Wi-Fi Indoor Location Method based on Improved Fingerprint Technique

One of the most popular indoor location techniques is fingerprint-based Wi-Fi location; however, the Wi-Fi location fingerprint database has issues including sparse samples and wireless access point (AP) distribution that greatly impact the location effect indoors. Because of this, we suggested a Wi-Fi indoor location technique that uses an improved fingerprint technique. First, to filter out more consistent and higher-quality APs during the fingerprint database construction phase, we employed an AP preference selection technique with combined reception percentage and variance. We then enlarged the fingerprint database in the appropriate area to increase the quality of the fingerprint database and lower the workload associated with its early establishment. In order to create a weighted K-Nearest Neighbors (WKNN) location technique, we finally fused the Pearson correlation coefficients at the matching location step. The WKNN location method using Pearson correlation coefficients and the AP-preferred fingerprint database improved location accuracy by 29.8%, according to test findings of real-world location scenarios. The technique can successfully reduce the cost of acquiring fingerprint databases while increasing location accuracy.

Introduction

The research field of indoor positioning is growing quickly right now; however, a straightforward and efficient technical framework and methodology have not yet been established [1]–[3]. Popular positioning technologies are Wi-Fi, Bluetooth, Ultra-Wideband (UWB), geomagnetism, inertial sensors, Light-Emitting Diode (LED), ZigBee, pseudo-satellite, computer vision, etc. [4], [5]. But the above technologies still have some problems and limitations, like being too expensive or not easy to use, and as a result, can’t meet all indoor positioning demands [6], [7]. UWB, computer vision, and other positioning technologies are capable of achieving centimeter-level accuracy [8]; however, the equipment costs are too expensive, and the algorithms are relatively complicated. Bluetooth and ZigBee technologies need the deployment of a large number of devices in advance, and their transmission range is limited [9]. Even though geomagnetic positioning technology does not need any extra equipment to deploy [10]. However, electromagnetic interference in indoor areas is quite critical, which can greatly reduce the accuracy of the matching process [11]. Millimeter-wave positioning, narrowband (NB) positioning, and other technologies are also being developed alongside the advancement of 5G technology [12]. Wi-Fi positioning offers several advantages over other indoor positioning technologies, including high positioning accuracy, robust models, strong efficiency, and resource accessibility [13]–[15]. In recent years, a large number of studies have been conducted on Wi-Fi indoor positioning methodologies that are based on location fingerprints [16]. For the purposes of modeling and measurement, the location fingerprint-based positioning method makes use of the strength of the Wi-Fi signal, this removes the requirement to figure out the exact spot of the access point (AP) [17]. On the other hand, because of the broad use and use of Wi-Fi devices as well as the popularity of smart mobile devices, location fingerprint positioning technology is able to be applied in the majority of indoor places, and it does not require any additional hardware during the installation of Wi-Fi networks [6], [18]. Thus, Wi-Fi positioning technology, which is based on location fingerprints, has the advantages of low cost and broad coverage [19], and its accuracy is capable of satisfying the indoor positioning requirements to a certain point, in comparison to other indoor positioning methods. On the other hand, in practical indoor scenario applications, Wi-Fi indoor positioning methods are greatly impacted by environmental factors, resulting in signal fluctuations that lower positioning accuracy [20]. Moreover, the quality of all APs cannot be controlled, resulting in a big gap in the quality of Wi-Fi signals that greatly impacts the positioning performance [21]. The initial stage of applying location fingerprint positioning needs the building of a location fingerprint database, which needs a specific amount of manpower and material resources [19], [22]. This article suggests a Wi-Fi indoor positioning method that is based on improved fingerprint technique in response to solve these above issues.

Related Works

Indoor positioning systems have gained much attention due to their critical applications in navigation, asset tracking, and emergency services within complex indoor environments. Wi-Fi-based systems, in particular, stand out due to their widespread availability and cost-effectiveness, despite the challenges associated with signal loss and system demands that are better handled by other technologies like Global Positioning System (GPS) or Bluetooth [23].

Wi-Fi fingerprinting is a popular method for indoor localization, using the signal strength from multiple APs to find out a device’s location. This technique, while popular, faces challenges such as environmental interference and AP distribution issues, which can severely affect accuracy. Studies such as those by Yang et al. [24] have explored these challenges in depth, highlighting the need for robust methodologies to improve reliability and performance.

The dynamic nature of Wi-Fi environments where AP availability and signal strength can fluctuate needs advanced algorithmic solutions to improve fingerprinting processes. The integration of statistical methods like the Pearson correlation coefficient has been shown to improve matching accuracy considerably, as detailed by Pei et al. [25].

AP selection strategies are important in optimizing the performance of fingerprinting techniques. Traditional methods frequently rely on simplistic Received Signal Strength Indicator (RSSI) based metrics that do not account for environmental variability or reception reliability. More advanced techniques, such as those discussed by Li et al. [26], incorporate signal variance and reception ratios to refine AP selection, thus improving the stability and accuracy of the resulting fingerprinting database.

This research builds on these foundational studies, introducing an improved fingerprinting method that integrates improved AP selection with Pearson correlation calculations. By adopting spatial interpolation techniques such as Kriging, which Atkinson and Lloyd [27], [33] have proven effective in predicting signal strength distributions across expansive indoor areas, this study aims to overcome the limitations identified in previous research.

By reviewing these developments, it is proved that great advancements have been made in the field. However, the quest for a highly accurate, low-cost indoor positioning system continues. This study contributes to this body of knowledge by proposing a method that leverages refined AP selection and advanced statistical tools to improve the reliability and accuracy of Wi-Fi-based indoor positioning.

Location Fingerprint Positioning Technology

Indoor Positioning Method based on Location Fingerprint

The fingerprint positioning method based on location can be divided into two stages: building the offline database stage and the online positioning stage. Fig. 1 shows the whole framework of the proposed indoor positioning system, presenting both the offline and online stages of the methodology.

Fig. 1. Framework for Wi-Fi indoor positioning system.

1. During the offline stage, location fingerprint data is collected, and the fingerprint database is constructed. At first, the RSSI feature values from all reference points (RPs) are collected applying fingerprint technology, followed by the preprocessing of the collected data to construct the fingerprint database. Table I shows the essential information that must be included in a fingerprint database.

Table I. Fingerprint Database Information

	MAC1	MAC2	MAC3	….. MACn
$F(x_1,y_1)$	$RSS{I}_{(x_1,y_1)}^1$	$RSS{I}_{(x_1,y_1)}^2$	$RSS{I}_{(x_1,y_1)}^3$	$RSS{I}_{(x_1,y_1)}^n$
…..
$F(x_1,y_1)$	$RSS{I}_{(x_i,y_j)}^1$	$RSS{I}_{(x_i,y_j)}^2$	$RSS{I}_{(x_i,y_j)}^3$	$RSS{I}_{(x_i,y_j)}^n$

Consider for example that there is a fingerprint database denoted by the S, and that the fingerprints that are stored in S are represented by the function $F(x,y)$, where $x$ and $y$ are the coordinates of the RP that corresponds to the fingerprint within the physical space. There are n wireless APs represented by the RSS data that is contained in $F(x,y)$, and each AP has its own unique MAC address that corresponds to it.

2. In the online stage, positioning algorithms are applied to match the fingerprint information of the test point with the information stored in the fingerprint database. This is done in order to find out the location of the test point. At this time, the positioning algorithm that is being applied will have a direct impact on the precision and efficiency of the positioning process.

WKNN Algorithm

In machine learning, the K-Nearest Neighbors (KNN) algorithm is a supervised learning technique [27]. When it comes to implementing indoor positioning based on location fingerprinting, the KNN algorithm provides the solution. When a test point X is to be measured, the Euclidean distance between all of the reference points in the fingerprint database and the test point X that is to be measured is computed. This distance can be expressed as the RSSI value:

(1) $$\begin{array}{r}{L}_i=\sqrt{(RSS{I}_1-RSS{I}_{i1}{)}^2+\dots +(RSS{I}_n-RSS{I}_{in}{)}^2}\end{array}$$

where $L_i$ represents the distance between the $i^{th}$ RP and the point that is being tested; $RSS{I}_1$, $RSS{I}_2$,....., $RSS{I}_n$ represent the signal strength characteristic values of the $n^{th}$ AP that can be received by the test point; $RSS{I}_{i1}$, $RSS{I}_{i2}$,$\dots$, $RSS{I}_{in}$ represent the signal strength characteristic values of the $n^{th}$ AP that can be received by the $i^{th}$ RP.

The Euclidean distance is used to find the k RPs that are closest to the test point. Then, the coordinates of these k reference points are averaged to obtain the location coordinates of the test point. The WKNN method is an improved algorithm that is based on the KNN algorithm [28], [29]. Based on the distance that separates each RP from the point that is being measured, it gives weights to the k RP that are closest to the measured point. The weight increases in accordance with the closeness of the distance. It is possible to express the coordinates of the test point as follows:

(2) $$\begin{array}{r}(x,y)=\frac{\sum _{k=1}^k{w}_k(x_k,y_k)}{\sum _{k=1}^k{w}_k}\end{array}$$

where $w_k={\displaystyle \frac{1}{L_k}}$ , is the weight of the $k^{th}$ RP.

Pearson Correlation Coefficient Integration Using the WKNN Algorithm

The WKNN algorithm with Euclidean distance weights the k nearest RPs. In a complex indoor environment, factors like as multipath, scattering, and reflection can influence the RSS measurement value, causing it to change from the logarithmic distance loss model. The Pearson correlation coefficient and the Euclidean distance are used to jointly determine the weight in order to more accurately characterize the correlation between samples.

The primary fingerprint-matching stages using the fusion of the Pearson correlation coefficient and the WKNN algorithm are as follows:

1. Calculate the Euclidean distance $L_i$ between the test point and every RP; then, add all the Euclidean distances acquired from every RP.

2. Figure out the Euclidean distances between the test points and every RP; then, choose the $k$ RP fingerprints with the lowest Euclidean distance for final positioning.

3. Calculate the Pearson correlation coefficient $r_i$ between each of the $k$ RPs and the test point.

4. Calculate the weights of the $k$ RPs. Combine the weights using the Euclidean distance and the correlation coefficient. The equation is as follows:

(3) $$\begin{array}{r}W=\frac{1}{[(A-r_i)\times L_i}\end{array}$$

where A is a constant; $r_i$ is the correlation coefficient; $L_i$ is the Euclidean distance. Finally, calculate the location of the test point.

Improved Fingerprint Technique

AP Optimal Selection Strategy Based on Reception Ratio and Variance

The existing AP selection strategies mainly include a random AP selection algorithm, an AP selection algorithm based on RSSI maximum mean (MM) [29], and AP screening algorithm based on the maximum cumulative difference (MCD) of RSSI mean. These methods do not take into account the impact of weak Received Signal Strength (RSS), low AP signal reception rate, and signal differences caused by different routing devices on the final positioning accuracy.

Taking the above factors into consideration, this article proposes an AP optimization strategy based on reception ratio and variance. The specific process is shown in Fig. 2. First, the collected RSSI data information is analyzed according to the characteristics of the Wi-Fi signal, and a suitable threshold is set according to its strength, and only the RSSI data within this threshold range is maintained; then, according to the AP classification, each AP is analyzed for all RPs, and the quantity of RPs that can receive the AP is calculated, which is the reception ratio. A threshold is set to filter out APs with a reception ratio lower than this threshold, and then the reception ratio characteristics of the remaining APs are kept for further processing. A large number of experiments have shown that when the reception ratio of an AP among all RPs is less than 60%, it will have a considerable negative impact on the positioning effect. Using the observation data of the long time series, the mean, range, and variance of each remaining AP are calculated, and the stability of each AP node is evaluated. The reception ratio of the AP node is combined with the stability, and finally, several APs with strong and stable signal strength are randomly selected.

Fig. 2. AP screening process.

Fingerprint Database Expansion

For indoor positioning based on a Wi-Fi fingerprint database, constructing a fingerprint database in the offline stage is an especially time-consuming and laborious process, and the construction of a fingerprint database directly affects positioning accuracy. In a real indoor environment, there are often a large number of locations where fingerprint data cannot be obtained normally. According to the propagation characteristics of Wi-Fi, we know that the Wi-Fi signal strength of the same AP point received by different RPs shows a certain correlation in space. Then, when it is impossible to obtain sufficient fingerprint data due to objective reasons and only sparse fingerprint data samples can be obtained, the fingerprint database can be expanded according to this feature. That is, based on the collected fingerprint data and its corresponding location information, virtual fingerprints are generated at other locations. Similarly, the abnormal values generated by the weak positioning areas in complex indoor scenes can also be replaced by fingerprints in this way.

The spatial interpolation method can use a given set of discrete points or sub-regions of spatial data to find the function that best represents the entire surface and predict the values of other points or subregions. Kriging interpolation is a method for optimal unbiased estimation of variables within a certain range of regions. Its theoretical basis mainly includes the theory of variation functions and structural analysis, which is one of the main contents of geostatistics [30]. The Kriging interpolation method conforms to the basic statistical characteristics of geostatistics, so using it for interpolation can not only calculate the prediction results but also obtain the prediction error. This characteristic is beneficial for evaluating the uncertainty of the prediction results to a certain extent [31].

The Kriging interpolation method weights the eigenvalues of the surrounding known points to obtain the predicted value of the location to be measured:

(4) $$\begin{array}{r}{\hat{Z}}_0=\sum _{i=1}^N{\lambda }_i{Z}_i\end{array}$$

where $\hat{Z}$ is the estimated value at the measured point; $Z_i$ is the measured value at the RP $i$; N is the number of RPs; ${\lambda }_i$ is the weight of the RP $i$, which is a series of optimal coefficients that can minimize the difference between the estimated value and the true value at the test point, that is:

(5) $$\begin{array}{r}minVar({\hat{Z}}_0-Z_0)\end{array}$$

The ordinary kriging interpolation method assumes that the space is uniform and the attribute values of each point in the space are uniform [32]. Therefore, any point (x, y) in the space has the same expectation and variance, that is:

(6) $$\begin{array}{r}E\left[z(x,y)\right]=E\left[z\right]=c\end{array}$$

(7) $$\begin{array}{r}Var[z(x,y)]={\sigma }^2\end{array}$$

At the same time, it is also necessary to meet the unbiased estimation condition:

(8) $$\begin{array}{r}E({\hat{Z}}_0-Z_0)=0\end{array}$$

The variogram function is an important part of kriging and simulating changes, and the spatial variability of each point in space is quantified through the variogram function [33]. Considering a point in space, the variogram can be defined as:

(9) $$\begin{array}{r}2\gamma \left(h\right)=E\{[Z\left(\mu \right)-Z(\mu +h){]}^2\end{array}$$

For a limited number of observations, a semi-variogram can be defined as:

(10) $$\begin{array}{r}\gamma \left(h\right)=\frac{1}{2N(h)}\sum _{i=1}^{N(h)}[Z\left({\mu }_i\right)-Z({\mu }_i+h){]}^2\end{array}$$

The semi-variogram can be described by an empirical model to quantify the spatial autocorrelation between different observations. Different empirical semi-variogram models are composed of range, sill, and nugget. The range refers to the range of variation of the values of the semi-variogram model. When the range is exceeded, the semi-variogram reaches a maximum value, that is, the sill value; the nugget value is the intercept of the semi-variogram on the y-axis. Although this value should be 0 in theory, for infinitesimal spacing, its variation is usually greater than 0 due to measurement errors, sampling intervals greater than 0, etc.

Experiment and Result Analysis

Experimental Environment

The experiment was conducted in conference room A103 in the Information Technology Building of Nanjing University of Information Science and Technology. The simulation layout diagram is showed in Fig. 3. The conference room is rectangular, with dimensions of 8 m × 10.7 m, covering an area of approximately 85.6 m². There are 11 groups of 15 workstations in the conference room, which can more realistically restore the real scene that people need to locate. The pedestrian activity area in the experimental site is divided into 0.7 m² × 0.7 m², forming 11 m² × 15 m² with a total of 165 m². The vertex of each small square is used as a RP. Points (0, 5) and (0, 10) are two pillars. It is difficult to collect Wi-Fi signals at point (6, 9). Excluding the above three points, there are a total of 162 RPs.

Fig. 3. Schematic diagram of simulation layout.

Constructing A Fingerprint Database

RSSI data was collected using a laptop equipped with an Intel 5300 NIC Wireless Network Adapter, and the software used for the collection was “CSI tool”. Other detailed configurations are shown in Table II.

Table II. Test Configuration Information

Target object	Purpose
8m × 10.7m	Test area dimensions
162	Number of RPs
CSI tool	Collection Software
Intel 5300 NIC	Network adapter used for collecting RSSI data
HP Pavilion Gaming Laptop 15	Device used for implementing and processing the positioning system described

A total of seven fingerprint database data collections were conducted in the experimental area. Each collection is conducted at the RP for 10 seconds, and the collected data is processed to form a corresponding fingerprint database. During the collection process, retain the RSSI data of all Wi-Fi that each point can receive, as shown in Table III.

Table III. Basic Information about the Fingerprint Database that was Used

Fingerprint database number	Number of reference points	Whether to include borders	Sampling ratio/%
A	162	Yes	100
B	106	Yes	65
C	90	Yes	55
D	49	Yes	30
E	122	No	75
F	90	No	55
G	106	No	65

Online Matching Positioning and Result Analysis

To verify the effectiveness of the AP optimization strategy based on reception ratio and variance proposed in Section 4.1, this optimization strategy is used to perform AP optimization on fingerprint database A and generate a new fingerprint database H. Use fingerprint database A and fingerprint database H respectively for positioning. The K values are selected as 3, 4, 5, and 6, and the average positioning error before and after AP optimization is shown in the table below. The positioning accuracy of the fingerprint database selected by AP has improved by an average of about 29.8% compared to the unoptimized fingerprint database.

As shown in Fig. 4, the probability of the positioning error of the unoptimized fingerprint database being less than 3 m is 79.4%. After optimizing the fingerprint database, the probability was 93.8%, an increase of 14.4% compared to before optimization. Fig. 5 further shows the comparison of unoptimized and optimized positioning errors across all fingerprint databases (A–G), highlighting the reduction in error achieved through the optimization strategy.

Fig. 4. Cumulative probability curve for positioning error.

Fig. 5. Positioning errors before and after optimization.

To verify the effectiveness of fingerprint database expansion, the positioning error analysis of the fingerprint database after fingerprint database expansion was performed. AP optimization was performed on fingerprint databases B, C, D, and fingerprint databases E, F, G, respectively, and the positioning effect was compared with fingerprint database H after fingerprint database expansion. Fingerprint databases B, C, and D have sample proportions of 65%, 55%, and 30% containing boundaries respectively. The average positioning error and its cumulative probability distribution are shown in Table IV. It can be seen that the positioning effect of fingerprint databases with sample proportions of 65% and 55% after fingerprint database expansion is similar to that of the full sample fingerprint database. The probability of positioning error less than 3 m is 72.6% and 70.4%, respectively, which is slightly higher than that of the full sample fingerprint database. That is, the positioning effect of using 65% and 55% fingerprint databases for positioning after expansion is comparable to that of the fingerprint database containing all RP information. Then, in the early stage of collecting fingerprint data, the workload can be reduced by nearly half. The fingerprint database D with a sample ratio of 30% has a relatively poor positioning effect, with an average positioning error of 2.751 m and a probability of 59.8% with an error less than 3 m.

Table IV. Average Positioning Error of each Fingerprint Database 2

Fingerprint database	H	B	C	D
Average positioning error (m)	2.421	2.463	2.481	2.751

The fingerprint databases E, F, and G have sample proportions of 75%, 55%, and 65%, respectively, that do not include the boundary of the house. The positioning results are shown in Table V. It can be seen that the positioning effect of the three fingerprint databases is similar to that of the full sample fingerprint database and even slightly better. The probabilities of average positioning errors less than three meters are 66.8%, 75.9%, and 73.4%, respectively.

Table V. Average Positioning Error of each Fingerprint Database 3

Fingerprint database	H	E	F	G
Average positioning error (m)	2.421	2.395	2.381	2.441

The sample ratio is 65%, and the average positioning error of fingerprint database B is 2.463 m, while fingerprint database E is 2.395 m and the sample ratio is 75%. For a 55% sampling ratio, fingerprint database F achieves an average positioning error of 2.381 m, which is lower than the 2.481 m error of fingerprint database C, highlighting the benefit of excluding weak RPs. The sample ratio for database D is 30%, with an average positioning error of 2.751 m, and fingerprint database G with a higher sampling ratio of 65%, achieves better performance with an average positioning error of 2.441 m. All of the result indicates that removing RPs located in weak areas such as the boundary of the house and expanding the fingerprint database results in better positioning performance.

Conclusion

Focusing on Wi-Fi indoor positioning research, this article presents a Wi-Fi indoor positioning method based on improved fingerprint technique because of the present lack of a simple and effective technical framework in the field of indoor positioning research. The use of a WKNN algorithm that integrates the Pearson correlation coefficient, combined with an AP optimization strategy based on reception ratio and variance, can effectively improve the accuracy of Wi-Fi fingerprint positioning; By using the Kriging interpolation method to expand the sparse sample measured fingerprint database, the effect of improving the fingerprint database can be achieved, and the positioning accuracy can be close to that of the real collected fingerprint database. This will help reduce the impact of outliers in weak points in complex indoor environments on positioning performance.