Robust angle-only initial orbit determination in cislunar space: A state transition tensors-enhanced two-sided shooting approach

Initial Orbit Determination (IOD) is critical for cislunar space domain awareness but faces challenges due to the complex, non-Keplerian dynamics of the cislunar environment. This paper proposes a novel angle-only IOD method tailored for cislunar space-based optical platforms, which consists of two core techniques. First, the iterative mechanism of IOD approaches is improved. The forward–backward shooting technique is employed to construct a state correction model that utilizes observation fitting constraints and state continuity constraints at the intermediate observation points to correct the unknown target's state parameters at both endpoint observation epochs. Compared with traditional one-way shooting methods, this model mitigates sensitivity from long-term propagation, thereby enhancing IOD convergence. Second, higher-order orbital nonlinearities are explicitly characterized. State transition tensors are introduced to formulate a second-order mapping from constraint deviations to state corrections. This yields more accurate corrections and wider convergence area than linearization-based methods. Numerical results demonstrate that the proposed method ensures robust convergence against initial guess errors, observation noise, and configuration variations, and can easily integrate additional observations to resolve multi-solution problem. Finally, an analytical state uncertainty estimation is derived to quantify the uncertainty of IOD results, which is further refined by the second-order extended Kalman filter incorporating additional observations.