For the problem of PAT, that is, determining the coordinates and the beginning time of an acoustic signal, it is necessary to carry out synchronized registration of acoustic signals of a source using a multichannel receiving system. Synchronously recorded signals are the signals with a delayed (long) front. A threshold method is proposed for determining the arrival time of noisy acoustic signals with a delayed front based on the evaluation of an adaptive threshold. An approach that allows to reduce the problem of determining the coordinates and the beginning time of an acoustic signal to solving a system of linear algebraic equations is proposed. Matrix A of the system of linear algebraic equations depends on the arrival times of synchronized registered signals (source coordinates). Therefore, when collecting data for a given geometry of the product and the location of the receivers, it is necessary to calculate areas, where matrix A is ill-conditioned. Areas of poor conditionality of matrix A should be excluded from the permissible areas of location of sources of acoustic signals. For these areas there will certainly be poor accuracy. The results of simulation and experimental testing of the developed PAT technologies are presented.