Distributed Least Absolute Deviations Estimation

Distributed algorithms are essential for reducing communication costs, computational complexity, and memory requirements while performing collaborative estimation using multi-agent systems. Additionally, robustness in estimators is important to prevent performance degradation when the measurement noise is non-Gaussian. Least absolute deviations estimators are known to be robust in the presence of gross errors or outliers in the measurements. To this end, we develop the distributed least absolute deviations (D-LAD) estimator for linear systems whereby the agents iteratively exchange information with their immediate neighbors via single-hop communications to gain a network-wide consensus on the estimates. Additionally, the D-LAD algorithm is implemented in a nonlinear framework to solve the problem of distributed orbit determination of a target body using a formation of spacecraft. Numerical simulations demonstrating the effectiveness of the D-LAD estimator in linear and nonlinear settings are provided.