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Time Varying Kalman Filter Processing to Predict the Future Errors of a GPS Receiver  Figure-2: A complete cycle of a Kalman filter algorithm. In this figure, Kk is the gain of the Kalman filter and Pk is the error covariance of the estimate ^Xk of the state vector at time k [7, 8]. Model Description A Kalman filter requires that the system model to be in state-space form. It has seen that there are linear correlations between the errors of each position components of a GPS receiver measurement. So we based the state-space on modeled errors of dx, dy, and dz, the errors of position components corresponding to x, y, and z, respectively. In this modeling the matrix parameters can be defined in the following time-varying ARMA form [9,10]: 
Where a1i(n),a2i (n),a3i(n),b1j(n),b2j(n),c1k(n),c2k(n) and c3k(n) for i=1,2,L,P,j=1,2,L,q and k=1,2,L are time-varying parameters produced by ARMA model. |