For the problem of sensor energy and communication networked bandwidth constraints in networked multi-sensor distributed estimation, a consensus-based fusion estimation algorithm by reducing transmission frequency and data dimensionality reduction is proposed. In order to meet the communication network bandwidth requirements, each sensor node randomly transmits partial components of the local estimation to other nodes. At the same time, each node randomly sends packets to other nodes for saving energy. For the given consensus weight, the optimization problem with the consensus estimator gain as the decision variable and the sum of the traces of the state fusion estimation error covariance matrix in the finite time domain of all sensor nodes as the cost function is established. Based on the Lyapunov stability theory, the sufficient condition for the existence of the consensus estimator gains which make the fusion estimation error without noise asymptotically stable is given. Then, a set of suboptimal estimator gains are obtained by minimizing the upper bound of the cost function. Finally, the effectiveness of the algorithm is verified by numerical examples.