Hope the following two exerpts explain principles of enhancing altitude measurement and their inflight application.
1. Integrated approach navigation system, method, and computer program product
Systems, computer program products, and methods for displaying navigation performance based flight path deviation information during the final approach segment to a runway and during landing of non-precision flight modes are provided. Improved graphical depictions of navigation performance based flight path deviation information provide pilots and flight crew members with clear, concise displays of the dynamic relationship between ANP and RNP, mode and aspect of flight and related procedures, intersecting flight paths, and current actual flight path deviation from a predefined flight path during the final approach segment to a runway and during landing. For example, an enhanced IAN display may include NPS-type deviation scales to show RNP/ANP relationships and predetermined RNP markers to alert the pilots and flight crew members that the FMC has transitioned from an NPS display for RNAV (LNAV/VNAV) flight procedures to an enhanced IAN display for a non-precision (non-xLS) approach and/or landing.
2.
COMPENSATION OF PRESSURE SENSOR ERRORS IN BARO-INERTIAL ALTITUDE DATA 
A system and method for improving the accuracy of altitude determinations in an inertial navigation system. The system utilizes pressure measurements which are taken by a barometric altimeter and converted into an estimated pressure altitude using any known pressure-to-altitude conversion. The estimated pressure altitude is then converted into a pressure correction value using a correction value generating formula that is a function of altitude. The pressure correction value is then multiplied by a pressure offset value for the barometric altimeter to generate a pressure offset error for the barometric altimeter. This pressure offset error is used in the present invention to modify the altitude estimation in order to generate an altitude determination having an improved accuracy. The present invention further determines an amount of observation noise in the barometric altimeter that is a function of pressure noise and altitude, where the altitude estimation is further modified to account for the observation noise.