We consider a class of stochastic linear systems that are subject to jumps of unknown magnitudes in the state variables occurring at unknown times. This model can be used when considering such problems as the estimation of systems subject to possible component failures and the tracking of vehicles capable of abrupt maneuvers. Using Kalman-Bucy filtering and generalized likelihood ratio techniques, we devise an adaptive filtering system for state estimation and the detection of the jumps. An example that illustrates the dynamical properties of our filtering scheme is discussed in detail.