## 2 Basic Concepts and Work Scope
### Positioning Data Aggregation Domains for Fingerprinting-Based Positioning
#### 2.4.2 Position Estimates from Aggregated Positions in the Position Domain  
Case 2 (in Table 2), in Figure 7b, consists of aggregating the positions in the position domain, at the output of \(n\) instances of the pattern-matching method, to estimate the position. In this case, a collection of several, say \(n\), sets or vectors of fingerprint samples is presented as the input. Each one of the \(n\) fingerprint vectors is individually input into the pattern-matching method to produce an independent position estimate at the output. The pattern-matching method applied to each input can be the same or differ. Here, we will consider the same method implementing the same model for all the inputs. The instances of the pattern-matching method can be processed sequentially or in parallel. The sequential implementation handles one input set or vector of fingerprints at a time. The parallel implementation handles multiple instances of the pattern-matching method to process each one of the input sets or vectors at once. Thus, for a given number of \(n\) input vectors of fingerprints, there are \(n\) output position estimates. Then, the \(n\) position estimates are aggregated in the position domain into a single final position estimate. This aggregation is carried out using a suitable function or operation, for example, the mean value or weighted  
Figure 7: Cases for pattern-matching methods and positioning data aggregation domains. (**a**) Position estimate without positioning data aggregation. (**b**) Position estimate from aggregated positions in the position domain. (**c**) Position estimate from aggregated fingerprints in the fingerprint domain.  
average, that computes the final position estimate. In the context of the work presented in this article, the \(n\) input vectors of fingerprints will be collected simultaneously at adjacent positions by means of the 2D sensor array when the 2D sensor array is in a fixed position in space. However, alternative approaches could be devised for the collection of fingerprints at adjacent positions (as discussed in Section 4.1).  
It is noted that in the literature, some authors consider collections of fingerprint vectors that are collected by moving a positioning device along a path. In some cases, each one of the fingerprint vectors is individually mapped to a position, and then a smoothing filter is applied to enhance the estimation of a new position by relying on the past position estimates. While this approach technically uses adjacent side information and also can be classified into this case, this approach is not considered to be within the scope of our work. The reasoning for this is that first, the filtering operates in the position domain, whereas we intend to operate in the fingerprint domain in order to extract as much information as possible from the fingerprints. Second, the usual movement of a positioning device along a path that is considered in the literature has a granularity or resolution that it is coarser than what we aim to obtain with the 2D sensor array. Third, unless the area in which the positioning is intended is comprehensively scanned in a particular way, the usual movement along a path is not suitable for considering side information in 2D. And fourth, the filtering process can be viewed as a weighted average of the adjacent position estimates with either a set of manually assigned weights or a set of weights statistically calculated using a few parameters. Regarding this approach, we argue that an NN with a suitable structure and size can operate as a more tailored model for the problem. Another aspect to consider is that by employing multiple sensors, the proposed approach based on the 2D sensor array will produce position estimates which would be equivalent to the future position estimates in solutions relying on collecting fingerprints by moving a positioning device along a path.