Recent Developments in the MDT Trigger Processor for the ATLAS Level-0 Muon Trigger at the HL-LHC

In order to improve the selectivity of the ATLAS hardware muon triggers in the HL-LHC era, the Monitored Drift Tubes (MDT) Trigger Processor (MDTTP) will be added to the first level of the ATLAS muon trigger system. The use of the MDT precision measurements allows to improve the transverse momentum estimation accuracy and provides an extra filtering of the low-quality fake muon triggers in the current system. The ongoing work on firmware development and performance validation is presented along with the evolution and latest status of the hardware.