Givens transformation techniques for Kalman filtering.

Abstract This paper examines the numerical stability and accuracy of a new Kalman filtering technique. The filter algorithm is based upon square-root-free Givens transformation methods and involves an upper triangular covariance factorization P = UDUT. Stability of the U-D algorithm is studied by applying this method and several other Kalman filter algorithms to a realistic orbit determination problem. This study demonstrates how the U-D filter can produce results which are orders of magnitude more accurate than those obtained with the conventional and stabilized Kalman algorithms. Computational efficiency of our algorithms is demonstrated by showing that CPU timing requirements for our U-D formulation differ negligibly from the conventional Kalman requirements.

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