TOA Estimation Using MP (Matrix Pencil) Algorithm

This section elaborates on the detailed procedure of TOA estimation using the MP (Matrix Pencil) algorithm. The algorithm's core methodology transforms the TOA estimation problem into solving a system of linear equations to achieve node localization. Specifically, the algorithm first constructs a Hankel matrix using distance information between sensor nodes, where matrix dimensions are determined by the number of available measurements. The implementation typically involves organizing time-delay measurements into a structured matrix format using vectorization operations. Subsequently, through matrix decomposition techniques such as Singular Value Decomposition (SVD), the algorithm separates the matrix into a coefficient matrix containing signal subspace information and a residual matrix representing noise components. The key computational step involves performing pseudo-inverse operations on the coefficient matrix using least-squares methods to obtain an estimation matrix. This process enables robust position estimation through eigenvalue extraction from the resulting matrix pencil formulation. The MP algorithm implementation for TOA estimation not only enhances localization accuracy in wireless sensor networks by mitigating multipath effects, but also provides significant reference value for subsequent research through its computational efficiency in handling ill-conditioned problems.