This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization,P =:UDUT, whereUis unit upper triangular andDis diagonal. An efficient and reliable algorithm forU-Dpropagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increases mapping efficiency. Cost comparisons of theU-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. TheU-Dtime update is shown to be less costly than the Schmidt method ; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.