In this paper, a parallelogram set-membership estimation (PSME) algorithm is proposed to perform osteotomy trajectory estimation in two dimension plane with high accuracy to achieve high-precision osteotomy by an orthopedic surgery robot and meet the safety requirements of the osteotomy. First, to realize the tight envelope of the estimated set on the osteotomy trajectory, a parallelogram envelopment expression is proposed that describes the state set and the observation set. Second, a minimum-area parallelogram envelope method is applied to quickly converge the osteotomy trajectory estimation set to a reliable range. Moreover, the unknown but bounded noise model solves the robustness problem of the algorithm under non-Gaussian conditions, and realizes the accurate estimation of the osteotomy trajectory in any noise environment. Finally, the simulated and experimental results demonstrate that the estimation accuracy and anti-noise performance of the PSME algorithm are better than other estimation algorithms. In the osteotomy experiment, the average osteotomy error is less than 1 mm, which meets the safety requirements of the osteotomy. Furthermore, PSME holds great potential in other estimation problems.