Four Dimensional Navigation, actually! X, Y, Z, plus Time. By incorporating strict time constraints, air traffic controllers can schedule and merge arriving aircraft more precisely, reducing holding patterns and optimizing fuel usage.

https://ntrs.nasa.gov/api/citations/19750022064/downloads/19...

>4D AREA NAVIGATION SYSTEM DESCRIPTION AND FLIGHT TEST RESULTS

>A 4D area navigation system was designed to guide aircraft along a prespecified flight path
(reference path) such that the aircraft would arrive at the approach gate at a time specified by
the ATC controller. Key components to achieve this requirement were:

>(1) stored reference trajectories;

>(2) a continuously recomputed capture trajectory to a selected waypoint on the reference trajectory so as to achieve the desired time of arrival;

>(3) electronic situation displays; and (4) a control system to follow the overall trajectory in space and time.

https://ntrs.nasa.gov/citations/19750015477

>Four-dimensional guidance algorithms for aircraft in an air traffic control environment

>Theoretical development and computer implementation of three guidance algorithms are presented. From a small set of input parameters the algorithms generate the ground track, altitude profile, and speed profile required to implement an experimental 4-D guidance system. Given a sequence of waypoints that define a nominal flight path, the first algorithm generates a realistic, flyable ground track consisting of a sequence of straight line segments and circular arcs. Each circular turn is constrained by the minimum turning radius of the aircraft. The ground track and the specified waypoint altitudes are used as inputs to the second algorithm which generates the altitude profile. The altitude profile consists of piecewise constant flight path angle segments, each segment lying within specified upper and lower bounds. The third algorithm generates a feasible speed profile subject to constraints on the rate of change in speed, permissible speed ranges, and effects of wind. Flight path parameters are then combined into a chronological sequence to form the 4-D guidance vectors. These vectors can be used to drive the autopilot/autothrottle of the aircraft so that a 4-D flight path could be tracked completely automatically; or these vectors may be used to drive the flight director and other cockpit displays, thereby enabling the pilot to track a 4-D flight path manually.

https://www.airbus.com/en/newsroom/stories/2020-12-4d-tbo-a-...

>4D-TBO: a new approach to aircraft trajectory prediction

>How four-dimensional trajectory data could contribute to aviation decarbonisation targets

>The real-time transmission of four-dimensional trajectory data has the incredible potential to greatly improve an aircraft’s trajectory prediction. By reducing the inaccuracy of current air traffic management (ATM) prediction models by approximately 30-40%, the Trajectory Based Operations in 4 Dimensions (4D-TBO) project is helping to pave the way to a more sustainable management of tomorrow’s air traffic.

https://skybrary.aero/articles/4d-trajectory-concept

>The 4D trajectory of an aircraft consists of the three spatial dimensions plus time as a fourth dimension. This means that any delay is in fact a distortion of the trajectory as much as a level change or a change of the horizontal position. Tactical interventions by air traffic controllers rarely take into account the effect on the trajectory as a whole due to the relatively short look-ahead time (in the order of 20 minutes or so).

>The implementation of 4D trajectory management is being researched by SESAR (Single European Sky ATM Research) in the EU and NextGen in the US.

>The 4D trajectory concept is based on the integration of time into the 3D aircraft trajectory. It aims to ensure flight on a practically unrestricted, optimum trajectory for as long as possible in exchange for the aircraft being obliged to meet very accurately an arrival time over a designated point.