Fault detection algorithm based on a discrete-time observer residual generator - a GPS application

The aim of this paper is to present a design methodology for an observer-based fault detection filter. This approach allows to compute a filter gain such that both fault detection and disturbance attenuation requirements are accomplished. The developments are based on H₂ and H_∞ optimization type methods in the discrete-time framework. The existence conditions for the observer-based detection filter are expressed in terms of feasibility of some matrix inequalities. An important advantage of the described approach is the possibility to extend the results to other classes of systems (as sampled-data systems, stochastic systems with Markovian jumps and corrupted with multiplicative white noise, etc.) for which disturbance attenuation type results expressed in terms of feasibility of appropriate Linear Matrix Inequality (LMI) systems, are available. In order to illustrate the derived theoretical results, a case study concerning the problem of Global Positioning System (GPS) integrity monitoring is considered.