Rapid estimation and detection scheme for unknown discretized rectangular inputs

An algorithm to detect unknown discretized rectangular inputs and to estimate the state simultaneously, has been described in this note. The discretized rectangular input is represented by a sequence of equal magnitude inputs to the state. Four alternate hypotheses are formed at every stage of observation and Bayes risks are compared to determine the correct one. A minimum variance estimate of the inputs is used to improve the estimate of the state. Computer results from a numerical example are shown to demonstrate that a possible divergence of the Kalman filter can be prevented by incorporating the detection scheme.