Decentralized Direction of Arrival Estimation

Direction-of-arrival (DOA) estimation using partly calibrated arrays composed of multiple subarrays is employed in various practical applications, such as radar, sonar, and seismic exploration. The state-of-the-art DOA estimation algorithms require the measurements of all sensors to be available at a processing center (PC). The processing power of the PC and the communication bandwidth of the subarrays increase with the number of sensors. Thus, such centralized algorithms do not scale well with the number of sensors. In this thesis, decentralized DOA estimation algorithms for partly calibrated arrays are introduced to avoid the drawbacks of the centralized algorithms. In decentralized DOA estimation, each subarray is assumed to possess modest processing power and to be able to communicate with the subarrays in its vicinity. Rather than sending the raw measurement to the PC, the subarrays process their measurements and communicate among each other to achieve the estimation task. In this dissertation, decentralized DOA estimation from the second order statistics of the measurements in two processing schemes, namely, coherent and non-coherent processing is considered. In coherent processing, the whole array covariance matrix including the inter-subarray covariance matrices is available, whereas only the subarray covariance matrices are available in non-coherent processing. The DOA estimation performance of coherent processing is superior to that of non-coherent processing, since more data is available in coherent processing, that is the inter-subarray covariance matrices. However, coherent processing is more restrictive than non-coherent processing, e.g., for coherent processing the subarrays must be synchronized in time. For coherent processing, decentralized DOA estimation is achieved based on the recently introduced decentralized power method for the eigendecomposition of the sample covariance matrix. Performance analysis of the decentralized power method is presented. An analytical expression of the second order statistics of the eigenvectors and eigenvalues obtained from the decentralized power method, which is required for computing the mean square error (MSE) of subspace-based estimators, is derived. Further, the decentralized ESPRIT algorithm, which yields fully decentralized DOA estimates based on the decentralized power method, is introduced. An asymptotic analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm is derived. Similar to the conventional ESPRIT algorithm, the decentralized ESPRIT algorithm requires a shift-invariant array structure. Using interpolation, the decentralized ESPRIT algorithm is generalized to arbitrary array geometries. The decentralized ESPRIT algorithm inherits the following shortcomings of the decentralized power method: (1) the large communication cost required by the power method to compute each eigenvector, (2) the power method is a batch-based algorithm, whereas in tracking applications, online algorithms are favored. To mitigate the aforementioned shortcomings, two decentralized eigendecomposition algorithms are proposed, which achieve lower communication cost and online update of the eigenvectors and eigenvalues of the measurement covariance matrix. The decentralized ESPRIT algorithm requires the number of sources to be available beforehand. A decentralized source enumeration algorithm is introduced, which in contrast to the conventional source enumeration algorithms, does not require the computation of all the eigenvalues of the measurement covariance matrix. As an alternative, for fully calibrated arrays, the decentralized Root-MUSIC algorithm is introduced, which exploit the structure of the array. An asymptotic analytical expression of the MSE of DOA estimates obtained from the decentralized Root-MUSIC algorithm is derived. For non-coherent processing, two DOA estimators are presented, namely, the Maximum Likelihood estimator (MLE) and a computationally simpler approach based on sparse signal representation (SSR). A sufficient condition for the unique identifiability of the sources in the non-coherent processing scheme is presented, which shows that under mild conditions, the number of sources identifiable by the system of subarrays is larger than the number identifiable by each individual subarray. This property of non-coherent processing has not been investigated before, where the state-of-theart non-coherent DOA estimation algorithms fail if the individual subarrays can not identify the sources. Moreover, the Cramer-Rao Bound (CRB) for the non-coherent measurement model is derived and is used to assess the performance of the proposed DOA estimators. The behaviour of the CRB at high signal-to-noise ratio (SNR) is analyzed. In contrast to coherent processing, the in this case CRB approaches zero at high SNR only if at least one subarray can identify the sources individually. Finally, the conventional non-coherent DOA estimation scenario, where all the subarrays are uniform linear and can identify the sources, is considered. Two DOA estimation algorithms, which outperform the state-of-the-art non-coherent DOA estimators, are presented.