This paper presents an experimental study of a strongly swirling turbulent flow with the formation of a precessing vortex core (PVC) that emerges at the outlet of a tangential swirler nozzle. The studies were carried out using a stereoscopic particle image velocimetry (SPIV) and two acoustic pressure sensors. An analysis of the velocity fields measured by the proper orthogonal decomposition (POD) showed that the precession motion of the vortex makes a significant contribution (more than 34%) to the turbulence kinetic energy, making it possible to consider the PVC effect as a prominent and convenient object for testing theoretical models describing precessing vortex motion. Estimates of the model parameters of the precessing vortex such as the vortex core radius, vortex precession radius, and vortex intensity based on statistical data obtained from uncorrelated PIV images are presented in the paper. The estimated parameters were compared with the parameters obtained by phase averaging the PIV images, and as a result, three-component velocity distributions were obtained relative to the vortex position. The analysis showed that the precession radius, vortex core size, and vortex circulation are normally distributed. The conditional averaging technique made it possible to determine the structural parameters of the PVC, which was confirmed to be a left-handed helical vortex. Due to the rapid disintegration of the PVC above the nozzle, only a portion of the spiral vortex was observed. Therefore, the helical vortex pitch was estimated in a local sense. Basically, all of the approaches gave similar results for the vortex parameters, providing access to the vortex dynamics. In particular, these cross-checked parameters were used to calculate the precession frequency on the basis of the available helical vortex model. The obtained frequency was found to be in good agreement with the experimentally measured precession frequency, confirming the adequacy of the theory.