Efficient Two-Dimensional Direction-of-Arrival Estimation for a Mixture of Circular and Noncircular Sources

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for a mixture of circular and noncircular sources is considered. In particular, we focus on a 2-D array structure consisting of two parallel uniform linear arrays and build a general array model with mixed circular and noncircular sources. The received array data and its conjugate counterparts are combined together to form a new data vector, based on which a series of 2-D DOA estimators is derived. Compared with existing methods, the proposed one has three main advantages. First, it can give a more accurate estimation in situations, where the number of sources is within the traditional limit of high-resolution methods. Second, it can still work effectively when the number of mixed signals is larger than that of the array elements. Finally, the paired 2-D DOAs of the proposed method can be obtained automatically without the complicated 2-D spectrum peak search and, therefore, has a much lower computational complexity

Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. In this paper, as a benchmark for these NC methods, we derive the closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources. Assuming a separable centro-symmetric R-D array, we show that in some special cases, the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain for two sources. Our analysis is supported by extensive simulation results.Comment: submitted to IEEE Transactions on Signal Processing, 13 pages, 4 figure

R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) non-circular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R-D antenna arrays and do not require a centrosymmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R-D NC ESPRIT-type algorithms is identical in the high effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6 figure

Recovery under Side Constraints

This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representationvector, and the nonlinear measurement structure. First, we demonstrate how a priori information in form of structural side constraints influence recovery guarantees (null space properties) using L1-minimization. Furthermore, for constant modulus signals, signals with row-, block- and rank-sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. Moreover, we discuss the linear mixing matrix design based on coherence minimization. Then we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase retrieval problem with and without dictionary learning

New Approaches for Two-Dimensional DOA Estimation of Coherent and Noncircular Signals with Acoustic Vector-sensor Array

This thesis is mainly concerned with the two-dimensional direction of arrival (2D-DOA) estimation using acoustic vector-sensor array for coherent signals and noncircular signals. As for coherent signals, the thesis proposes two algorithms, namely, a 2D-DOA estimation algorithm with acoustic vector-sensor array using a single snapshot, and an improved 2D-DOA estimation algorithm of coherent signals. In the first algorithm, only a single snapshot is employed to estimate the 2D-DOA, and the second is an improved algorithm based on the method of Palanisamy et al. Compared to the existing algorithm, the proposed algorithm has the following advantages: (1) lower computational complexity, (2) better estimation performance, and (3) acquiring automatically-paired 2D-DOA estimates. As for noncircular signals, we propose real-valued space PM and ESPRIT algorithms for 2D-DOA estimation using arbitrarily spaced acoustic vector-sensor array. By exploiting the noncircularity of incoming signals to increase the amount of effective data, the proposed algorithms can provide a better 2D-DOA estimation performance with fewer snapshots, which means a relatively lower sample rate can be used in practical implementations. Compared with the traditional PM and ESPRIT, the proposed algorithms provide better estimation performance while having similar computational complexity. Furthermore, the proposed algorithms are suitable for arbitrary arrays and yield paired azimuth and elevation angle estimates without requiring extra computationally expensive pairing operations

Algorithm for Geodetic Positioning Based On Angle-Of-Arrival of Automatic Dependent Surveillance-Broadcasts

This paper develops a non-precision, three-dimensional, geodetic positioning algorithm for airborne vehicles. The algorithm leverages the proliferation of Automatic Dependent Surveillance – Broadcast (ADS-B) equipped aircraft, utilizing them as airborne navigation aids to generate an RF Angle-of-Arrival (AOA) and Angle-of-Elevation (AOE) based geodetic position. The resulting geodetic position can serve as a redundant navigation system for use during locally limited Global Navigation Satellite System (GNSS) availability, be used to validate on-board satellite navigation systems in an effort to detect local spoofing attempts, and be used to validate ADS-B position reports. The navigation algorithm is an implementation of an Extended Kalman Filter (EKF) that is loosely based on Simultaneous Localization and Mapping (SLAM), in that it tracks ADS-B capable aircraft while simultaneously determining the geodetic position and velocity of the host vehicle. Unlike SLAM, where the absolute location – latitude/longitude – of the landmarks is unknown and must be estimated as the vehicle encounters them, the absolute position of the airborne navigation aids is typically well-known and periodically reported in the ADS-B data set. Because the absolute position of the navigation aids are known, the resulting host vehicle position will also be an absolute, rather than a relative position. Secondarily, the continuous tracking of the airborne navigation aids allows reported ADS-B positions to be validated against the estimated navigation aid position; thereby, concurrently accomplishing ADS-B validation and host vehicle geolocation. This research has demonstrated through a series of simulated Monte-Carlo tests that the algorithm is capable of generating valid position estimates, along with a reliable estimate of its accuracy, across a variety of anticipated input conditions. With multiple GNSS quality navigation aids available, mean position errors below 225 meters were observed. As the quality of the navigation aids decreased, so too did the accuracy of the algorithm. Utilizing navigation aids with an accuracy of 4 nautical miles (95% containment) resulted in mean position errors on the order of 0.75 nautical miles. These results demonstrate that the method is feasible, and even under worst case conditions, the accuracy of the position estimate generated by the algorithm was sufficient to allow an aircraft to navigate to its destination