Apparatus and method for detecting tire having decreased pressure, and program for detecting tire having decreased pressure

The detection appatatus includes means for detecting rotation speed information of the respective wheels of a vehicle; means for estimating, a frequency characteristic of the wheel rotation speed information; and means for determining, based on the estimated frequency characteristic, a tire having a decreased air pressure. The frequency characteristic estimate means includes, to a time-series signal including the wheel rotation speed information: means for time-series estimating a third order or more linear model parameter; means for generating pseudo input data; means for estimating, based on the estimated linear model parameter and the pseudo input data, output data to a linear model; means for identifying, based on the pseudo input data and the estimated output, a linear model parameter for which the order is reduced to a second order; and means for estimating, based on the identified parameter for which the order is reduced to the second order, a resonance frequency of a tire torsional direction. The decreased air pressure determination means is so configured as to determine a tire having a decreased air pressure based on the estimated resonance frequency of the tire torsional direction.