Toward adaptive robust state estimation based on MCC by using the generalized Gaussian density as kernel functions

In this paper, a generic formulation is proposed for robust state estimation (RSE) based on maximum correntropy criterion (MCC), leading to an adaptive robust state estimator. By using the generalized Gaussian density (GGD) as the kernel function, the proposed formulation theoretically unifies several existing RSE models, each of which is optimal for a specific type of measurement noise and error distribution. As the noise and error distribution is generally unknown ex-ante and time-varying in operation, a statistical learning scheme is proposed to heuristically identify the actual distribution type online. Afterwards, the optimal RSE can be properly selected so as to adapt to the variation of noise and error distribution types. Simulations are carried on a rudimentary 2-bus system and the standard IEEE-118 bus system, illustrating the correctness and effectiveness of the proposed methodology.