This study proposes two iterative reweighted (IRE) algorithms for systems whose data are contaminated by outliers. For the negative effect caused by the outliers, traditional least squares (LSs) and gradient descent (GD) algorithms cannot obtain unbiased estimates, while the variational Bayesian (VB) and expectation–maximization (EM) algorithms have the assumption that the prior knowledge of the outlier is available. To deal with these dilemmas, two IRE algorithms are developed. By assigning suitable weights for each dataset, unbiased parameter estimates can be obtained. In addition, the weights of the corrupted datasets become smaller and smaller with the increased number of iterations, and then, the contaminated data can be picked out from the datasets. The proposed algorithms do not require the prior knowledge of the outliers. Convergence analysis and numerical experiments show the effectiveness of the IRE algorithms
