Road profile modeling by subspace identification methods

In this paper, spectral models of road profiles using nonparametric and subspace identification methods are developed from road elevation measurements. First, power spectra of road profiles are estimated on uniform grids of frequencies by averaging and windowing from road measurements. These results are illustrated on the data sets obtained from the University of Michigan Transportation Research Institute archives by computing Welch spectrum estimates for left and right vehicle tracks. Then, curve fitting by the single and two-slope approximations are applied on the Welch estimates. Rational approximations, by considering a recent subspace algorithm, the regularized nuclear norm and the regularized and reweighted nuclear norm heuristics are performed for a further shaping of power spectrum estimates. Preliminary results show that the regularized and reweighted nuclear norm heuristic algorithm yields best fits to the data by low order rational spectra without distorting too much the homogeneous road assumption. Finally, for comparision of the roughness evaluation the IRI roughness index is calculated for different algorithms assuming that road excitations are zero-mean Gaussian processes.