PSNR is an obvious extention to a long standing engineering measurement, Signal-to-Noise (SNR).
"Objective Video Quality Measurement Using a Peak-Signal-to-Noise-Ratio (PSNR) Full Reference Technique."
This is not a standard, but rather a technical report (TR) issued by Committee T1 - Telecommunications, Alliance for Telecommunications Industry Solutions (ATIS). This TR describes what arguably is the "clasical" PSNR measurement, where calibration must be perfect but is not specified (i.e., left up to the implementor), and PSNR is calculated using only the luma pixels.
"Reference algorithm for computing peak signal to noise ratio of a processed video sequence with compensation for constant spatial shifts, constant temporal shift, and constant luminance gain and offset "
To address PSNR's calibration problems, ITS developped an exhaustive search calibration version of Peak-Signal-to-Noise Ratio (PSNR). This version of PSNR is used by the Video Quality Experts Group (VQEG) as a baseline measurement, when analyzing the accuracy of proposed metrics. This version of PSNR is included in the ITU-T Recommendation J.340.
Both versions of PSNR are availble for free in the ITS VQM software.