Minimum variance deconvolution estimator for discrete systems with random observation delays

This paper is concerned with the optimal deconvolution problem for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal recursive white-noise estimator is presented based on the stochastic Kalman filtering theory. The obtained estimator is indeed a fixed-point white-noise smoother, which is with time-varying, stochastic gains, and is optimal for any packet delay generating process. Also, a fixed-lag white-noise smoother is developed according to the fixed-point one. Finally, the simulation results are given which support and illustrate the theoretical developments.