Discrete Observer Design for Systems with Unknown Exogenous Inputs

A design procedure is developed for determining optimal discrete observers for estimating system states and unknown exogenous system inputs. This procedure is based on augmenting a standard system observer with an input model. The augmented model is then transformed into the discrete z-domain to determine relevant input/output transfer function matrices. The transfer functions matrices are used to develop transfer function relationships between unknown exogenous inputs and the observer estimate of these inputs. Then it is shown that the optimal observer gains can be determined by implementing the observer as a Fisher filter. An example of the procedure is demonstrated with a third order point-mass tracking filter.