Robust noise-power estimation via primal-dual algorithms with measurements from a subset of network nodes

Noise power or signal variance is an important performance parameter or indicator used for many applications in signal processing and wireless communications. This paper investigates power estimation of random noises on sensor networks by using measurements taken over a subset of nodes. In many circumstances, the power values are typically smooth on the network, that is, the powers measured by neighboring nodes tend to have similar values. Using this smoothness, the power-estimation problem is formulated as a regularized optimization problem involving minimization of a sum of non-negative log-likelihood and the total variation. To find its optimal solution, a primal-dual hybrid gradient (PDHG) algorithm is developed, which uses primal- dual updates to achieve good estimation results. To further improve the estimation performance, two variants of the PDHG algorithm are also proposed: one has faster convergence by using a variable step-size searching strategy, and the other is robust to outliers and can identify abnormal nodes by using an outlier-rejection scheme. Several numerical experiments confirm the efficiency of our proposed algorithms.