To address the issues of low estimation accuracy and poor stability in traditional target pose tracking when handling rotational motion, this paper proposes a sequence-independent fusion estimation method for distributed target pose tracking. Firstly, the state and invariant error dynamic equations are constructed on matrix Lie groups, and the system error state transition matrix is decoupled from the estimated state. This approach allows for a more precise description and handling of uncertainties in rotational motion, thereby improving the robustness of the filter. Then, considering the randomness of fusion sequences, a sequence-independent fusion strategy based on Lie groups is designed, enabling effective data fusion on Lie groups under any fusion sequence condition and ensuring global estimation consistency. Finally, simulations and experiments are conducted to verify the effectiveness and superiority of the proposed method.