Optimal stochastic fault detection filter

Properties of the optimal stochastic fault detection filter for fault detection and identification are determined. The objective of the filter is to monitor certain faults called target faults and block other faults which are called nuisance faults. This filter is derived by keeping the ratio of the transmission from nuisance fault to the transmission from target fault small. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the ratio of the transmissions is zero, the optimal stochastic fault detection filter is equivalent to the unknown input observer if all invariant zero directions are included with the nuisance fault directions. Detection filter designs can be obtained for both linear time-invariant and time-varying systems.