Observability and optimal measurement location in linear distributed parameter systems†

Observability and the optimal location of measurements are developed for a class of linear distributed parameter systems whose solutions can be represented by eigen-function expansions (the so-called modal form). A key question studied is the effect of measurement locations on the observability of this class of systems. Since observability is realty a prerequisite to state estimation, an algorithm is developed to determine a set of measurement locations which, in some sense, lead to the beat state estimates. This is accomplished by minimizing the trace of the steady-state covariance matrix of the state estimates.