This article addresses the combined estimation issues of parameters and states for multivariable systems in the state-space form disturbed by colored noises. By utilizing the Kalman filtering principle and the coupling identification concept, we derive a Kalman filtering based partially coupled recursive generalized extended least squares (KF-PC-RGELS) algorithm to jointly estimate the parameters and the states. Using the past and the current data in parameter estimation, we propose a Kalman filtering based multi-innovation partially coupled recursive generalized extended least-squares algorithm to enhance the parameter estimation accuracy of the KF-PC-RGELS algorithm. Finally, a simulation example is provided to test and compare the performance of the proposed algorithms.