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A numerically improved covariance error analysis algorithm is derived using the matrix factorization P = UDUT. The algorithm employs computationally sound transformation techniques to ensure increased precision and stability. The advantages of this approach are demonstrated by applying the U-D and conventional evaluation algorithms to a representative orbit determination problem. Throughout the comparison study the conventional covariance method continually experiences serious accuracy degradations and often produces useless or inconsistent results. The UD algorithm, on the other hand, demonstrates its inherent stability by consistently matching the extended precision reference results. Moreover, the U-D method is found to be efficient and easy to implement, requiring no more storage or computation than the conventional covariance algorithm.