This paper presents a new method to solve a dynamic sensor fusion problem. We consider a large number of remote sensors which measure a common Gauss-Markov process and encoders that transmit the measurements to a data fusion center through the resource restricted communication network. The proposed approach heuristically minimizes a weighted sum of communication costs subject to a constraint on the state estimation error at the fusion center. The communication costs are quantified as the expected bitrates from the sensors to the fusion center. We show that the problem as formulated is a difference-of-convex program and apply the convex-concave procedure (CCP) to obtain a heuristic solution. We consider a 1D heat transfer model and 2D target tracking by a drone swarm model for numerical studies. Through these simulations, we observe that our proposed approach has a tendency to assign zero data rate to unnecessary sensors indicating that our approach is sparsity promoting, and an effective sensor selection heuristic.