A sequential filtering algorithm is presented for attitude and attitude - rate estimation from Global Positioning System ( GPS ) differential carrier phase measurements . A third - order , minimal - parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter 's state , which renders the resulting estimator computationally efficient . Borrowing from tracking theory concepts , the angular acceleration is modeled as an exponentially autocorrelated stochastic process , thus avoiding the use of the uncertain spacecraft dynamic model . The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm , which can enhance the method 's robustness and accuracy . Numerical examples are used to demonstrate the performance of the method .