AbstractIn offshore engineering, objects, e.g., drill pipes, anchor chains, and some small components, may accidentally fall into the water from ships or offshore platforms, which can cause casualties on decks or damage underwater equipment. The damaged equipment may further harm the environment, such as oil leaking from a damaged wellhead. Therefore, for economic and environmental reasons, a requirement for predicting the trajectory of dropped objects is needed. In this paper, we first propose the state–space motion model of dropped cylinders based on three-degree-of-freedom equations. Instead of being deterministic, the trajectory of the falling cylinder is described as a stochastic process by adding a small perturbation, being Gaussian distributed, to the initial state. Second, three probabilistic methods for state estimation, i.e., the Monte Carlo (MC) method, the unscented method, and the Cubature method, are employed in the envelope prediction of the dropped objects and provide reliable results. The MC method is a classic method for solving stochastic problems and has been applied to study the motion of falling objects. However, it always requires a sufficiently large sample, which results in large computation loads and is not applicable in practical utilization, especially in real-time applications. Simulation results show that the accuracy of the unscented method and the Cubature method are comparable to the MC method, while the computation time is only 0.5% of the MC method. Therefore, the two alternatives other than the MC method significantly improve their application possibilities and provide an effective way for the envelop prediction of dropped cylindrical objects in marine transportation or offshore operations. Furthermore, compared with the unscented method, the Cubature method is a density-assumed method, making itself handy for dynamic and real-time risk assessment of falling objects transported and installed at sea.