d-MUSIC : an algorithm for single snapshot direction-of-arrival estimation




Howell, Randy Keith

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The d-MUSIC algorithm estimates the direction-of-arrival of two closely spaced sources using a single array snapshot. To make the problem full rank, d-MUSIC utilizes additional information, specifically the derivative of the input snapshot vector. The combined vector set yields a rank two signal space projector that can be used to estimate the source directions. To construct this projector, an estimate for the center of the target cluster is required. In many radar low angle tracking problems involving distant aircraft, the center of the target plus multipath cluster is known a priori (flat earth approximation). Otherwise, d-MUSIC estimates the source bearings for a grid of center angles and selects the grid point where the signal space of the solution is most consistent with the input vector. Following the approach of Stoica and Nehorai [10], a theoretical estimate for the d-MUSIC error variance is derived and compared to the Cramér-Rao bound for the case of a known cluster centroid (typical air traffic control problem). The algorithm nearly attains the Cramér-Rao bound, displaying a low sensitivity to signal correlation. A number of Monte Carlo tests are also performed to compare the performance of MUSIC to the two d-MUSIC algorithms (cluster center known or unknown). These tests demonstrate that both versions of d-MUSIC is highly resilient to signal correlation whereas MUSIC is not. The algorithm is field tested using data from a X-band radar tracking a low flying helicopter. The receive array is a 6 channel vertical linear array of horns with an array aperture of nearly 19 wavelengths. As the flat earth approximation is not appropriate to this experiment the grid search version of d-MUSIC is employed (unknown cluster center). The array is calibrated using the method of Wylie et al. [30] to restore the Toeplitz structure of the covariance matrix. With a spacing of 16% to 35% of a beamwidth between the direct and multipath signals, the d-MUSIC rms error for the source spacing is 9.6% of a beamwidth for the 4 data collections while MUSIC resolved the two signals for 2 of the 4 cases with a rms error of 18.1%.



Algorithms, Vector analysis