Motivated by applications of the Internet of Vehicles where a large amount of data is available through communication, we consider the problem of reducing communication costs when estimating the dynamical state of a system. More specifically, assuming the knowledge of sensor specifications, such as noise characteristics, we solve the problem of determining which sensor’s data are necessary to satisfy given timevarying constraints on the estimation errors. By receiving only the necessary data, instead of all available data, we reduce the communication and processing bandwidth usage. We formulate a moving horizon sensor selection problem and present an approximate, yet computationally tractable, solution to the problem by employing a greedy heuristic approach. For the heuristic, we define a metric that measures the contribution of each sensor data to the constraints in relation to its communication cost. We validate our solution on two collision avoidance examples and compare the performances of our approach with the conventional Kalman filter using all available sensor data. The simulation results show that our approach significantly reduces communication costs without compromising the system’s performance, such as safety guarantee, with high probability.