Change-Point Detection in Signal Parameters with Given Probability

A time series in the form of a noisy signal given in parametric form is considered. It is assumed that there is a change point consisting of an abrupt change in the parameter. We propose an approach to constructing an algorithm for detecting the change point with a given probability of detecting the moment of the change point with a delay no larger than a given one. For this purpose, a detection function is constructed as a measure of the difference between the future and current structures. An alarm is generated when the detection function exceeds a certain threshold. For a fixed value of the parameter change, the threshold is found as a quantile of the maximum of the detection function values within the permissible delay. To obtain the distribution of the maximum, an approximation for the joint distribution function of the values of the detection function is constructed based on the calculated expectation and covariance matrix, as well as an estimate of the univariate distributions. The approach is demonstrated using two examples, a change in the value of constant signal and a change in the frequency of a cosinusoidal signal. The selection of the threshold is made based on a given set of parameter values after the change-point so that the probability of correct detecting the change-point moment is not less than a given one. The numerical examples confirm the validity of the algorithm.