A study of stochastic processes associated with sonar detection

This paper describes a study which was made on the fluctuating output of a typical sonar system. The sonar output time series was compared to predictions of the λ-σ and Gauss-Markov models which have previously been used to model these outputs. A new technique, Autoregressive Integrated Moving Average (ARIMA) was used for the first time to model the fluctuating output of a sonar system. The ARIMA model produced predicted values which had errors less than 3 decibels for lead times equal to more than one-third of the length of the actual time series. This paper also contains a comparison of various measures of effectiveness between the λ-σ, Gauss-Markov and ARIMA models with the actual data. These comparisons included one property, mean time to gain contact, and the ARIMA models agreed with the data, whereas the λ-σ and Gauss-Markov predictions did not show as good an agreement.