  State and parameter estimation is essential for process monitoring and
control. Observability plays an important role in both state and parameter
estimation. In simultaneous state and parameter estimation, the parameters are
often augmented as extra states of the original system. When the augmented
system is observable, various existing state estimation approaches may be used
to estimate the states and parameters simultaneously. However, when the
augmented system is not observable, how we should proceed to maximally extract
the information contained in the measured outputs is not clear. This paper
concerns about simultaneous state and parameter estimation when the augmented
system is not fully observable. Specifically, we first show how sensitivity
analysis is related to observability of a dynamical system, and then illustrate
how it may be used to select variables for simultaneous estimation. We also
propose a moving horizon state estimation (MHE) design that can use the
variable selection results in a natural way. Extensive simulations are carried
out to show the efficiency of the proposed approach.
