Cooperative adaptive cruise control (CACC) communicates the relevant preceding vehicle state data to the follower (ego) vehicle to improve the vehicle following capabilities. In general, the CACC utilizes the preceding vehicle's desired acceleration from wireless communication as a feedforward term in the controller of the ego vehicle, which dominantly determines the total control input. However, communication loss would degrade CACC to adaptive cruise control (ACC), where the lack of the feedforward term during communication loss would increase the inter-vehicular distance or, otherwise, may lead to collision during vehicle emergency braking. This paper proposes a control algorithm with an adaptive Kalman filter estimating the acceleration of a preceding vehicle, and the estimated acceleration is implemented as a feedforward signal in the ego-vehicle CACC controller in case of communication loss. The proposed control algorithm is evaluated by the experiments using mobile robots that emulate driving. In addition, the simulations of real vehicles are also conducted. The results of simulations and robot experiments show that the performance of implementing the adaptive Kalman filter during communication loss is better than fallback to ACC and the normal Kalman filter based on the Singer model.