A Narrow-Down Approach Based on Machine Learning for Indoor Localization

Abstract

Over the past decade, the demand and research for indoor localization have burgeoned and Wi-Fi fingerprinting approach has been widely considered because it is cheap and accessible. However, most existing methods lack in terms of positioning accuracy and high computational complexity. To cope with these issues, we formulate a two-stage, coarse and accurate positioning narrow-down approach (NDA). Furthermore, a three-step source domain refinement (SDR) scheme that involves outlier removal, stable AP’s weight enhancement, and a data averaging technique by applying the K-means clustering algorithm is also proposed. The collaboration of SDR scheme with the training data selection, area division, and overlapping schemes reduces the computational complexity and improves coarse positioning accuracy. The effect of the proposed SDR scheme on the performance of the support vector machine (SVM) and random forest algorithms is also presented. In the final/accurate positioning phase, a set of lightweight neural networks (DNNs), trained on different sub-areas, predict the user’s location. This approach significantly increases positioning accuracy while reducing the online computational complexity at the same time. The experimental results show that the proposed approach outperforms the best solutions presented in the literature.

1. Introduction

With the advancement in technology, the indoor positioning and tracking of smart devices has gained much popularity in the Internet of Things environment [1]. The demand for indoor localization is higher than that of outdoor localization. Globally, people spend 80 to 90% of their time indoors and about 70% of smartphone usage is in closed areas [2]. A recent report published on American lifestyle states that Americans, on average, spend 93% of their life indoors [3]. Consequently, research on indoor localization is gaining importance day by day. The global positioning system (GPS) is the most popular technique used for outdoor positioning and is commonly used in transport vehicles and smartphones [2]. In indoor environments, GPS exhibits poor performance because of the absorbance and distraction of signals from construction materials. The interpretation of accuracy is not the same between outdoors and indoors. A few meters of inaccuracy indoors is more effective than outdoors, which may lead to a different room or a different building. Traditional location-based systems (LBSs) are not efficient enough to meet the navigational challenges of these GPS-denied environments. No absolute real-time solution has been proposed yet that would be cost-effective, less time-consuming, more accurate, and generic. The Wi-Fi fingerprinting approach is the most popular because of its cost-effectiveness and accessibility [4]. The existing WiFi-RSSI-based positioning algorithms can be classified into geometric-related techniques and fingerprinting-based techniques [5], wherein fingerprint-based methods have superiority because wireless signal variances can be captured more accurately. However, the dynamics of routers, random signal interference, and moving obstacles cause uncertainty in measuring the wireless signal strength at reference points (RPs), which in turn degrades the accuracy of indoor positioning. Mostly machine learning (ML)-based algorithms, like K-nearest neighbor (KNN) [6], naive Bayesian (NB) [7], support vector machine (SVM) [8], random forest (RF) [9], and deep neural network (NN) [10], have been used to find the user’s indoor location from the fingerprints. Indoor localization methods can be divided into two categories [11]. (1) Classification methods: The whole localization area is divided into sub-areas and then a classification algorithm finds the sub-area where the target resides. (2) Regression methods: A regression-based algorithm finds the user’s exact location by utilizing Wi-Fi-based RSS (received signal strength) vectors. In this article, we aim to reduce the training and response time while increasing positioning accuracy. We propose a narrow-down approach that consists of coarse and accurate positioning phases. To deal with the first problem, in the coarse positioning phase, we propose a source domain refinement (SDR) scheme that reduces 80% of training data for classification. Furthermore, we also divide the whole localization area into sub-areas, as proposed by Jingxue Bi in [12]. To reduce the response time, we select a support vector machine whose response time is far better than the random forest algorithm for classification. We reduce the propagation delay of the regression-based algorithm by making it lightweight and by training it on each sub-area. The combination of SVM, SDR, and the group of distributed neural networks, namely DNLoc, alongside the concept of area division and localization, dramatically increases indoor localization accuracy. The main contributions of this paper are:

• This study proposes a narrow-down approach (NDA), which comprises the coarse and accurate positioning phases.
• The contribution is to select specific reference points (RPs) to train the classification algorithm, while the key considerations are to reduce the offline storage as we do not use all the RPs for training, and the chosen training points for the classifier are distant enough to share minimum RSSI characteristics. This strategy increases classification accuracy.
• We also propose a three-step source domain refinement (SDR) scheme to reduce the computational complexity of training data and enhance the classification accuracy at the same time.
• A very lightweight DNN-based multivariate regression (DNN-MVR) model, trained independently on each sub-cluster, is presented. The proposed methods are evaluated on a public dataset to show their reliability and robustness.

We organize the remaining article as follows. Section 2 discusses the related works. Section 3 explains the system design. Section 4 demonstrates the experimental evaluations. Conclusion remarks are discussed in Section 5.

2. Related Work

In the literature, many Wi-Fi RSSI-based machine learning (ML) approaches have been proposed for indoor localization. For example, Nafisa et al. [3] proposed a zone-based indoor localization system using neural networks with a slight modification in traditional counter propagation network (CPN). The proposed scheme reduces the number of empty clusters and performs better than the basic CPN by increasing 1% in accuracy. However, it is lacking in finding the exact user’s location coordinates. A hidden Markov model-based indoor localization scheme is proposed in [4], but the random forest algorithm outperforms the proposed method. Zhang et al. [5] proposed a Wi-Fi RSSI-based indoor robot positioning system that is pluggable to existing Wi-Fi network infrastructures. They integrated the deep neural network with fuzzy forests to increase accuracy. If we use both the RSSI’s value and direction to train the random forest algorithm, then its accuracy can be increased [13]. Minhui et al. [14] proposed an algorithm to divide the whole localization area into sub-areas by using the Gaussian mixture model. RF algorithm was utilized to predict the corresponding area and the final location was estimated using an adaptive KNN algorithm. Xiang et al. [15] utilized a deep learning framework alongside a logistic regression algorithm and Pinto et al. [16] utilized the K-means clustering algorithm to divide the localization area into different sets of log-distance propagation models, while Bayesian inference improves the positioning accuracy. A random forest algorithm using a software-defined network (SDN) framework is presented in [17]. The proposed model uses cross-validation for training and performing indoor localization. Dong et al. [18] proposed a novel adaptive cluster splitting (ACS) and access point (AP) reselection scheme in each sub-cluster splitting process. In the online phase, a decision tree-based exhaustive search algorithm finds the user’s location. Saddam et al. [19] proposed an algorithm consisting of clustering and searching. A measuring device determines the user’s location, based on the strongest AP, in a radio map. An AP’s similarity-based clustering approach is proposed in [20]. Li et al. [21] proposed a heterogeneous knowledge transfer framework for fingerprinting-based indoor localization. After removing the redundant knowledge in the source domain, the authors derived a cross-domain mapping to construct a homogeneous feature space, where they combined the mapping and weights learning into a joint objective function and solved it using a three-step iterative optimization algorithm. However, they utilized online fingerprint knowledge to train a model that makes this approach less realistic. Xiansheng et al. [22] presented a robust model by fusing derivative fingerprints of RSS with multiple classifiers (DIFMICs). This model outperforms many machine learning-based models proposed in the literature for indoor localization. Li et al. [23] proposed a probabilistic model to intelligently estimate the user’s location by evaluating the label’s credibility. Zhang et al. [24] presented a hybrid localization model by joining the convolutional neural network (CNN) and Gaussian process regression (GPR) algorithms. The hybrid model improved in performance by 45.8% and the GPR algorithm further increased the localization accuracy. Soro et al. [25] proposed a wavelet scattering framework (WSF)-based neural network for an indoor localization method that is not affected by the handset orientation, and Li et al. [26] proposed a hybrid fingerprint quality evaluation model (HFQEM) that can find the location by evaluating the hybrid fingerprint quality in different sub-areas. The authors of [27] present a sequence learning problem, where a recurrent neural network (RNN) with a regression output are used to estimate three-dimensional positions. The authors of [28] propose a convolutional neural network (CNN) model based on RSSI fingerprint datasets. This model contains four convolutional layers and two fully connected (FC) layers. The proposed model can complete a test with an average location error of approx. 1.44 m and an accuracy of 94.45%. The authors of [29] propose a lightweight combination of extreme learning machine (ELM) and CNN. The Conv1D layer is used to extract spatial characteristics of the radio map, and the Pooling1D layer reduces the dimensionality. The result shows that the proposed model is approx. 58% faster than the benchmark.

3. System Design

Wi-Fi RSSI-based indoor localization is a two-stage process [13]. In the first stage, the localization area of interest is composed of reference points (RPs) and test points (TPs) [30]. A database containing offline FPs is created where each entry (RSS vector/FP) is associated with a reference point (RP). A localization algorithm like DNN, RF, or SVM is trained on the offline database. In the second stage, the already-trained localization algorithm tries to find the user’s location by matching online FPs with the database. Distinct from the traditional ML approaches, we process the dataset by using a three-step SDR-scheme sub-area overlapping technique and also utilize lightweight neural networks that are trained on each sub-area independently. The architecture of the proposed model is illustrated in Figure 1, which mainly consists of five components: area division and overlapping, training data selection for classification and regression, source domain refinement (SDR) scheme, coarse positioning phase, and accurate positioning phase. The proposed scheme consists of two phases: coarse and accurate positioning. For the coarse positioning phase, specific points are selected as reference points (RPs). A three-step domain source refinement (DSR) scheme is applied to these RPs to obtain a refined dataset and a classifier is trained on this refined dataset to find the relevant sub-area where the user can reside in. For the accurate positioning phase, the training dataset is divided into several sub-areas to train a deep neural network (DNN) on each sub-area independently. We will explain the aforementioned components in the following sections.

3.1. Area Division and Overlapping

The continuous radio propagation makes it difficult to divide whole areas into distinct clusters. An overlapping between adjacent clusters is required to reduce classification error [12]. We utilized the same concept of area overlapping as given in [12]. The whole area is divided into sub-areas as shown in Figure 2. In the classification/coarse positioning phase, the uncertainty in finding the relevant sub-area is the highest at the intersection of different sub-areas. For example, let the actual position of some object, e.g, “T”, be in area 1, but because of the sharp boundary, the classifier might predict it in area 2. This problem would cause an error later, as the regression algorithm, in the accurate positioning phase, tries to find the object’s localization coordinates in the wrongly predicted area. To reduce this uncertainty, it is worthwhile to increase the margin or overlapping between interconnected areas. Furthermore, if there is no overlapping, the reference points lying at the boundary would have to belong to only one sub-area but not the other one, which in turn reduces the localization accuracy in that particular area. To avoid these problems, we need to introduce an overlapping among sub-areas. Neighboring sub-areas would share all the RPs lying in the overlapped area. In Figure 2, the red squares show the RPs and both red diamonds and green circles represent the test points. The classification algorithm will run on the preprocessed dataset to find the relevant sub-areas of the online fingerprints.

3.2. Training Data Selection

To train the coarse positioning algorithm (e.g., classifier). Instead of using all the RPs for training purposes, we selected only those RPs lying in the black dotted rectangles, as shown in Figure 3. There are two key considerations for this particular selection. First, the reduction in the offline computational complexity without compromising the classification accuracy. Second, distant training points among neighboring areas have a low risk of sharing similar features. This strategy increases classification accuracy. Figure 4 depicts the training points used to train regression-based algorithms in the accurate positioning phase. We select all the RPs lying in any particular area to train their corresponding DNN-MVR model. We did not reduce training data in the final positioning phase because DNN is more sensitive to overfitting; however, to reduce the training time, we divided the whole area into sub-areas and used a set of single-layered lightweight neural networks.

3.3. Source Domain Refinement (SDR)

This section deals with the offline data SDR scheme to remove the redundant knowledge from the source domain and make it more efficient for finding the user’s localization area. The tree-step refinement plan consists of the following steps.

3.3.1. Data Averaging Technique

In order to reduce the training data in the source domain, which in turn reduces the classifier’s computational complexity and offline data storage, we use the K-means clustering algorithm to make small groups of similar fingerprints in the source domain. K-means is an unsupervised clustering algorithm that is used to cluster given data into K number of clusters [31]. The algorithm iteratively assigns the data points to one of the K clusters based on how near the point is to the cluster’s centroid. After making K clusters, we calculate the mean vector of each group. Those mean vectors from each group are stored in a source file and then used to train the classification algorithms. Assuming that we have ${\left(x_o^n\right)}_{n=1}^{N_o}$ RSS vectors in the source domain and we want K clusters, the K means algorithm tries to pick K points as the initial centroids from the dataset. If each cluster’s centroid is denoted by $c_k$, then each data point x is assigned to a cluster based on

$$Argmi{n}_{(c_k\in C)}=euclidean{(c_k,x)}^2,$$

(1)

where “C” is the total number of clusters.

3.3.2. Outlier Removal Scheme

In order to increase the classification accuracy and reduce overfitting, we presented an outlier removal technique. Any distant observation from the other observations can be considered as an outlier [32]. Assuming that total “N” RSS vectors are obtained in step 1 and the total number of sub-areas is “A”, in order to distinguish the outliers from other fingerprints in each area, we calculate the mean vector ${\delta }^a$ of each area “a”, where $a\in A$. The Euclidean distance ${\gamma }_i^a$ of each fingerprint $x_i^a$ from its $a^{th}$ area’s mean vector ${\delta }^a$ is

$${\gamma }_i^a=Euclidean(x_i^a-{\delta }^a).$$

(2)

Here, all the RSS vectors showing the value of Euclidean distance above a certain threshold, $T{h}_a$, would be considered as an outlier. The value of $T{h}_a$ is chosen arbitrarily.

3.3.3. Stable AP’s Weight Enhancement

APs showing less signal fluctuations are more stable and hence are more reliable in the online signal matching process [18]. It has been observed that if we add some bias to the stable AP’s RSSI measurements of each area independently, it will increase the difference among the fingerprints of different areas. Consequently, the classification accuracy will be increased. However, the values of the bias terms are arbitrary, and large values can change the originality of the RSS vectors significantly, which decreases the accuracy. The stability of an AP is directly proportional to its frequency of occurrence. The procedure is explained below. Assuming that total “L” APs are detected in $D_{R1}$ dataset, a total number of sub-areas are “A”, and $N_a$ represents the total number of training samples present in the $a_{th}$ sub-area, where $a\in A$:

1.

We define a detection vector $d_a^l=[d_a^{l,1},d_a^{l,2},\dots ,d_a^{l,N_a}]$, where $d_a^{l,n}\in \{0,1\}$, is the detection indicator for the $l^{th}$ AP of $n^{th}$ sample in the sub-area “a”. When the value of a particular RSSI feature is above a threshold, $T{h}_a$, the corresponding AP is detected, and the value of $d_a^{l,n}$ would be considered as 1 or otherwise, 0. The detection vector $d_a^l$ is calculated for each AP in each sub-area.

2.

For the current sub-area “a”, the sum $S_a^l$ for the $l^{th}$ AP’s detection indicators $d_a^{l,n}$ can be calculated as:

$$S_a^l=\sum _{n=1}^{N_a}{d}_a^{l,n}$$

(3)

And the distinction vector $K_a\in R^{(L\times 1)}$ can be written as, $K_a=[S_a^1,S_a^2,\dots ,S_a^L]$, which we can normalize by dividing the whole vector $K_a$ by the maximum entry in the vector $K_a$:

$$G_a=\frac{K_a}{max\left(K_a\right)}$$

(4)

3.

Sort $G_a$ in descending order, where each entry is the stability indicator of the corresponding AP in sub-area “a”. Now, select those APs whose stability indicator is greater than a threshold $T{h}_a^{\prime }$ and add a small bias $b_a$ into the RSSI measurements of the selected APs. Remember that the values of $T{h}_a^{\prime }$ and $b_a$ are arbitrary.

3.4. Sub-Clustering Algorithms

3.4.1. Support Vector Machine (SVM)

SVM is a supervised learning discriminant technique that solves the convex optimization problem analytically, and unlike generative ML approaches, it does not suffer from the multi-local minima [33]; in other words, it always returns the same solution. Owing to a better data generalization performance, the regularization of non-linear datasets, theoretical guarantees regarding overfitting, relatively easier implementation, and a higher transparency in operation than neural networks [34], we choose SVM as a classifier. In multi-class support vector machine (MCSVM) problems, mainly two approaches, one against-one (OAO) and one-against-all (OAA), are used to classify data. The latter approach is faster than the former [34], and hence is why we adopt this approach. It constructs “K” SVM models for k classes. The nth SVM is trained with nth class samples, treating them as positive samples, and the rest as negative. The dataset is not linearly separable, so we use the Gaussian RBF kernel function for its better performance than the linear and polynomial kernel functions [35].

3.4.2. Random Forest (RF) Classifier

Random forest (RF) is an ensemble tree-based supervised learning algorithm. The building blocks of RF are decision trees (DTs) and the final prediction of the RF is obtained by combining the majority vote of different DTs [36]. RF exhibits great performance with heterogeneous feature space and high dimensional data. RF is insensitive to overfitting, however, it is computationally demanding with high-dimensional data and large forest size [37]. DT makes predictions by applying feature-based splits, and it depends on the impurity of the dataset. Features with the lowest impurity or Gini index are treated as root nodes.

3.4.3. Multi-Variate Regression-Based DNN Algorithm

A deep neural network (DNN) model consists of multiple stacked hidden layers and it is able to approximate any arbitrary function (i.e. linear/non-linear) to any degree of accuracy [38]. The training process is involved in finding the optimal weights, so that the loss function is minimal [39]. We develop our multivariate regression approach based on the lightweight deep neural network (MVR-DNN). A quick response, less training time, high localization accuracy, and generalization are the key considerations. The process of finding the optimal network size is very complicated, and no reliable method exists in the literature to find the proper size of the neural networks [40]. Researchers use their intuition and experience to find the best architecture to solve their problems. A small network requires less memory to store weights, involves less computational work, and shows a fast response as there are very short propagation delays [41]. In contrast, larger networks exhibit poor generalization. Cybenko et al. [42] proposed that a single hidden-layer network is enough to approximate a non-linear decision boundary. We utilized a single hidden layer to construct our proposed model and utilized rectified linear function (Relu) as the activation function since they help reduce the vanishing gradient problem [43]. We have applied the mini-batch gradient descent (GD) optimization technique to boost the training process, as batch gradient descent (BGD) can be very slow since they are involved in redundant computations for large datasets. Although, stochastic gradient descent resolves this redundancy, it falls prey to local minima. Mini-batch gradient descent has two advantages [44]: (1) it shows a more stable convergence and (2) it makes computing the gradient very efficient. Common mini-batch sizes range between 50 and 256. Our proposed model is a supervised training algorithm, where the training samples are split according to their measuring space. We trained our proposed model on each sub-area’s dataset separately; consequently, each sub-area has its own trained model, and this strategy works well to reduce computational complexity and increase localization accuracy, as shown in the Section 4.4. Each model consists of an input layer, a hidden layer(s), and an output layer. Each neuron in the input layer represents an input variable from the training samples, so the number of input layer neurons is equal to the length of the input feature vector (i.e., RSS Vector). The output layer has two nodes because the response of the DNN-based MVR model is the actual 2D position of the object.

4. Experiment Evaluations

To make a comparison with the literature, we evaluated our model on an open-sourced public database containing Wi-Fi RSSI measurements.

4.1. Experimental Setup

The experiments were simulated on a Microsoft Windows 10 education OS with a 1.10 GHz Intel (R) Core (TM) i7-10710 CPU and 10 GB RAM by utilizing Scikit-learn version 1.0.2. with Python bindings.

4.2. Data Description

The proposed scheme is evaluated on the dataset using Wi-Fi RSS measurements collected on the third and fifth floor of the library environment, as shown in Figure 5, at Universitat Jaume I in Spain [30]. The total area of both floors is about $308.4{\mathrm{m}}^2$. All the samples were collected by a trained person using a Samsung Galaxy S3 smartphone over the span of 15 months. During the first month, 15 offline datasets were collected, and we utilized them to train our model. The model performance is evaluated on the 75 online databases that were collected during the whole 15 months. Each floor contains 24 reference points and 106 test points.

4.3. Evaluation Metrics

Our proposed scheme follows the narrow-down approach (NDA) that consists of two stages. To measure the performance of the classification model, we use “Accuracy” as a metric:

$$AccuracyScore=\frac{tp+tn}{tp+fn+tn+fp},$$

(5)

where $tp$ is true positive, $tn$ is true negative, $fp$ is false positive, and $fn$ is false negative. In the second stage, DNLoc finds the final location of the targeted object in the already-predicted area. To measure the performance of the model, we use the average distance error:

$$AED=\frac{1}{N_T}\sum _{p=1}^{N_T}{\parallel (y_{test}^{\prime }-y_{test})\parallel }_2$$

(6)

where $N_T$ represents the total number of online testing samples. $y_{test}^{\prime }$ and $y_{test}$ are predicted and actual labels of the test data, respectively, and both comprise 2D positioning components.

4.4. Experiment Results

4.4.1. Classification Performance

We evaluated our classifiers on the third floor for 15 months.

Table 1. Classifier’s training and response time (s).

Classifier	Training Time		Response Time
	Unprocessed Data	Refined Data
SVM	0.15	0.01	0.0009
RF	9.7	4.7	0.0019

shows the training time and average response time of both classifiers using the full training dataset and refined dataset.

Figure 6a,b depict the compression ratio (CR) of the SDR scheme on the training data for classification. We divide the training data, by using the K-mean clustering algorithm, where each cluster contains five samples on average. We utilized only the mean RSS vector of each cluster; hence, the compression ratio is $80\%$. The overall impact of data compression on the classification accuracy is negative, as depicted in Figure 7a,b. To improve the classification accuracy, we apply the three-step SDR scheme on the reduced dataset. Figure 8a,b illustrate that the proposed SDR scheme improves accuracy by reducing overfitting as can be seen in the later months. It is seen that the refined dataset improves the classification accuracy by approximately $4\%$ for RF and $2.23\%$ for SVM. Figure 9a,b show the comparison of full, reduced, and SDR-scheme-refined datasets in terms of accuracy.

4.4.2. Regression Performance

In the regression/final positioning phase, the DNLoc algorithm finds the user’s final location in the already-predicted area and we compare its performance in terms of accuracy and online computational time with the best papers published on the same dataset like TransLoc [21], DFMIC [22], SmrtLoc [23], and aslo with some other papers in the literature like ViVi [45], KAAL [46], UFL-ECLS [47], EMSS [48], and MSSE [49]. We utilized both third and fifth floor datasets over the span of 15 months.

Table 2. Number of samples and training time for DNLoc.

Floor	Sub-Area	Offline Samples	Online Samples	Training Time (s)
3	1	1800	9000	45.7
3	2	1800	9000	33.4
3	3	1800	9000	42.1
3	4	1800	9000	20.15
5	1	1800	9000	23.6
5	2	1800	9000	59.2
5	3	1800	9000	37.3
5	4	1800	9000	66.27
Total/Average	8	14,400	72,000	327.72

shows the number of samples used to train and test the proposed MVR-DNN model in each area. The training time is also presented in the last column.

Table 3. AED and percentile errors of DNLoc.

Floor 3
Sub-Area	AED (m)	25th Percentile (m)	50th Percentile (m)	75th Percentile (m)	95th Percentile (m)
1	2.02	1.2500	1.9000	2.6500	3.7900
2	2.316	1.51	2.20	2.93	4.0
3	1.94	1.21	1.862	2.577	3.6073
4	2.34	1.4000	2.1900	3.0200	4.2700
Floor 5
1	1.99	1.1500	1.8460	2.5900	3.4780
2	2.38	1.4320	2.2000	3.0800	4.3500
3	1.79	1.0000	1.6000	2.2500	3.1100
4	1.95	1.1000	1.7300	2.3400	3.2800

shows the AED and percentile error of the DNLoc model.

Table 4. Positioning error measures (in meters) and average response time (in milliseconds) for different methods.

Methods	25th Percentile	50th Percentile	75th Percentile	AED	Response Time
MSSE [49]	1.58	3.01	4.86	3.34	10.4
KAAL [46]	1.65	3.28	4.68	3.26	12.6
ViVi [45]	1.79	3.39	4.37	3.21	41.2
Wi-Fi-FAGOT [47]	1.55	2.47	3.88	2.79	228
SmartLoc [23]	1.23	2.29	3.46	2.58	281
DNLoc	1.2565	1.9410	2.68	2.09	100

shows the response time and AED comparison with that of the literature. Figure 10 depicts the AED of DNLoc as compared to other Wi-Fi RSSI-based best techniques in the literature and shows that DNLoc outperforms the other methods, reporting an AED of 2.09 m. TransLoc [21], SmartLoc [23], EMSS [48], Wi-Fi-FAGOT [47], VIVI [45], and KAAL [46] incur an AED of 2.21 m, 2.588 m, 3.9 m, 2.68 m, 2.7 m, 3.23 m, and 3.25 m, respectively. Figure 11 shows the cumulative distribution function (CDF) of different techniques juxtaposed with DNLoc. DNLoc reduces the 85th percentile of DIFMIC, Wi-Fi-FAGOT, KAAL, MMSE, and MUCUS by $15.7\%$, $37.64\%$, $45.8\%$, $48.9\%$, and $66.8\%$ respectively, demonstrating that DNLoc outperforms all other methods.

5. Discussion and Conclusions

A narrow-down approach is presented for indoor localization that involves coarse and accurate positioning phases. Training points’ selection, area division, and overlapping strategies are presented to reduce the uncertainty in finding the actual user’s location. In the coarse positioning phase, the SDR scheme involves data averaging, outlier removal, and stable APs’ weight enhancement techniques, which are presented. The SDR scheme compressed $80\%$ of classification training data and increased classification accuracy. In the final/accurate positioning phase, a set of MVR-DNN models, trained on each sub-area, is utilized to find the final user’s location. Our experimental results establish the superiority of the proposed model over the existing machine learning approaches. It is worthwhile to find the proper size of clusters as the classification accuracy may vary with it. The selection of the optimal size and parameters of the neural networks, the effect of environmental dynamics, data collection overhead, and possible changes in signal strengths over time, which are dependent on a person’s movements, as well as object displacements, an analysis of the bias effect to increase the weight of the RSS vectors of RPs, and a better area classification strategy could all be potential future research topics. Our proposed model is simple, generic, and flexible that can be applied to find the user’s location coordinates accurately in any indoor environment.