Source localization based on SVD without a priori knowledge

A weighted least squares (WLS) estimation procedure based on singular value decomposition (SVD) is proposed for the source localization problem under an additive measurement error model. In practical situation, the respective sensor reliability may differ. The WLS solves the problem by assigning different weights to the sensors. However, the existing WLS-based methods require a priori information, such as variance of measurement noise or the initial point of optimization. This can be a problem in an environment where the measurement noise variance cannot be accurately estimated or the initial point is not given. Although a priori information is not required and can be implemented in real-time processing, since the maximum likelihood (ML) is a Taylor-series based iterative method, it requires a more computational time and resources. Therefore, we have proposed a new analytical algorithm that needs no a priori knowledge of noise statistics or initial information and requires less computational time. We have adopted SVD and estimated the weight using the inverse of the difference between the estimate and the measurement. The proposed method has been found to be more accurate than the existing LS-based methods such as BLUE-LSC, MDS.