A data processing program has been applied for the new beam position monitor (BPM) system of the storage ring at Hefei Light Source (HLS). The new BPM system in the upgrade project will be equipped with Libera Brilliance BPM processors to replace the old Bergoz MX-BPM processors. The embedded Linux system on Libera has completed some important work, including instrument status check, data acquisition, position calculation, EPICS IOC data release, and so on. A new EPICS record type has been developed to recalculate the beam position with log-ratio method. The property of the new position data was analyzed in the time and frequency domain. The results show that the rms value of beam position measurement resolution can be up to submicron. Preliminary studies have been carried out on the measurement of the tune and the beam lifetime with this new BPM system.