State estimation of a distributed system is typically done by processing the measurements of all the subsystems at a central estimator. This is the case because of the availability of several optimal centralized estimation methods. Alternatively, one has to compromise on the accuracy of estimates and run distributed estimators neglecting interactions. A low complexity block distributed Kalman filtering technique is proposed in this manuscript under the name of Approximate Distributed Kalman Filter (ADKF). ADKF distributes estimation while considering interactions, such that the accuracy of estimates is similar to the central estimator yet the computational complexity at each subsystem is significantly lower. The proposed ADKF algorithm is implemented on a continuous stirred tank reactor system, having multiple reactors in series. The simulation results show that the accuracy of estimates obtained from the proposed ADKF algorithm is comparable to the central estimator. © 2018 IEEE.