## 2 Basic Concepts and Work Scope
### Spatial Side Information  
In the field of fingerprinting-based positioning, research is focused on how to obtain and extract as much information as possible from the sources generating the fingerprints in the time, space, and frequency domains, in addition to proposing different pattern-matching methods for processing such information. The use of filters to process a time-series of fingerprints can be seen as one of the first attempts to exploit side information in the time domain. When multiple fingerprints are collected at the same static position, increasing the number of samples reinforces the statistics to obtain a better position estimate. When multiple fingerprints are collected in a geographical area by moving a positioning device along a path and when the displacement is slow compared with the sampling rate, it can be assumed that the previous position estimates are closer to the current position. Thus, past position estimates provide side information that can be exploited to estimate the current position in a combination of the time and space domains. Further information from other sources, like inertial sensors, contributes to the local information about the relative distances between samples. Information on the distances between samples provides additional information that helps to enhance the estimation of the position when compared to the assumption of the locality of neighboring samples without the relative distance information mentioned above. This constitutes information from the space domain that it is then associated with the collected fingerprints and processed using a suitable pattern-matching method to further enhance the position estimate. In the space domain, we can also consider different antenna arrangements, as well as a strategic geographical distribution of the fingerprint sources, that helps to incorporate and exploit the side information in the space domain. Finally, the availability of multiple subcarriers from Orthogonal Frequency Division Multiplexing transmissions is exploited to increase the number of amplitude and phase fingerprint sources in the frequency domain. In this article, we focus on 2D side information in the space domain. We use _spatial side information_ to refer to any information that can be extracted around the target position that we intend to estimate. We call it _spatial_ because the side information has associated a position, relative or not, whether known or estimated, with the target position. In fingerprinting-based positioning, the side information is most likely additional fingerprints collected at physically adjacent positions to the position to be estimated. The motivation for considering spatial side information lies in exploiting more and correlated information. In the case of using the proposed 2D sensor array, we have additional knowledge on the relative position of one fingerprint sensor or receiver to that of the other ones. We consider this side information analogous to the encoding of information in a transmitter of a generic communications system, in which adjacent bits are related to each other by means of an encoder implementing a code such as a convolutional or turbo code [77; 78]. As in a communications system, we expect to obtain a gain from the use of side information, making the pattern-matching method more robust to the variations in the RSS fingerprints. Spatial side information can be obtained either (1) by one sensor sampling fingerprints in the time domain, with a known or estimated relative movement around the target position, or (2) through simultaneous sampling of the fingerprints with an arrangement of multiple sensors, like in an array or matrix arrangement, in which the relative position of each sensor is known. In this study, we consider the latter case, with a 2D sensor array simultaneously sampling multiple fingerprints around the position to be estimated. The typical case found in the literature is case (1) cited above.