An observer that can simultaneously identify the state variables and inputs of a linear time-invariant system from outputs (measurements) and their first derivatives is derived. The sufficient conditions for the existence of the observer are also derived. These conditions provide the basis for a procedure to choose the minimum set of measurements necessary to observe the behavior of a system with unknown inputs. The technique can also provide a set of measurement signals that decrease the noise effects on the estimated result. An example is used to illustrate the measurement signal selection procedure. Simulation is used to demonstrate that the observer works well, even in the presence of measurement noise. The measurement signal selection technique can be utilized with other estimation methods such as various deconvolution techniques, which do not provide any criteria for measurement selection. Application of this observer to machine diagnostics is discussed.

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