A guided missile or projectile and associated guidance control are provided to control a path to a point of intersection with a potentially moving target. A new path is repetitively recomputed and acceleration orthogonal to the path is applied to minimize heading error and thereby to converge on the target. The gain of the control function is partly proportional to heading error, but the gain is reduced approaching the point of convergence. In this way, the guidance control is more responsive to actual variance of the true heading error and is less responsive to random error in sensing the target heading, which random error would otherwise increase in its contribution to corrective guidance movements approaching the point of intersection.