## Apollo Propulsion Flight Analysis Project

MetaCalculus emerged in the Apollo program culminating about 170 man years of mathematical software development in propulsion state-estimation at TRW. State estimation is an automation of the scientific method, minimizing the error between simulations and telemetry data. It is characterized in philosophy as “epistemic correlation”. Years of application in the ballistic missile flight analysis projects in the USAF Thor, Atlas, and Titan development programs led to its use in Apollo.

Apollo Working Paper 1196 laid out the overall plan for what became Task 19 in the Apollo Spacecraft Support Contact with TRW, dedicated to mathematical reconstruction of rocket engine mission behavior.

This work resulted in a mathematical breakthrough which led to MetaCalculus—the extension beyond simulation languages to seamless higher mathematical languages supporting nested numerical processes of simulation, correlation, and optimization.

The breakthrough was the discovery of a nested form of automatic differentiation, called digital calculus arithmetic (DCA). This breakthrough allowed dynamic partial differentiation of simulation models and solution algorithms, the lack of which had previously inhibited the implementation of the inverse methods of correlation and optimization associated with differential equations solutions.

The DCA technique was first applied as part of the Apollo Propulsion Analysis Program (APAP) in a subsystem known as the Model Compiler, now identified as MC1 – the origin of MetaCalculus.The state-estimation algorithm engines of APAP included MAFIA (Mack Alford's Filtering Algorithm), and a Kalman Filter known as SVEAD, developed by Bill Lear. APAP was applied for all the Apollo missions, as described in the following reports, the first of which summarizes the workings of the software: