Detection and estimation of abrupt changes in input or state

Disturbances which may be represented as step changes in the state of a linear, discrete-time, dynamical system are considered. A test for detection of such disturbances is presented. It employs variables computed in fixed-interval optimal smoothing. Several interpretations of the test are offered. The optimal estimate of the state change is shown to be one of the quantities forming the test statistic. Examples show the simplicity and effectiveness of the technique.