We describe algorithms for reconstructing tune, closed‐orbit, beta‐function, and phase advance from four individual turns of beam orbit acquisition data, under the assumption of coherent, almost linear and uncoupled betatron oscillations. For estimation of the beta‐function at, and phase advance between, position monitors, we must also assume at least one anchor location consisting of two monitors separated by a drift. Assuming beam position monitors with surveying and reading errors, and assuming an imperfect lattice with gradient and surveying errors, the algorithms were submitted to a Monte Carlo analysis to find the likely measurement accuracy of the optics functions in the KAON Factory Booster ring racetrack lattice. The results of this study are reported. This paper is a much abridged version of a TRIUMF design note. © 1994 American Institute of Physics