A vehicle speed estimator includes a unit (801) that selects a minimum rotation speed among rotation speeds of wheels detected by a rotation speed detector and calculates a reference wheel speed of a construction vehicle at every predetermined time. The unit (801) includes: a variable filter processor (814) that performs a low-pass filter processing to the minimum rotation speed, the variable filter processor (814) having a variable time constant; and a time constant changer (810) that changes the time constant of the variable filter processor (814) in accordance with travel conditions of the construction vehicle.