With the increase of load fluctuations and the integration of stochastic distributed generations (DGs), there have been more and more research interests in forecasting-aided state estimation. In this paper, we propose a robust generalized maximum likelihood (GM)-estimator based power system forecasting-aided state estimation, which integrates the statistical characteristics of both loads and DGs, i.e., spatial and temporal correlations. A first order vector auto-regressive model (VAR(1)) is developed to capture the statistical characteristics of load and DGs, facilitating short-term loads and DGs forecasting. These forecasted power injections are further combined with power balance equations to derive a new state transition model, where the relationship between forecasted state vector and predicted power injections is expressed explicitly. After that, a redundant batch regression model that simultaneously processes predicted state vector and received observations is derived, allowing the development of a robust estimator. To this end, we propose a robust GM-estimator that leverages modified projection statistics and a Huber convex score function, to bound the influence of observation outliers while maintaining its high statistical estimation efficiency. Finally, the iteratively reweighted least squares algorithm is adopted to solve the GM-estimator. Numerical comparisons on IEEE benchmark systems with DGs integration demonstrate the efficiency and robustness of the proposed method.