COLLABORATIVE Wi-Fi FINGERPRINTING INDOOR POSITIONING USING NEAR RELATION

: I ndoor positioning is of great importance to the era of mobile computing. Currently, much attention has been paid to RSS-based location for that it can provide position information without additional equipment. However, this method suffers from many challenges: (1) fingerprint ambiguity; (2) labor-intensive of fingerprint collection; (3) low efficiency of fingerprint matching. To get over these drawbacks, we provide a collaborative WiFi fingerprinting indoor positioning method using near relation. The base idea of this method is that interpolation method is used to enrich sparse Wi-Fi fingerprint. Near relation boundary is provided and Wi-Fi fingerprints is constrained to this region to reduce fingerprint ambiguity, which also can improve the efficiency of fingerprint matching. Extensive experiments show that a positioning accuracy of 3.8 m can be achieved with the near relation under 1 m interpolation density.


INSTRUCTION
With the increasing popularity of mobile and pervasive computing, the location service based on indoor positioning has attracted much attention due to its wide applications in living, production, commence, and public services (Xia et al., 2017;Hu et al., 2018). Recent years have witnessed a lot of work on indoor positioning. Single source location (e.g., received signal strength, radio frequency identification, ultra wideband and visible light) and multi-source location based indoor positioning strategy are differentiated by the inference techniques such as the time of arrival, the time difference of arrival and the angle of arrival (Mainetti et al., 2014;Tang et al., 2019;Ren et al., 2019;Leca et al., 2020). RSS-based location has attracted much attention and is regard as one of the most promising solution for indoor positioning, for that it can provide position information without additional hardware and deploying investment (Brena et al., 2017;Zafari et al., 2017). RSS-based localization mainly contains two stages: offline and online (Ge et al., 2016;Chen et al., 2017;. During the offline stage, the RSS fingerprints dataset mapping relationship between signal fingerprints and spatial locations is established. Next in the online stage, estimating location by matching the online RSS fingerprint collection with the offline fingerprint dataset (Du et al., 2107;Subedi et al., 2019). However, the RSS-based method faces many challenges: (1) Fingerprint ambiguity due to the multi-path reflection of RSS in indoor complex environment, which result two different locations may have similar RSS fingerprints and low positioning accuracy . (2) Fingerprint collection is labor-intensive and time-consuming (Hu et al., 2018). (3) Low efficiency in fingerprint database matching . The literature on fingerprinting-based indoor localization is long and rich. The major reason of ambiguity issues come from two aspects: position ambiguity and RSS ambiguity (Han et al., 2015). The ambiguity of RSS can be reduced by adding the fingerprints dimension (Li et al., 2016), using scene information (Liu et al., 2017) or PDR (Chen et al., 2015) to narrow the fingerprint * Corresponding author database. Li (Li et al., 2016) extended the fingerprints dimension from one point to multiple points to avoid the ambiguity of RSS. A multi-dimensional dynamic time warping (MD-DTW) algorithm is provided for matching. Liu (Liu et al., 2017) used the camera of a smartphone as "eye" to recognize the environment. With scene information constrained, the searching range of fingerprint database is narrowed down and RSS ambiguities are decreased. Chen (Chen et al., 2015) used pedestrian dead-reckoning (PDR) to track user movements and restricted the fingerprints to a circle center at the PDR positioning result. The interpolation method is widely used to encrypted fingerprint Shen et al., 2019;). Voronoi Tessellation (Lee et al., 2012), Inverse Distance Weighting (IDW) (Zuo et al., 2018;Li et al., 2018), and Delaunay (Jan et al., 2015) are well-known methods. Lee (Lee et al., 2012) refined the propagation model for each cell of the target area tessellated by a higher-order Voronoi diagram. This method can take into account the signal fading caused by walls and obstacles more accurately, but the location of access point (AP) must be obtained in advanced. The basic idea of IDW is to provide weight for the data points based on their distance to the estimated point. The closer is the known data point to the estimated point, the more weight it is (Moghtadaiee et al., 2019). The linear interpolation method is based on Delaunay triangulation. The IDW and linear interpolation algorithm are compared to estimate the missing RSS values (Talvitie et al., 2015). To overcome the drawbacks of traditional RSS-based indoor positioning method, our paper used Delaunay-based interpolation method to enrich sparse Wi-Fi fingerprints, which reduce the labor of fingerprint collection. Near relation is provided to constrain the Wi-Fi fingerprints matching space, which not only reduce the fingerprint ambiguity, but also improve matching efficiency. The contributions of our paper are as follow: (1) We identify the opportunity of near relation to resolve the fingerprints ambiguity. To the best of our knowledge, it is the first work combing spatial relationship in semantic descriptions with fingerprints.
(2) A near relation-based indoor positioning under sparse Wi-Fi fingerprinting scheme is provided. IDW and Delaunay based interpolation method are adopt to encrypt the sparse Wi-Fi fingerprinting. Near relation region is provided to narrow the searching space of fingerprinting and resolve the fingerprinting ambiguity.
(3) To evaluate our method, an experiment is conducted and the result demonstrate that a positioning accuracy of 3.8m is achievable with near relation constrain under 1m interpolation density.
The remainder of this paper is organized as follows. Section 2 describes the system overview and method. Section 3 presents the related experiments. Section 4 summarizes this work and discusses future research directions.

System overview Definition 1. RO (Reference Object):
An RO is any feature with a name in a place description. Generally, there are reference objects (ROs) and their related spatial relations (SRs; i.e., topology, direction and distance) and target objects (TO) in a place description. A TO is the place that is to be described or located. Take the place description "near LaoFX" as example. LaoFX is the RO (Reference Object). Additionally, ROs are polygons indoors due to scale. The architecture of the proposed system is similar to traditional fingerprinting localization system which contains two stages: offline and online stage. In the offline stage, the near relation boundary and a fingerprint database should be built. In the online stage, the near relation for the RO (Reference Object) should be selected to narrow the search space of fingerprinting before positioning.

Interpolation method
The interpolation method is based on Delaunay. After conducting the Delaunay triangle based on the known data, the entire interpolation process consists of interpolation and extrapolation. Interpolation and extrapolation refer to estimate the data inside and outside the Delaunay triangles respectively.

A. Interpolation
The first step is to determine in which triangle the interpolated point inside. After this, the value of interpolated data can be calculated as: Where P1(x1,y1), P2(x2,y2), P3(x3,y3) are the vertices of Delaunay triangle that Pinterp(x,y) inside in and 1 + 2 + 3 = 1.

B. Extrapolation
The value of extrapolated data equals to the known point closest to it.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII-B4-2020, 2020 XXIV ISPRS Congress (2020 edition)

Known Data
Interpolation Data Exterpolation Data x y Figure 4. Illustration of interpolation and extrapolation data.

Experiment step
The experiment is conducted in a shopping mall with enough Wi-Fi signals. The test area is approximately 30000m 2 . The distance between each reference point (RP) is 6m. As shown in figure 5, there are 55 RPs. The Wi-Fi RSS are collected by Honor KIW-AL10 smartphone and the signal sampling frequency is 1 Hz. For each RSS, the RSS collection at each RP lasted for 2 minutes. Wi-Fi signal distribution in the test environment is shown in Figure 6. The x-and y-axis indicate the relative coordinate, and the z-axis shows the number of Wi-Fi signal.

Localization Results and Evaluation
10 participants are selected to walk around the test experiment and asked to select the near RO to describe their positioning. Different people may have different choices. The participants include 4 males and 6 females, and their age range from 20 to 48. Their trajectory is shown in Figure 8. We mark numbers for each track point. The fingerprint matching algorithm we used is WKNN, and the parameter K is 3. Figure 8. Distribution of track points. To verify the accuracy of interpolation, when collecting RPs, we add a RP between each RPs. As shown in figure 9, the mean positioning error with non-interpolation and Delaunay-based interpolation density of 3m are 6.10m and 6.23m respectively. The accuracy of the interpolation method can be used to positioning to some extent. The large positioning error comes from fingerprints ambiguity and the location of ambiguity fingerprints is shown in Figure 10.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII- B4-2020, 2020 XXIV ISPRS Congress (2020 edition)

Dela+3m
Error ( Figure 11 shows positioning error with different interpolation methods (IDW and Delaunay) and interpolation density (3m and 1.5m) without near relation. The mean error of IDW+3m, IDW+1.5m, Dela+3m, Dela+1.5m are 6.3m, 5.9m, 6.2m and 5.8m respectively. IDW+3m represent IDW interpolation method and 3m interpolation density.  Figure 11. Positioning error with different interpolation methods (IDW and Delaunay) and interpolation density (3m and 1.5m) without near relation. Figure 12 shows positioning error with different interpolation methods and interpolation density considering near relation. The mean error of Near+IDW+3m, Near+IDW+1.5m, Near+Dela+3m, Near+Dela+1.5m are 5.0m, 4.2m, 4.3m and 3.9m respectively. Near+IDW+3m represent IDW interpolation method and 3m interpolation density considering near relation.  Figure 12. Positioning error with different interpolation methods (IDW and Delaunay) and interpolation density (3m and 1.5m) considering near relation. Compared Figure 11 and 12, as interpolation density increases, the positioning accuracy that with near relation or not all improves. As shown in Figure 13, the positioning accuracy is no longer improved when the interpolation density increase to 1m and the positioning accuracy is about 3.61m. Figure 13. Positioning error of different interpolation methods (IDW and Delaunay) and interpolation density (3m and 1.5m) considering near relation.

CONCLUSION
In this paper, we develop a collaborative Wi-Fi fingerprinting indoor positioning method using near relation, which use Delaunay-based interpolation method to encrypt sparse Wi-Fi fingerprint. The interpolated fingerprint is restricted to near boundary, which not only can narrow down the search space of fingerprint but also decrease the RSS ambiguities. The experiment shows that a positioning accuracy of 3.61m can be The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII-B4-2020, 2020 XXIV ISPRS Congress (2020 edition) achieved with near relation constrain under 1m interpolation density. The near boundary provided in this paper is raster-based which has low efficiency. In practical applications, the near boundary should be generated in advance and placed on the server. Additionally, studying other near boundary generation methods and interpolation algorithms (e.g., Kriging) are our future works.