Filtering and error analysis via the covariance factorization

Kalman filter algorithms based on the UDU^Tcovariance factorization are discussed, with special attention given to algorithm implementation efficiency. A 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 analysis is a new, highly efficient algorithm mechanization of the arbitrary gain covariance update formula.