Greedy Sensor Selection Based on LU Factorization for Linear Least Squares Estimation

For linear least squares estimation of parameters in wireless sensor networks, we focus on construction of the best subset of sensors that minimizes the estimation error which requires computation of the inverse of large matrices. We manipulate the estimation error based on the LU factorization, resulting in the factored triangular matrices, the inverse of which can be iteratively obtained without large matrix inversion. We then derive an analytic selection rule in a greedy manner which facilitates a fast selection process. We also discuss the complexity of different selection methods with an emphasis on a reasonable complexity of the proposed method. We finally validate the merit of the proposed algorithm through numerical experiments in the aspect of estimation performance and complexity as compared with previous methods.