Linear optimal estimator for system subject to random delay and packet dropout without time stamping

This note is concerned with the linear estimation problems for discrete-time systems where the measurements are subject to random time delay and packet drop. Due to the time stamping being assumed to be unavailable in this paper, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time-stamping, a new observation is defined by the summation of all the measurements received in the same time. Then the random time delay measurement system is converted into a constant-delay measurement system with multiplicative noises by using binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by combining the transformation of ARMA model to state-space model and the standard Kalman filtering. A simulation example is given to show the effectiveness of the proposed estimator.