## 2 Basic Concepts and Work Scope
### Positioning Data Aggregation Domains for Fingerprinting-Based Positioning  
As was introduced in Section 2.2 and depicted in Figure 5, the pattern-matching method maps an input set of fingerprints to a position estimate. Here, fingerprints are assumed to belong to a fingerprint domain (also referred to as the signal space in the literature [76]) and positions to a position domain. In this context, the availability of  
Figure 6: Differentiation of the position estimate made by the infrastructure (_infrastructure-based positioning_) in the uplink direction (**a,b**) and the position estimate made by a mobile positioning device (_mobile-device-based positioning_) in the downlink direction (**c–e**). Triangles represent base stations, and cubes represent positioning consumers or positioning devices.  
multiple sets of fingerprints associated with a position could be handled either in the fingerprint domain, before the input to the pattern-matching method, or, alternatively, in the position domain at the output of the pattern-matching method. In this last case, fingerprints are input into the pattern-matching method individually, one set or vector at a time, resulting in one output position estimate for each input set of fingerprints. So, because the ultimate goal is to estimate one final position, the availability of multiple position estimates associated with a position must be handled in the position domain to produce a final position estimate.  
As a reference, the most commonly observed approach in the literature consists of feeding multiple sets of fingerprint samples into a pattern-matching method to obtain multiple position estimates, with each one associated with an input set of fingerprints. Then, the multiple position estimates are aggregated in the position domain. In the case of multiple position estimates for a fixed position, the usual approach to obtaining a final position estimate is to aggregate the multiple position estimates through averaging. In the case of multiple position estimates being obtained through the movement of a positioning device along a path, the usual approach is to aggregate the multiple position estimates by relaying on a filter that smooths the past position estimates in the position domain.  
The actual aggregation of the fingerprint data, before their input into the pattern-matching method, in the fingerprint domain is usually carried out by averaging the fingerprints. In this case, multiple sets of fingerprints are aggregated into a single set; thus, any additional information that could be obtained from the complete set is removed and lost. The actual exploitation of the information contained in multiple sets of fingerprints has received less attention in the literature, although this was found in a few articles (discussed in Section 3.2).  
In the articles surveyed (Section 3), we did not observe classification of or differentiation between the positioning data domains for the fingerprints and positions. Because some of our pattern-matching methods work in one domain or the other, we need to make this distinction by introducing the classification of the cases listed in Table 2. The cases listed in the table are based on the input to, and output from, the pattern-matching method and based on the positioning data aggregation domains.  
The three cases of pattern-matching methods and positioning data aggregation domains listed in Table 2 are associated with the three cases depicted in Figure 7. These cases are explained next.