AC power system state estimation process aims to produce a real-time “snapshot” model for the network. Therefore, a grand challenge to the newly built smart grid is how to “optimally” estimate the state of voltages with increasing uncertainties, such as intermittent wind power generation or in-consecutive vehicle charging. Mathematically, such estimation problems are usually formulated as Weighted Least Square (WLS) problems in literature. As the problems are non-convex, current solvers, for instance the ones implementing the Newton’s method, for these problems often achieve local optimum, rather than the much desired global optimum. Due to this local optimum issue, current estimators may lead to incorrect user power cut-offs or even costly blackouts in the volatile smart grid. Frequent topology changes, poor measurement accuracy, and malicious attack can further deteriorate the state estimate. To solve the problem, in this paper, we propose utilizing historical data of Energy Management System to efﬁciently obtain a good state estimate. Speciﬁcally, kernel ridge regression is proposed in a Bayesian framework based on robust Nearest Neighbors search. To enable online data-driven SE, techniques such as dimension reduction and k-dimensional tree indexing are employed with 1000 times speed up in simulations. Further numerical results show that the new method produces an state estimate excelling current industrial approach.