LOCATION AND TRACKING OF SOURCES THROUGH PREPROCESSING AND EIGEN-DECOMPOSITION

Abstract

This project investigates and proposes two new algorithms for source direction estimation in place of the conventional MUSIC algorithm. The first proposed algorithm is developed to estimate the direction of an unknown source by using a linear array in the presence of known interferences. It functions in a two-dimensional situation where only the azimuth angle is involved. Specifically, the algorithm is developed based on the use of preprocessing to eliminate the effects of the known interferences and the determination of the eigenvector associated with the largest eigenvalue of the resulting transformed covariance matrix. The performance of the algorithm is investigated through analytical formulation and computer simulation and compared with that of the conventional MUSIC algorithm which works on the assumption that the directions of all the sources are unknown. It is found that in situations such as small source separation, low source powers and small number of samples available for estimating the covariance matrix, the conventional MUSIC algorithm has a high chance of breaking down, while the new algorithm cnn still function properly and maintain an unbiased estimate. The second proposed algorithm is developed to locate and track both the azimuth and elevation angles of unknown sources in a three-dimensional environment. Starting from some initial estimates of the source locations, the new algorithm attempts to obtain better estimates and track the position of each source in a repetitive cyclical manner. The refinement of a particular source location estimate starts from the employment of a preprocessor to remove the effects due to the other sources. Next, the eigenvector associated with the largest eigenvalue of the transformed covariance matrix is found and the difference between its ideal value and itself is determined. Finally, a gradient calculation is performed to obtain an estimate for the difference between the assumed source location and the actual position. The advantages of using this new algorithm rather than performing a thorough MUSIC search in the two­dimensional spectrum are that the implementation complexity can be reduced considerably and that the algorithm is well-suited to be employed for continuous adaptive filtering purposes in a tracking scenario.