This dataset contains polarimetric observations of several GNSS satellites done with two antennas at Allen Telescope Array in the E1 (1575.42 MHz) frequency band. The dataset consists of power spectra and cross-spectra for the X and Y linear polarizations of each antenna. A total of 1024 FFT channels are used with an input sample rate of 24.576Msps (IQ sampling) to give a frequency resolution of 24kHz. The |X|^2, |Y|^2 and X*conjugate(Y) cross-spectra are coherently averaged in windows of 0.1 seconds. Note: only one out of every four 1024 IQ sample vectors was processed in order to reduce the CPU load during data recording, so the effective averaging of each spectrum is only 25ms. The recording was done with antennas 1h and 4g on 2020-10-24, and it includes several minutes of measurements for the Galileo satellites E01, E13, E26, E31, E33, and the GPS satellite G05. The hardware configuration was as follows: the antennas were connected to RFCB LO d, which was tuned to a frequency of 1475.42 MHz and used an output IF of 512 MHz. A USRPs N321 and a USRP N320 were connected to the IF output of the RFCB. Each of the USRPs was used to digitized both polarizations from one of the antenna. The USRPs used external 10 MHz reference and PPS coming from the observatory distribution system. LO sharing was configured between all of the USRPs channels. The dataset contains a flat .tar.xz archive with several files having names such as E01_2020-10-24T11:37:38.353705_0xx. The beginning of the filename indicates the target of the observation, then there is the UTC timestamp corresponding to the beginning of the observation, and finally a code that indicates the measurement channel. The first character of the code is either 0 or 1 to indicate antenna 1h or antenna 4g respectively. The remaining characters can be either xx or yy for the power spectra of polarizations X and Y respectively or xy for the cross-spectra of polarizations X and Y. The timestamp for the data is only approximate, because it refers to the instant at which the data collection script started. The USRPs take some 10 to 30 seconds to initialize after this. The format for the xx and yy power spectra files is raw binary in IEEE 754 32 bit floats, with every 1024 elements of the file constituting a power spectra. The format for the xy cross spectra files is raw binary in IEEE 754 32 bit floats. Each pair of floats represents the real and imaginary parts of a complex number. Every 1024 pairs of floats constitute a cross-spectra. Consecutive spectra are separated 0.1 seconds apart in both cases. More information about the dataset can be found in the blog post "ATA polarimetry test with GNSS satellites" by the first author.