To wage a preceding-vehicle sleuthing apparatus, own-vehicle controlling equipment and preceding-vehicle sleuthing medium confident of sleuthing a foregoing container in a more sure manner, a preceding-vehicle sleuthing equipment (1) comprises: a millimetre gesture radiolocation (11); a measuring-target-point-group generating conception (131) environment measuring-target points supported on echolike waves, and single-connecting those measuring-target points having the aforementioned qualifying velocities to thereby create measuring-target saucer groups, respectively; a group-relative-velocity determining conception (132) extracting those measuring-target saucer groups which meets conditions for foregoing vehicle, respectively; and a profane enduringness judging conception (133) regarding those measuring-target saucer groups as foregoing vehicles, apiece of which has a sort of perceived nowadays coequal to or large than a formal continuance (N1).

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