Detection of Signals with a Random Moment of Occurrence Using the Cumulative Sum Algorithm

Abstract

A method for detecting signals with a random moment of occurrence based on the algorithm of cumulative sums with a reflecting screen under the influence of non-Gaussian noise is presented. An example of detecting a signal exposed to non-Gaussian quasi-deterministic additive noise is used for obtaining the dependences of the probability of false detection on the value of the signal-to-noise ratio for different values of the detection threshold. An increase in the detection threshold value, as well as the value of the signal-to-noise ratio, leads to a decrease in the probability of false detection. It is shown that the case of coordinated noise has the highest probability of correct detection. The algorithm for detecting a signal against the background of pulse noise and fluctuating non-Gaussian noise is analyzed and curves for probability of correct detection are obtained. It is found that the mismatch of the cumulative sum algorithm and the real density of probability distribution of noise leads to a decrease in the probability of correct detection. It is shown that the cumulative sum algorithm allows not only to solve the problem of detecting a signal in real time, but is also simple enough to be used when solving some practical problems.