In this article the idea of inversion-based direct input reconstruction for robust detection, separation and estimation of multiple simultaneous faults in the presence of persistent disturbances which proved to be non-separable by conventional decoupling methods in linear dynamical systems is presented. In particular, it is shown how in a specific filtering structure a residual generator, relying on the inverse representation of the system, by means of estimation of the inverse dynamics can be designed providing robust fault decoupling. In the development of the method three solution approaches are contrasted with each other. In the first approach the traditional H filter providing the classical disturbance attenuated non-decoupling solution is presented. Then, in a novel solution, an H detection filter on the inverse system is designed providing detection residuals by exact fault decoupling; the estimation of the inverse dynamics is obtained by means of the optimal filter, thus ensuring H disturbance attenuation on the residual output. Finally, an observer-based residual generator for the estimation of the inverse dynamics is designed resulting in detection residuals with exact fault and disturbance separation, which characterises this novel idea in its extremes. The feasibility of the solution to problems not solvable earlier is demonstrated based on an aircraft monitoring application example that was originally considered in Douglas and Speyer (1995) and Chung and Speyer (1998).