In order to solve the problem of distributed pose state estimation for networked navigation systems(NNSs) with bandwidth constraints and network topology random switching constraints, a distributed finite time-domain FIR fusion estimation algorithm is proposed based on the model of the the discrete-time filtering augmented system under the above network constraints. The target node receives the general data packet and tracking data packet processed by quantization effect and saturation effect from the set of adjacent nodes. Under the premise of unbiased constraint, the estimation error of state estimation meets the minimum variance as the criterion, and the influence of colored noise is fully considered. The finite time domain FIR estimator and its difference form are designed, the target is obtained through the ordinary data packet, and a unified mechanism of local state estimation is established. At the same time, considering the network constraints, the tracking data packet is introduced into the system fusion process. Under the premise of determining the time-varying weighting matrix based on the mean square criterion, the linear algebraic equation satisfied by the optimal weight and the difference form of fusion error covariance are given. The regional estimation value of the target node state is weighted fused with the cooperative estimation value sent by each neighbor node randomly to obtain the global fusion estimator of the target node state. Finally, an example is given to verify the effectiveness of the algorithm.