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# Data Association in the Large

## Data Association

### 5.3. Data Association in the Large

Fortunately, with accurate laser measurements, there are usually few association con-flicts in our application because of precise data association in the small contributed by kinematic and geometric information.

5.3. Data Association in the Large

An example of the data association in the large problem has been illustrated in Section 3.5. When the robot reenters a visited area, loop detection or place recognition has to be done in order to build a globally consistent map (Stewart et al., 2003; Thrun and Liu, 2003;

H¨ahnel et al., 2003).

For data association in the small and in the cluttered, the uncertainty and the ambigu-ity of the robot and objects’ pose estimates can be described well in practice. But for data association in the large, because of accumulated errors and unmodelled uncertainty, the distribution estimates may not describe the uncertainty properly, which means gating can not be performed correctly. Figure 5.4 illustrates the data association in the large problem where the distribution estimates are modelled improperly and can not correctly indicate where the true poses of the robot and objects are. For dealing with this problem, in this section we propose three principles: covariance increasing, information exploiting, and ambi-guity modelling where the latter two have been used for solving data association in the small and in the cluttered.

Figure 5.4. Data association in the large.

Covariance Increasing

Although the distribution may not describe the uncertainty properly, it still provides useful information for recognizing the current measurement in the built map. In the track-ing literature, (Li, 1998) has presented a theoretical conclusion that the covariance matrix from the Kalman filter should be increased for dealing with the missed detection problem.

Similarly, instead of searching the whole built map, only the built map within the gate of the increased covariance is verified. Because of the unmodelled uncertainty sources, it may

be difficult to decide how much the covariance matrix should be increased theoretically. In practice, the covariance matrix can be increased in the way of wave propagation until loops are detected. Note that loop detection is only activated whenever there is an inconsistency in the global map. Figure 5.5 illustrates an example of covariance increasing.

Figure 5.5. Covariance increasing.

Information Exploiting

For loop closing, not only recognizing but also localizing the current measurement within the global map has to be accomplished. As addressed in data association in the small, including geometric information can be greatly beneficial to data association or recognition. Unfortunately, because of temporary stationary objects, occlusion, and low object saliency scores, recognizing and localizing places are difficult even with the proper informa-tion about which porinforma-tions of the built map are more likely.

Because of temporary stationary objects such as cars stopped by traffic lights and parked cars, the currently built stationary object maps may be very different from the global stationary object map. Since the environments are dynamic, stationary objects may be occluded when the robot is surrounded by big moving objects such as buses and trucks.

In practice many areas such as bushes and walls do not have high object saliency scores.

In these situations, recognition and localization may be incorrect even with the use of geo-metric information.

In order to deal with the above situations, big regions are used for loop-detection instead of using raw scans. In large scale regions, large and stable objects such as build-ings and street blocks are the dominating factors in the recognition and localization pro-cesses, and the effects of temporary stationary objects such as parked cars is minimized.

It is also more likely to have higher saliency scores when the size of the regions is larger.

In other words, the ambiguity of recognition and localization can be removed more eas-ily and robustly. Because the measurements at different locations over different times are

5.3 DATA ASSOCIATION IN THE LARGE

accumulated and integrated into the local region, the occlusion of stationary objects is re-duced as well. Figure 5.6 shows a grid-map pair of the same regions built at different times. Although the details of grid-maps are not the same in the same region because of the described reasons, full grid maps contain enough information for place recognition and localization.

Because grid maps are used, visual image registration algorithms from the computer vision literature can be used for recognition and localization. Following the sampling and correlation based range image matching algorithm, we use the correlation between grid maps to verify the recognition (searching) results, and we perform recognition or searching between two grid maps according to the covariance matrix from the feature-based SLAM process instead of sampling. The search stage is speeded up using multi-scale pyramids.

Figure 5.7 shows the recognition and localization results of the examples in Figure 5.6 using different scales.

(a) Grid-map 1 (b) Grid-map 16

Figure 5.6. The grid-map pair of the same region built at different times: Grid-map 1 and Grid map 16. Different moving object activities at different times, occlusion and temporary stationary objects are shown.

(a) 1/8 Scale (b) 1/4 Scale

(c) 1/2 Scale

Figure 5.7. Recognition and localization results using different scales of grid map 1 and grid map 16. Two grid maps are shown with respect to the same coordinate system.

Ambiguity Modelling

In cases that information exploiting provides more than one feasible recognition re-sult, the ambiguity should be described properly for a later but firm decision as addressed in data association in the cluttered.

Since the ambiguity in our experiments can be removed quickly and reliably using the described information exploiting based algorithms, we increase the difficulty of the problem by cutting the data set of 21 grid maps into 2 disjoint sequences. We assume that these two sequences are collected from two robots and the relative starting locations of these two robots are unknown. Now the problem is to built a joint map using these two sequences. Figure 5.8 shows these two sequences, one is grid map 1-14 and another is grid map 15-21. Figure 5.9 and Figure 5.10 show the details of these grid maps.

Because the relative starting locations of these two sequences are unknown, recogniz-ing and localizrecogniz-ing places have to be performed globally in which the saliency score of a grid map may not be good enough to remove the ambiguity. Figure 5.11 shows the bar graph of the maximum correlation values of the grid map pairs between the grid map 1-14 sequence and the grid map 15-21 sequence. Figure 5.12 shows two slices of Figure 5.11 in which mul-tiple possible matches are found in the place recognition of grid map 12 and grid map 13.

5.3 DATA ASSOCIATION IN THE LARGE

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Figure 5.8. Two sequences. The relative starting locations of these two sequences are assumed to be unknown.

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Figure 5.9. Details of grid map 1-9. Measurements associated with moving object are filtered out.

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Figure 5.10. Details of grid map 10-21. Measurements associated with moving ob-ject are filtered out.

In other words, grid-map 12 and grid-map 13 can not remove the ambiguity. Practically, it can be solved by selecting a larger grid map or using multiple consecutive grid maps to increase the saliency score for removing the ambiguity. Figure 5.13 shows that the ambigu-ity is reliably removed with the use of multiple consecutive grid maps where hypothesis k consists of the sequence pair between the grid map sequence k-k+5 and the grid map

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