Filtering and error analysis via the UDU^{T} covariance factorization

Kalman filter algorithms based on the UDUTcovariance factorization are discussed, with special attention given to algorithm implementation efficiency. A U-D factored covariance error analysis algorithm is formulated, and its efficiency and numerical stability are demonstrated in a representative orbit determination problem. The numerical results are compared with those obtained using covariance error analysis formulae, and the comparison highlights the numerical superiority of our algorithm A by-product of the U-D analysis is a new, highly efficient algorithm mechanization of the arbitrary gain covariance update formula.

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