How do I convert a PWM signal (with a specific duty cycle) to its respective analog value, for an application in a low voltage, high current circuit?
This seems like a case of the XY problem. I think you would be better served asking for what you really want, a 16V 50A supply for a tethered drone, rather than asking for how to adapt an entirely unsuited PWM motor controller to the task of supplying a constant voltage.
An LC filter will only work when the PWM driving it is symmetrical. IE, it must source and sink equal current. If it only sources current, the output from an LC filter will be highly nonlinear, in fact it will look like an exponential charge curve. And a fixed PWM through an LC filter will yield a voltage that changes with load.
16V @ 50A is 800W. So give the power supply some headroom, and relax the restriction on voltage because LiIon cells drop during use anyway...
Mean Well sells a 15Vdc 1kW 66.7A output switch mode power supply, the SE-1000-15. Mouser Electronics sells it for about $170 USD. Short circuit and overload protection.
Here is the datasheet: Mean Well SE-1000-15