Commonly Used Localization Algorithms for Linear Arrays

Linear arrays are a common sensor array structure widely used in fields such as acoustics, radar, and communications. For linear array signal processing, commonly used localization algorithms primarily include Conventional Beamforming (CBF), Minimum Variance Distortionless Response (MVDR), and Multiple Signal Classification (MUSIC). These algorithms are suitable for different scenarios and requirements, effectively estimating the azimuth angle or distance of signal sources.

Conventional Beamforming (CBF) is the most fundamental localization algorithm. It enhances signals from specific directions by adjusting the weights of array elements while suppressing interference from other directions. Its computation is straightforward, but its ability to suppress noise and interference is limited. CBF is suitable for environments with high signal-to-noise ratios (SNR) and minimal interference. In MATLAB implementation, this typically involves computing the steering vector for the target direction and applying phase shifts through vector inner products.

The MVDR algorithm optimizes upon CBF by minimizing output power while maintaining constant gain in the target direction. This enables more effective suppression of interference and noise, making it suitable for high-precision localization in complex interference environments. Implementation requires calculating the inverse of the covariance matrix of received signals, which can be achieved using MATLAB's inv() function or the more stable pinv() pseudo-inverse function.

The MUSIC algorithm belongs to the subspace class of methods, utilizing the orthogonality between signal and noise subspaces to achieve high-resolution localization. It is particularly suitable for scenarios with multiple signal sources, capable of distinguishing signals with close angles. However, it has higher computational complexity and strict requirements for SNR. Implementation involves eigenvalue decomposition of the covariance matrix (using eig() or svd() functions) and peak searching in the spatial spectrum.

Each algorithm has its own advantages and disadvantages. In practical applications, appropriate localization methods should be selected based on environmental conditions and performance requirements.