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Intuition Here's one way: Let's rotate your diagram. Now the rocket is a cannonball! Physics It has a fixed acceleration "downwards" i.e. perpendicular to the vector from its firing location to its target. I drew it above as a dashed green line. Let's call that the reference horizon. (Note that this reference horizon is constant! The rocket was fired ...

It may not be the elegant solution you are after, but I've found that if I slow the missile, if it's going to miss, as it approaches the target, it effectively tracks and turns quicker and can hit the target. You could increase the turn rate of the missile as it gets closer, rather than reducing the speed, but this might give players a 'wow I'm sure that was ...

It looks like the problem is that the missile is simply pointing itself at the target without regard for it's current velocity. Assign your missile a maximum angle by which the thrust can deviate from the line of motion. At each guidance iteration you calculate it's velocity perpendicular to the target. Figure out how much it must tip it's engine in order ...