The goal of this study is to use Gaussian process (GP) regression models to estimate the state of colored noise systems. The derivation of a Kalman filter assumes that the process noise and measurement noise are uncorrelated and both white. In relaxing those assumptions, the Kalman filter equations were modified to deal with the non-whiteness of each noise source. The standard Kalman filter ran on an augmented system that had white noises and other approaches were also introduced depending on the forms of the noises. Those existing methods can only work when the characteristics of the colored noise are perfectly known. However, it is usually difficult to model a noise without additional knowledge of the noise statistics. When the parameters of colored noise models are totally unknown and the functions of each underlying model (nonlinear dynamic and measurement functions) are uncertain or partially known, filtering using GP-Color models can perform regardless of whatever forms of colored noise. The GPs can learn the residual outputs between the GP models and the approximate parametric models (or between actual sensor readings and predicted measurement readings), as a member of a distribution over functions, typically with a mean and covariance function. Lastly, a series of simulations, including Monte Carlo results, will be run to compare the GP based filtering techniques with the existing methods to handle the sequentially correlated noise.