The joint communication and sensing (JCAS) technique has drawn great attention due to its high spectrum efficiency by using the same transmit signal for both communication and sensing. Exploiting the correlation between the uplink (UL) channel and the sensing results, we propose a sensing-aided Kalman filter (SAKF)-based channel state information (CSI) estimation method for UL JCAS, which exploits the angle-of-arrival (AoA) estimation to improve the CSI estimation accuracy. A Kalman filter (KF)-based CSI enhancement method is proposed to refine the least-square CSI estimation by exploiting the estimated AoA as the prior information. Simulation results show that the bit error rates (BER) of UL communication using the proposed SAKF-based CSI estimation method approach those using the minimum mean square error (MMSE) method, while at significantly reduced complexity.