State observers

State estimators are algorithms for deriving state estimates from measurements. Based upon proper manipulation of system models, they allow, for example, the estimation of state variables such as accelerations from position measurements. Applications can be found in instrumentation, flight reconstruction, and in providing inputs to state feedback control laws. The most famous state estimators are the Luenberger observer and the Kalman filter. The basic form of the former does not explicitly consider the possibility of noise on the measurements and it is in many respects related to pole-placement controllers. Hence it is reasonably accessible theoretically and we introduce it at this point. We concentrate on discrete time formulations simply because implementation is likely to be on digital computers, but analogous results hold for continuous-time observers. Nonlinear observers are briefly mentioned.