How to get Down Velocity in NED frame from Adafruit ultimate GPS using NMEA messages?

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I am using Adafruit Ultimate GPS v3 with the nmea_navsat_driver ROS package. I am able to use the nmea_serial_driver node to publish /fix and /vel topics.

However, I don't see Z-axis velocity being published (it is always zero). Upon searching, I found that the Ultimate GPS uses GlobalTop Technology Inc. FGPMMOPA6H GPS Standalone Module and it gives out only the following NMEA messages:

GGA, GSA, GSV, RMC, VTG

And these NMEA messages do not give out Z-axis or Down velocity (NED). So my question is, how do I get this velocity from NMEA messages? Is there another ROS package which does post processing on NMEA sentences and gives out this velocity?