Estimating the states of moving underwater objects based solely on bearing measurements from passive sensors is difficult due to the significant nonlinearity introduced by the conversion from polar to Cartesian coordinates, the absence of range information, and the inherent limitations of passive sensing in terms of observability. Passive sensors do not provide direct measurements of range or velocity, leading to ambiguity in the target's position and motion, which complicates the state estimation process. The nonlinearity can be addressed by nonlinear Bayesian filters, particularly the particle filter (PF). However, due to the necessity of a priori knowledge of the probability distribution to obtain posterior probabilities, the particle filter may underperform or even be invalid if incomplete knowledge of the dynamic models of moving objects is present. To address these problems, a sequential bearing-only state estimation framework is proposed in this paper, which integrates PF and unknown input observer during initialization and prediction stages to estimate the state of the moving object. A numerical simulation ultimately illustrates its efficacy regarding estimation precision.