A processing apparatus for a target detection apparatus includes a processor and associated memory. The processor and associated memory are configured to: generate, for a plurality of reflection points at which transmitted radio waves are reflected by a target, a plurality of instantaneous data sets, each of which includes a projected relative velocity of a said reflection point with respect to a host vehicle; calculate, for each of the plurality of instantaneous data sets, a projected ground velocity of the reflection point with respect to the host vehicle based on the projected relative velocity and a velocity of the host vehicle; align starting points of the calculated projected ground velocities to a predetermined point; and estimate a movement direction of the target from an intersection of perpendicular lines to the projected ground velocities whose starting points are aligned.