On the Symmetry between State Estimation and Reference Tracking

Both constrained state estimation and constrained reference tracking could be formulated as optimization problems, and the symmetry between these two problems could be shown. As variables in the stochastic model, both the mean of process noise and the mean of measurement noise do not have to be zero. The main contributions of this paper are that we take the mean of process noise and the mean of measurement noise, which do not have to be zero, and show the symmetry between constrained state estimation and constrained reference tracking for this case. In other words, we study the symmetry between state estimation and reference tracking with an additional constraint on the measurement noise and the process noise. By this symmetric relationship, the constrained state estimation problem can be solved as a constrained reference tracking problem, and vice versa, despite the presence of more general process and measurement noise.