution as distributed arrays without position errors, inversely proportional to the whole array aperture

Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective

The signal processing community currently witnesses the emergence of sensor array processing and Direction-of-Arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and availability of powerful and affordable multi-antenna hardware platforms. The history of advances in super resolution DoA estimation techniques is long, starting from the early parametric multi-source methods such as the computationally expensive maximum likelihood (ML) techniques to the early subspace-based techniques such as Pisarenko and MUSIC. Inspired by the seminal review paper Two Decades of Array Signal Processing Research: The Parametric Approach by Krim and Viberg published in the IEEE Signal Processing Magazine, we are looking back at another three decades in Array Signal Processing Research under the classical narrowband array processing model based on second order statistics. We revisit major trends in the field and retell the story of array signal processing from a modern optimization and structure exploitation perspective. In our overview, through prominent examples, we illustrate how different DoA estimation methods can be cast as optimization problems with side constraints originating from prior knowledge regarding the structure of the measurement system. Due to space limitations, our review of the DoA estimation research in the past three decades is by no means complete. For didactic reasons, we mainly focus on developments in the field that easily relate the traditional multi-source estimation criteria and choose simple illustrative examples.Comment: 16 pages, 8 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Estimation of DOAs of Acoustic Sources in the Presence of Sensors with Uncertainties

Direction of Arrival (DOA) estimation finds its practical importance in sophisticated video conferencing by audio visual means, locating underwater bodies, removing unwanted interferences from desired signals etc. Some efficient algorithms for DOA estimation are already developed by the researchers . The performance of these algorithms is limited by the fact that the receiving antenna array is affected by some uncertainties like mutual coupling, antenna gain and phase error etc. So considerable attention is there in recent research on this area. In this research work the effect of mutual coupling and the effect of antenna gain and phase error in uniform linear array (ULA) on the direction finding of acoustic sources is studied. Also this effect for different source spacing is compared. For that, estimates of the directions of arrival of all uncorrelated acoustic signals in the presence of unknown mutual coupling has been found using conventional Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT). Also DOAs are computed after knowing the coupling coefficients so that we can compare the two results. Simulation results have shown the fact that the degradation in performance of the algorithm due to mutual coupling becomes more if the sources become closer to each other. Also we have estimated DOAs in the presence of unknown sensor gain and phase errors and we have compared this results with the results we got by considering ideal array. Finally in this case also the effect of gain and phase error as the source spacing varies has been tested. Simulation results verify that performance degradation is more if the sources become closer