A Two-Dimensional Statistical Model of an Uneven Road Surface

This paper describes a mathematical model of an uneven road surface where the statistical characteristics of the roughness are isotropic. A spectral density matrix is obtained in consideration of a correlation of the roughness between the right and the left tracks. By the spectral factorization of the rational spectral density matrix, which results from the approximation of the cross-spectral density function, the transfer function matrix is formulated, and the minimal realization of the shaping filter is obtained analytically. The results of the numerical simulation using the shaping filter are in good agreement with the analytical ones.