Linear Unbiased State Estimation with Random One-Step Sensor Delay

Sensor delay and observation uncertainty often occur in modern computer-based systems, e.g., when the measurement is transmitted to a remote controller through a network medium. In this paper, we revisit the Kalman filter design problem for a stochastic dynamic system with random one-step sensor delay, and derive the optimal unbiased state estimation algorithm. Both full- and reduced-order filters are studied, and the results compare favorably with those of the existing algorithms in examples via simulation.