In current missile, what is the guidance law used at terminal phase in homing missile guidance?
According to this easy to read brief introduction:

Optimal Homing Guidance Laws


  Other Optimal Homing Guidance Laws, many modern guidance laws require
  an estimate of time-to-go (tgo), which is the time it will take the
  missile to intercept the target or to arrive at the closest point of
  approach (CPA). The tgo estimate also is a critical quantity for
  missiles that carry a warhead that must detonate when the missile is
  close to the target.