An Augmented Lagrangian Approach for Distributed Robust Estimation in Large-Scale Systems

Nonlinear estimation using maximum-likelihood estimation and maximum a posterior probability approaches is frequently employed for large-scale cyber-physical and complex systems in the big data era. Efficient distributed processing and robust estimation algorithms resilient to outliers are of great importance. This paper proposes a novel method for distributed solution of these robust estimation problems with equality constraints based on the augmented Lagrangian method (ALM). Specifically, a novel covariance normalization method and an automatic method for selecting regularization parameter with improved performance are proposed. Under the ALM framework, nonlinear equality constraints and nonsmooth L₁ regularization can be incorporated. The proposed method is illustrated with two emerging applications respectively in robust distributed power system state estimation (DSSE) with nonlinear zero injection constraints and gene regulatory network (GRN) identification. Experimental results in DSSE show that the covariance normalization method improves considerably the convergence speed over the alternating direction method of multipliers algorithm and the robust statistics employed effectively mitigates the adverse effects of extreme outliers. Zero-injection constraints can be effectively incorporated. For GRN identification, putative genes and connectivity for a yeast dataset with 1.57 million variables can be identified via sparsity and piecewise temporal continuity penalties and they generally align well with literature.