A marginalized particle filter (MPF) is designed for attitude estimation problem. Unit quaternions are used to parameterize rotations. The linear structure in the gyroscope bias dynamics enables us to completely decouple its evolution from quaternion particles. We further show that the linear part of the proposed MPF reaches a steady state, similar to what Kalman filter does for controllable and observable linear stochastic systems. Although the steady-state MPF is similar to the particle filter in structure, it has two advantages: (i) the theoretical superiority of marginalizing linear substructure, and (ii) the reduction in total computational time. Numerical simulations are performed to demonstrated the performance of the proposed filter.

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