Distributed-parameter filtering and estimation with dynamic measurements and multiple time domains

This paper presents two methods of dealing with time delayed measurements in optimal state estimation. For measurements with pure time delays, we develop a procedure which first transfers the delayed measurement back in time by the amount of pure delay. Then, using optimal estimation techniques, we make a best estimate of the current state based upon these past measurements. We also present a method to adjoin the measurement dynamics to an optimal estimator. We present this new transformation by considering measurement dynamics as constraints upon the system. The paper also demonstrates how singular perturbation can be used to simplify optimal state estimation. Then finally, the three techniques are applied to a system with two time scales in the states, one time scale and a pure time delay in the measurement.