Synergy of delayed states and missing data in Wireless Sensor Networks using Kalman Filters

Estimation of future data in systems with delayed state is a challenging problem. In this paper, two methods of using Kalman Filter in such systems is presented. In the first method, the delayed states are incorporated in the state matrix, while in the second method the delayed states are incorporated into the state equation form. Comparisons of the results made by applying the above methods on delayed state systems show that the second method predicts the data with more accuracy. The Kalman Filter with delayed states in the state equation is then modified to account for the missing measurements, which is a common phenomenon in the Wireless Sensor Networks. The performance of the obtained equations are then evaluated for the delayed state systems in the presence of missing measurements.