Square root information filtering and smoothing has, over the last few years, come to be recognized as a reliable and effective method for computing numerically accurate estimates in problems where high precision is required. Unfortunately, the algorithms employed often project an image of being too costly in terms of both computation and storage requirements. We show that in the case of orbit determination (and in problems of a similar nature), introducing ‘pseudo-epoch’ coordinates and exploiting problem structure dramatically reduces computation and storage requirements. This paper, in the main an expository SRIF review directed at the orbit determination problem, also contains a new smoothed estimate U-D covariance factorization algorithm. This new algorithm is numerically well conditioned and is a significant computational improvement on previous SRIF based smoothing algorithms.