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It is high if and only if the distance between the observation and prediction is small. Thus, the cost is defined by the reciprocal of the observation likelihood 1/λ . If the observation likelihood lies below a certain threshold, the cost are set to a maximum value. This refers to the fact that the features are regarded as different features with probability one. 4 Experimental Results The first mapping experiment is performed on a wheeled robot equipped with a perspective camera and a laser range scanner (see Figure 3).

2. MLS map and mobile robot used for the localization experiments. The area represented by this map spans approximately 195 by 146 meters. The blue / dark grey line shows the localized robot poses. The yellow / light grey line shows the pure odometry. The traversed trajectory has a length of 284 meters. The top right part depicts the robot Herbert used for the experiments. 5 Experiments Our approach has been implemented and tested in real world experiments. The robot used for the experiments is a Pioneer II AT system equipped with a SICK LMS laser range scanner and an AMTEC wrist unit, which is used as a pan/tilt device for the laser (see Figure 2).

Figure 3(a) shows the results for the localization rate. From these results we can see that the localization rate of the wavelets-PCA approach is always better than of the PCA approach under all different choices of eigenvalues. Figure 3(b) shows the results of comparing the localization time of both approaches under different numbers of eigenvalues, where we can clearly see that the wavelets-PCA approach is faster. This is because the input for the PCA stage in the case of the wavelets-PCA approach is the wavelet vector which has less dimensions than the whole image as in the case of PCA.