Performance analysis of total least squares methods in three-dimensional motion estimation

An algorithm is presented to obtain the total least squares (TLS) estimates of the motion parameters of an object from range/stereo data or perspective views in a closed form. TLS estimates are suitable when data in both time frames are corrupted by noise, which is an appropriate model for motion analysis in practice. The robustness of different linear least squares methods is analyzed for the estimation of motion parameters against the sensor noise and possible mismatches in establishing object feature point correspondence. As the errors in point correspondence increase, the performance of an ordinary least squares (LS) estimator was found to deteriorate much faster than that of the TLS estimator. The Cramer-Rao lower bound (CRLB) of the error covariance matrix was derived for the TLS model under the assumption of uncorrelated additive Gaussian noise. The CRLB for the TLS model is shown to be always higher than that for the LS model.>