Commonly, a non-cooperative space target is tracked using angle-only data. An approach utilised in many tracking problems is to perform an initial orbit determination (IOD) step and then transition to sequential estimation. In this paper, a space-based passive tracking strategy is proposed that combines IOD and sequential estimation. For the space-based IOD problem, a modified Laplace’s method is derived, in which the non-spherical effect of Earth is considered and more than three pairs of angle measurements are fused. For the sequential estimation, a robust filtering algorithm, termed the robust square-root cubature Kalman filter, is developed. An adaptive factor is introduced in the developed algorithm, to ensure robustness to measurement malfunctions. Simulation results demonstrate that the proposed strategy can be used in actual engineering applications.