The hardest part of landing Falcon 9 isn't the rocket. It's the state estimation.
Before the onboard computer can make a single throttle decision, it needs to know exactly where it is, how fast it's moving, and which way it's pointing , all at the same time, all in real time, all from sensors that each carry some margin of error.
It fuses GPS, IMU, and radar altimeter data together using an algorithm called an Extended Kalman Filter. Each sensor is wrong in a slightly different way. The filter combines them to produce an estimate that is more accurate than any single sensor alone.
If the state estimate drifts by even a small margin at supersonic speed, the landing burn fires at the wrong time. The rest doesn't matter.
Every autonomous system, self driving cars, drones, spacecraft , lives or dies on state estimation before any of the exciting control logic even runs. Getting the math right on "where am I right now" is the unglamorous problem that everything else depends on.
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