Minimal-Order Models for False-Alarm Calculations on Sliding Windows

A procedure is developed to obtain practical numerical results in connection with the m-out-of-n sliding-window detection problem. This effort was motivated by difficulties with previous approaches involving approximation, Markov models, and Monte Carlo simulation. Generating-function methods were found to be unsatisfactory for window lengths greater than 6 due to their complexity. Instead, a Markov model is described that is then constructively reduced to the minimum number of state variables. The results are derived for binary strings with intersymbol correlation. Computational aids are discussed for obtaining design information, such as quantiles, from the minimal-order Markov models. Numerical results are given comparing the methods of the paper with a "jumping" window approximation for an 8/10 problem.