# An Improved MbICP Algorithm for Mobile Robot Pose Estimation
## 2 Scan-Matching Algorithm
### Improved MbICP Algorithm
#### 2.4.2 Rejection of Incorrect Correspondences  
After establishing correspondence based on the new procedure, a set of correspondence pairs are obtained, which may contain a few incorrect correspondence pairs with large distance. Therefore, a rejection strategy that is based on the corresponding distance is required to protect the follow-up calculation from transformation. One of the most commonly used methods is the standard-deviations-from-mean approach, which removes values that are more than \(n\) standard deviations from the mean. The value of \(n\) is decided according to the practical situation. However, this method is unreliable because extreme values may distort the mean and standard deviation. For example, given a sequence of correspondence distances, \(X\) = {12.281, 12.270, 12.712, 11.932, 11.053, 10.768, 11.077, 11.685, 6.393, 6.001, 5.549, 38.760, 86.305, 34.497, 2.988, 3.227, 1.297, 3.539, 6.409, 12.477, 12.381). The rejection result when using the standard-deviations-from-mean approach is depicted in a dot plot (as shown in Figure 9a). The mean is approximately 14.93, which obviously deviates from the center of the data set, and the standard deviation is also considerably distorted. Only 86.305 is rejected as an extreme value, while 38.760 and 34.497 are ignored even though they are obviously also extreme values. Figure 8: Correspondences that were established based on the new procedure (red dots-reference scan, blue dots-object scan). Figure 7: (**a**) Interpolation process (red dots-scanned points in reference scan, blue dots-scanned points in object scan); (**b**) correspondences that were established by the new procedure (red dots-scanned points in reference scan, blue dots-scanned points in object scan). The MAD-from-median method is another rejection method, which removes values that are more than two median absolute deviations (MAD) from the median. Instead of utilizing the mean and standard deviation to measure the center and discreteness degree of the data set, this method uses the median and MAD to represent the clustering and statistical dispersion of the data set. The median is not greatly skewed by extreme values and thus can provide a better idea of the typical value than the mean can. The MAD, which is defined as the median of the absolute deviations from the median of the data set, is also robust to extreme values. The rejection result when using the MAD-from-median method is depicted in Figure 9b. The median is 11.07, which is a good representation of the center. Here, 38.760, 86.305 and 34.497 are all rejected as extreme values. Thus, the MAD-from-median method can more clearly differentiate extreme values and is herein adopted to reject correspondences with large distances. \[\mathrm{d}_{rej}=\mathrm{median}(X)+2\times MAD \tag{5}\]  
Therefore, we calculate the rejection threshold \(\mathrm{d}_{rej}\) by using Equation (5) and reject correspondences with distances above \(\mathrm{d}_{rej}\), which are likely incorrect correspondences. This rejection strategy is risky because \(\mathrm{d}_{rej}\) may be distorted by the greatly varying density distributions of point clouds. When a mobile platform moves forward in a long narrow corridor, point clouds tend to be quite dense near the sensor but sparse in more distant regions from the sensor. However, the object point clouds cannot be moved closer to the reference point clouds because of the absence of an initial pose from the odometer. The dense points that are distributed within the corridor (rectangle 2 in Figure 10a) can hardly find actual correspondence points and are likely to establish incorrect correspondences with minor distances, which are unhelpful but are in the majority. The sparse points that are distributed within the frontal obstacles (rectangle 1 in Figure 10a) are likely to establish correct correspondences with relatively large distances, which are vital to bring two point clouds closer but are in the minority.