Robust Unscented Unbiased Minimum-Variance Estimator for Nonlinear System Dynamic State Estimation With Unknown Inputs

Abstract

In this letter, a two-stage robust unscented unbiased minimum-variance (RU-UMV) estimator is proposed for nonlinear system dynamic state estimation with unknown inputs. In the first stage, by leveraging the statistical linerization and the relationship between unknown input vector and states, we derive a batch-mode regression form. It is shown that the application of weighted least squares for this form yields the same results as the UMV unscented Kalman filter. However, it lacks robustness to outliers. To deal with, robust generalized maximum-likelihood (GM)-estimator together with the projection statistics (PS) is developed, yielding robust state estimates. The latter are further used in the second stage for robust unknown input vector estimation. As a result, both innovation and observation/measurement outliers can be effectively suppressed. Illustrative examples are provided to demonstrate the robustness of the proposed method.