Common Localization Algorithms for Linear Arrays

In this article, we introduce commonly used localization algorithms for linear arrays that enable precise target positioning. First, we present the CBF algorithm - a spatial filtering technique based on beamforming principles. This algorithm can be implemented by calculating the array response vector and applying phase shifts to steer the beam toward specific directions. Next, we discuss the MVDR algorithm, a spatial filtering method grounded in minimum variance unbiased estimation theory. Its implementation involves computing the inverse of the covariance matrix to minimize output power while maintaining unity gain in the Look direction. We describe how to handle matrix inversion challenges using diagonal loading techniques. Finally, we introduce the MUSIC algorithm, a spectral estimation-based spatial spectrum search technique. This algorithm employs eigenvalue decomposition of the covariance matrix to separate signal and noise subspaces, followed by a peak search in the MUSIC spectrum to identify source directions. We explain practical considerations for effective subspace separation and peak detection. By understanding the operational principles and implementation approaches of these algorithms, you will gain better insight into their practical application for target localization in real-world scenarios.