Predictive filter theory proposed recently can be characterized by inherent advantages of estimating modelling error and overcoming the disadvantage of the Kalman filter theory. A one-step ahead error is minimized to produce optimized filter performance in the form of the predictive filter. The main advantage of this filter lies in the ability to estimate both state vector and system model error. In this paper, attitude estimation results based upon the predictive filter theory is addressed. Mathematical formulation for estimating bias signal is peformed by using the predictive filter theory, and attitude estimation based upon vector observation is presented. From the results of this study, the potential applicability of the predictive filter is highlighted.