Abstract
The paper provides the theoretical proof of earlier published experimental evidence of the favorable properties of a new method for State Estimation - the Generalized Correntropy Interior Point method (GCIP). The model uses a kernel estimate of the Generalized Correntropy of the error distribution as objective function, adopting Generalized Gaussian kernels. The problem is addressed by solving a constrained non-linear optimization program to maximize the similarity between states and estimated values. Solution space is searched through a special setting of a primal-dual Interior Point Method. This paper offers mathematical proof of key issues: first, that there is a theoretical shape parameter value for the kernel functions such that the feasible solution region is strictly convex, thus guaranteeing that any local solution is global or uniquely defined. Second, that a transformed system of measurement equations assures an even distribution of leverage points in the factor space of multiple regression, allowing the treatment of leverage points in a natural way. In addition, the estimated residual of GCIP model is not necessarily zero for critical (non-redundant) measurements. Finally, that the normalized residuals of critical sets are not necessarily equal in the new model, making the identification of bad data possible in these cases.