Localization of multiple nodes based on correlated measurements and shrinkage estimation

Accurate covariance matrix estimation has applications in a wide range of disciplines. For many applications the estimated covariance matrix needs to be positive definite and hence invertible. When the number of data points is insufficient, the estimated sample covariance matrix has two fold disadvantages. Firstly, although it is unbiased, it consists of a large estimation error. Secondly, it is not positive definite. A shrinkage technique has been proposed in the fields of finance and life sciences to estimate the covariance matrix that is invertible and contains relatively a small estimation error variance. In this paper, we introduce the shrinkage covariance matrix concept in the area of multiple target localization in wireless networks with correlated measurements. For localization, we use the low cost received signal strength (RSS) measurements. Unlike most studies, where the links between sensor nodes (SNs) and targets nodes (TNs) are independent, we use a realistic model where these links are correlated. Optimization in location accuracy is achieved by weighting each link via the shrinkage covariance matrix. Simulation results show that using the estimated shrinkage covariance improves the location accuracy of the localization algorithm.