Distributing calculations of a central Kalman filter requires subsystem level expressions for the propagation and update steps of the Kalman filter. It is difficult to obtain subsystem level expressions due to the inverse term present in the update step. In this manuscript, a non-iterative way of decomposing the inverse of a matrix is presented. This decomposition allows rewriting the update equations of the Kalman filter subsystem-wise. Subsequently, a Co-acting Kalman Filter (CoKF) is proposed using these decomposed central Kalman filter equations to perform distributed state estimation. The convergence of the CoKF algorithm is established under the assumption that each subsystem is observable. Two variants of the proposed CoKF, namely (m-CoKF and p-CoKF), suitable for applications on opposite ends of computation and communication resource spectrum, are presented along with the trade-offs involved. A comparison of the proposed method with existing distributed Kalman filters is also presented. The proposed CoKF algorithm is implemented on a standard wireless sensor network example with 200 nodes. The simulation results demonstrate the accuracy of the proposed CoKF algorithm relative to the central Kalman filter. © 2020 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd