The aim of this article is to investigate how to estimate parameters and states jointly for the linear stochastic system with deterministic control inputs. The cross-correlation between process noise and measurement noise in Kalman filtering re-formation cycles is utilized to derive a Kalman filtering with correlated noises based recursive generalized extended least squares (KF-CN-RGELS) algorithm for jointly estimating parameters and system states. The performance analysis of different correlation coefficients between process and measurement noises shows that the accuracy of the identified parameters and states is proportional to the positive correlation coefficients. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.