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> This is how old air-to-air missiles worked. They would steer until the image of the target stopped moving.

That seems to be a weird way of describing "steer so the target is always in center of the image".

I implemented this once in a video game. If the missile steers so it bears directly on the target, but has limits on its ability to turn, then it will often miss the target or spin around the target.

If you instead steer so the target’s bearing doesn’t change, and ignore whether that bearing is in the center or somewhere else, the missiles are much more likely to hit.

Not necessarily on center. Constant bearing but decreasing range will result in a collision.

Exactly! If the target was in the center, that would mean the missile was pointed to the target's current location. The target would quickly drift out of view!

Instead you want to intercept the target. You want to reach the point where the target will be, and at the same time as you. So keep the target to the side, at a constant angle.

Imaging missiles typically have the sensor mounted on a gimbal so the target can be centered in the image even when the missile body is not pointed at the target. But yes, the line-of-sight to the target will generally be off of the missile boresight.

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