In problems of Satellite Geodesy, the computing load of the HWB (and FKF) method is roughly proportional to the square of the total number of the state and calibration parameters only and not of the measurements that are billions. Reliable solution Reliable operational Kalman filtering requires continuous fusion of data in real-time. Its optimality depends essentially on the use of exact variances and covariances between all measurements and the estimated state and calibration parameters. This large error covariance matrix is obtained by matrix inversion from the respective system of Normal Equations. Its coefficient matrix is usually sparse and the exact solution of all the estimated parameters can be computed by using the HWB (and FKF) method. The optimal solution may also be obtained by Gauss elimination using other sparse-matrix techniques or some iterative methods based e.g. on Variational Calculus. However, these latter methods may solve the large matrix of all the error variances and covariances only approximately and the data fusion would not be performed in a strictly optimal fashion. Consequently, the long-term stability of Kalman filtering becomes uncertain even if Kalman's observability and controllability conditions were permanently satisfied. Description The Fast Kalman filter applies only to systems with sparse matrices, since HWB is an inversion method to solve sparse linear equations (Wolf, 1978). The sparse coefficient matrix to be inverted may often have either a bordered block- or band-diagonal (BBD) structure. If it is band-diagonal it can be transformed into a block-diagonal form e.g. by means of a generalized Canonical Correlation Analysis (gCCA). Such a large matrix can thus be most effectively inverted in a blockwise manner by using the following analytic inversion formula: of Frobenius where a large block- or band-diagonal (BD) matrix to be easily inverted, and, a much smaller matrix called the Schur complement of . This is the FKF method that may make it computationally possible to estimate a much larger number of state and calibration parameters than an ordinary Kalman recursion can do. Their operational accuracies may also be reliably estimated from the theory of Minimum-Norm Quadratic Unbiased Estimation (MINQUE) of C. R. Rao and used for controlling the stability of this optimal fast Kalman filtering. Applications The FKF method extends the very high accuracies of Satellite Geodesy to Virtual Reference Station (VRS) Real Time Kinematic (RTK) surveying, mobile positioning and ultra-reliable navigation. First important applications will be real-time optimum calibration of global observing