Mobile geolocation techniques for indoor environment monitoring

Abstract

Advances in localization-based technologies and the increase in ubiquitous computing have led to a growing interest in location-based applications and services. High accuracy of the position of a wireless device is still a crucial requirement to be satisfied. Firstly, the rapid development of wireless communication technologies has affected the location accuracy of radio monitoring systems employed locally and globally. Secondly, the location is determined using standard complex computing methods and needs a relatively long execution time. In this paper, two geolocalization techniques, based on trigonometric and CORDIC computing processes, are proposed and implemented for Bluetooth-based indoor monitoring applications. Theoretical analysis and simulation results are investigated in terms of accuracy, scalability, and responsiveness. They show that the proposed techniques can locate a target wireless device accurately and are well suited for timing estimation.

1. Introduction

Recently, mobile location estimation has attracted significant attention for various types of applications. These applications have stimulated research on location-finding techniques [1, 2, 3, 4]. Location-finding refers to the process of obtaining the location information of a mobile station (MS) with respect to a set of reference positions within a predefined space [5]. Global Positioning System (GPS) is the most popular technology used in mobile and wireless networks. It is reliable and accurate in free space and line-of-sight (LOS) environments, but its performance deteriorates greatly in non-line-of-sight (NLOS) indoor and urban areas. Other techniques have been developed to work in ubiquitous and pervasive mobile environments.

Network-based location-estimation techniques based on radio signals between mobile devices and access points (APs) have been widely adopted. Currently, given that many buildings are equipped with Wireless Local Area Network (WLAN) access points (shopping malls, museums, hospitals, airports, etc.), it may be practical to use these access points to determine user location in these indoor environments. However, indoor localization techniques are always associated with a set of challenges such as NLOS signals, obstacles, and the mobility of humans.

In the literature, a variety of wireless location techniques have been studied and investigated [2, 6, 7]. Location-estimation techniques can be divided into three general categories: proximity, triangulation, and scene analysis. Within the triangulation category, location estimation of an MS is based on the measured radio signals (or RS) from its neighborhood APs. The representative algorithms for network-based location estimation are time of arrival (ToA), time difference of arrival (TDoA), and angle of arrival (AoA). These algorithms use location parameters received from different sources, and are based on the intersections of circles, hyperbolas, and lines, respectively. The ToA scheme estimates the MS’s location by measuring the arrival time of the radio signals coming from different wireless APs, while the TDoA method measures the time difference between the arriving radio signals. The AoA technique is utilized within the AP by observing the angles of the signals coming from the MS. The equations associated with network-based location estimation schemes are inherently nonlinear.

Network synchronization is a crucial functionality in wireless applications where nodes are required to operate under a collaborative fashion [8]. Cooperative wireless networks play an important role in both data communication and nodes localization [9]. Cooperative locationaware networks employ two types of measurements: (a) measuring the range to estimate the distance between each pair of nodes, and (b) measuring the waveform to identify the range and channel state associated with each link [10].

Bluetooth is a wireless standard operating in the 2.4-GHz ISM (industrial, scientific, and medical) band and is used for wireless personal area networks (WPANs). For the purpose of exchanging information between wireless devices, Bluetooth technology provides high security, low cost, low power consumption, and small product size. A unique ID is assigned to each Bluetooth tag, allowing users to easily locate a static or mobile target. Several researchers have been developing Bluetooth-based localization systems [11,12]. However, the signaling process is the major drawback of Bluetooth technology.

This work considers designing new geolocation techniques for confined areas based on triangular and COordinate Rotation DIgital Computer (CORDIC) algorithms. The first contribution, named Triangular Convergence Location (TCL), is based on received signal strength (RSS) information and a trigonometric triangulation process applied in a wireless propagation environment consisting of three APs. The second contribution, called COrdic Localization (COL), is based on a rotation process applied on two vectors issued from two APs. These two algorithms have been proposed to determine the position of an MS under LOS and/or NLOS environments. The MS’s position is obtained by confining the estimation based on the signal variations and the geometric layout between the MS and the APs in indoor environments.

The rest of this paper is organized as follows: Section 2 surveys various related works on wireless location estimation techniques. Section 3 provides the computational details of the proposed geolocation techniques, TCL and COL. The simulation results and performance evaluation of the proposed techniques are described in Section 4. Finally, section 5 concludes the paper and mentions future research objectives.

2. Literature review

Accurately locating a wireless node or device is an active research topic. The literature provides different solutions, namely RSS, ToA, EToA, AoA, TDoA, and fingerprinting (Fig. 1). The main process involved in positioning is based on coordination and communication between wireless devices and existing infrastructure (Table 1).

Fig. 1. Basic architecture of geo-localization techniques.

Table 1. Comparison of various indoor localization techniques.

ToA is one of the most basic triangulation methods used for 2D position measurement [13,14]. ToA enables locating a node by calculating the time of arrival of the signal from the node to three base stations (BSs). The propagation time can be directly translated into distance, based on the known signal propagation speed. Therefore, to determine the time difference between the transmitter and receiver, synchronizing the wireless device with the locating reference stations is required. The main advantage of ToA is its immunity to multipath effects.

EToA is an extended version of ToA designed by simplifying the recursive and intensive computing of the localization process [15]. In EToA, the computing process is only performed by the MS with a view to improving handover latency. EoTA is an efficient technique that calculates the coordinates of the mobile station based on basic vector functions (shift, addition, and rotation). EToA can directly authenticate and associate with the nearest base station without a scanning phase, which represents the major part of the handover latency. It replaces the scanning phase with a localization mechanism that is completed within a fixed number of iterations. The major advantages of EToA are low computational cost and simplicity of implementation.

In [16], the authors proposed a ToA-based iterative geolocation algorithm alternating between two steps: probability density function (PDF) estimation and parameter estimation (PE). The first step approximates the PDF of the exact measurement error via adaptive kernel density estimation. The second step resolves a position estimate from the approximate loglikelihood function via a quasi-Newton method. This algorithm performs similarly to maximum likelihood estimator (MLE), the geolocation accuracy of which is comparable to that of other studies found in the literature. However, this accuracy is achieved at a higher computational cost.

The study in [17] used ToA measurements based on cooperative and robust localization in mixed LOS and NLOS conditions. It proposed an iterative localization approach to reduce the impact of NLOS propagations. This approach mitigates the impacts of scattering, diffraction, and reflection caused by the presence of multiple obstacles between the transmitter and receiver nodes. It uses the least-median deviation to estimate the initial positions of the sensor nodes. Moreover, it improves the convergence likelihood and estimation accuracy of the covariance matrix of the measured noise.

DOLPHIN (Distributed Object Locating System for Physical-space Internetworking) [18] is an ultrasonic peer-to-peer positioning system using both RF and ultrasonic signals. This system focuses on innovative positioning hardware and techniques to determine positions inside buildings or in the underground. DOLPHIN is easy to configure and provides a high degree of accuracy in three dimensions. It allows accuracy of 2 cm on a test bed of 3 m in size.

Cricket [19] is an indoor location system which utilizes RF and ultrasound based on static transmitters and mobile receivers. The system has been successfully implemented to obtain full 3D real-time coordinates of a mobile device based on a purpose tailored Matlab program. Cricket allows easy flexibility and programmability of devices as a beacon or as a listener. However, cricket suffers from multipath signals which requires high redundancy of range measurements as well as speed of ultrasound which is highly correlated to the temperature. A later version, called Cricket Compass [20], is designed to determine orientation as well as position of mobile devices.

The Active Bat [21] is an ultrasonic positioning system based on pulse transmission between roaming Active Bat tags and fixed ultrasonic receivers mounted on the ceiling. The active Bat computes the tag’s coordinates and provides direction information by performing multilateration based on the time-of-flight of the ultrasonic pulse between them. This positioning system allows an accuracy of 9 cm within a range of 50 m. However, Active Bat employs centralized system architecture and requires a large number of precisely positioned ultrasonic receivers.

The RSS approach uses the strength of the received transmission to estimate the distance between nodes. This is performed by calculating the attenuation in the propagation path. The ratio of the transmitted to the received power is used to estimate the position of the node. Indoor location tracking using RSS [22,23] employs three or more nodes to perform finegrained device tracking, similar to ToA [24]. Using the method of ranging, where the distance between two nodes is predefined, the coordinates of the device are computed using lateration or angulation approaches.

Extensive researches for indoor positioning system (IPS) has focused on the machine learning approaches such as Extreme Learning Machine (ELM) [25]. In this context, [25] proposed the ELM in order to overcome the shortcomings faced by the traditional positioning methods and provide higher positioning accuracy and robustness. The major contribution of that work consists of a Gaussian filter combined with ELM. This positioning system has been tested in a real experimental environment and provided an accuracy of 70 cm within an area of 11 m x 6 m.

TDoA utilizes an estimation method involving the downlink positioning reference signal (PRS) of long term evolution (LTE) [26] technology. As conventional correlation approaches are unable to calculate the time difference when the sampling interval is shorter than a second, this phase is used to estimate the TDoA by constructing a one-to-one relationship table between the time delay and phase. Simulation-based results along with theoretical analysis support TDoA's ability to accurately estimate the time difference within one sampling interval. Additionally, TDoA satisfies LTE requirements for locationawareness services.

In [27], the authors proposed a TDOA-based indoor visible light positioning (VLP) system using cross correlation. It uses virtual local oscillator for cross correlation in order to reduce the hardware complexity. It applies cubic spline interpolation to reduce the sampling rate and enhance the time-resolution of cross correlation. As result, this system provides an average accuracy of 9.2 cm in an area of 1.2m x 1.2m.

The Angle of Arrival (AoA) technique is based on the bearing measurement or the direction of arrival measurement. This technique calculates the angle at which the signal arrives from the BS to the unknown wireless node [28]. In AoA measurement, at least two BSs are needed to calculate the position. AoA's accuracy depends on the directionality of the antenna and is sensitive to the presence of shadowing and multipath effects in the measurement environment. AoA does not provide high localization performance unless large antenna arrays are used [29].

For indoor positioning, the authors of [30,31] proposed localization approaches based on fingerprinting, in which fingerprint matching is employed to determine wireless device location. A fingerprint consists of the features of the scene at certain locations of interest that can be used to form a fingerprint database [32]. This enables determining the location of a particular object by fingerprint matching from the database. Fingerprint-based indoor localization approaches are carried out in software and do not require specialized hardware. In addition, such approaches do not require time synchronization. Recently, support vector classification (SVC) involving multiple classes and support vector regression (SVR) have been successfully utilized for location fingerprinting [33,34].

Proximity-based methods can only provide an approximate position of a device based on link or connection information [35]. The target location is approximated to the position of the access point directly connected with the user. When more than one antenna detects the same mobile target, the location is defined by the antenna receiving the strongest signal. This method is relatively simple to implement. It can identify which cell site the device is using at a given time [36]. This type of localization method is mostly used in GSM and has an accuracy range of 50–200 m. It has high variance, which sometimes might not satisfy the requirements of the positioning application.

Recently, wireless sensors have been used for a variety of new monitoring and control applications, especially target positioning and tracking [36]. Communication and measurement between multiple pairs of sensors is required to achieve localization for all sensors. Most sensor-network-based localization techniques use RSS measurements [37,38]. Four sensor-based localization configurations exist: (1) static sensor nodes and static anchor nodes [39], (2) mobile sensor nodes and static anchor nodes [40], (3) static sensor nodes and mobile anchor nodes [41], and (4) mobile sensor nodes and mobile anchor nodes [42]. The study in [43] surveys recent localization techniques considering wireless sensor networks and their fundamental limits, challenges, and applications.

Recently, cooperative techniques have been introduced for localization and navigation to improve the accuracy and reliability of position information. Information exchange and cooperation in the network is crucial for the design of location-aware networks. To perform these tasks, nodes are required to operate under a common clock without being affected by various imperfections caused by both internal and environmental issues. In this context, [9] explored cooperative network localization and navigation in terms of theoretical foundation, technologies and spatiotemporal cooperative algorithms. Later, [10] developed an experimentation methodology suited for localization in cooperative wireless networks. It established a database based on range and waveform measurements using cooperative wireless channels. Then, evaluation of network localization algorithms has been performed under various LOS and NLOS conditions. Recently, [8] analyzed the asymptotic synchronization performance of large-scale networks for both absolute and relative synchronization. [8] used Cramer-Rao bound, cooperative dilution intensity (CDI) and relative CDI concepts in order to characterize interaction between agents and evaluate the network synchronization in both dense and extended networks.

3. Proposed solutions

The proposed solutions locate a mobile device in an indoor environment, enabling the support of tracking applications. It is based on computing the distance between an AP and the mobile device and then employing a geometrical approach for localization. The position of the mobile device is determined using two RF positioning techniques. In the first technique, the device is located by the intersection point of three circles. Each circle has a radius equal to the distance between the mobile device and the AP under consideration, as illustrated in Fig. 3. In the second technique, the position of the mobile device is determined by the intersection of two vectors rotated using the CORDIC algorithm.

Fig. 3. Network architecture and geometric representation of triangles for MS positioning.

3.1 System model

The mobile geolocation system considered in this study is based on four major concepts:

• The indoor environment is equipped with multiple APs organized in a triangular structure/architecture, i.e., at any time, a mobile station can be located by two or three APs.

• Each AP is capable of detecting the mobile station’s RSSI and measuring the corresponding/associated distance.

• A centralized geolocation system is designed to determine the relative position of the mobile device. A positioning algorithm is integrated to estimate the position of the mobile device by computing metrics from the APs.

• Additional iterations can easily be built into the positioning algorithm for more accuracy as well as to track the mobile device.

3.2 Signal transmission model

The path-loss model allows calculating the distance between a mobile device and an AP of known location. Various path-loss models exist. Generally, path-loss models use trilateration to determine the location of the mobile device [44,45]. However, measurements from indoor radio communication channels [46] have shown the presence of outliers that result in heavytailed measurement noise. Therefore, Bluetooth-based transmission in indoor environments can be affected by noise, multipath and signal attenuation. Therefore, NLOS factors should be considered by the proposed algorithms to provide accurate localization in realistic conditions.

3.3 Triangular Convergence Localization – TCL

In geometrical triangulation, researchers assume that the measured noise is additive and the NLOS error is a large positive bias where the measured ranges are greater than the acceptable values [2]. These techniques require three wireless links to be established simultaneously with three access points. Therefore, they assume that the MS is located in the overlapping region (ABC) of the transmission ranges of the three access points (Fig. 2). However, (a) the MS may be elsewhere in the triangle defined by three access points, and (b) in some cases, no overlapping area may exist [47,48]. In this section, we propose improvements, including a geometric localization process able to coordinate with the MS with low computational cost based on the locations of three access points.

Fig. 2. Three neighboring APs and the associated overlapping area.

The TCL technique is based on the network architecture given in Fig. 3, containing three access points and an MS. The MS is located inside the triangle defined by the three access points (AP₁ , AP₂ , AP₃ ) and coordinated by the distance d_j (j = 1,2,3) far from each access point AP_j . The MS position defines three triangles: AP₁MSAP₂ , AP₂MSAP₃ , and AP₃MSAP₁. TCL focuses on them successively in order to reduce the localization field of the MS. TCL is an iterative geometric process, which consists of reducing the localization field until it converges on the MS location.

The main assumptions of TCL are as follows:

• AP coordinates are predefined

• D is the distance between two APs

•d₁ + d₂ > D, d₂ + d₃ > D, and d₃ + d₁ > D

where:

A₀ , B₀ , and C₀ are the orthogonal projections of the MS on the sides (AP1, AP2), (AP2, AP3), and (AP3, AP1), respectively.

d1, d2, and d3 are the distances separating the MS from AP1, AP2, and AP3, respectively. The MS is able to measure the distance dj based on the power received from APj.

θ12 is the geometrical angle \((\mathrm{MS}-\mathrm{AP} \widehat{1, \mathrm{AP}} 1-\mathrm{AP} 2)\). θ₁₃ , θ₂₁ , θ₂₃ , θ₃₁ , and θ₃₂ are defined similarly.

TCL focuses primarily on the triangle AP₁MSAP₂ . The same tests will be repeated for the triangles mentioned above (AP₂MSAP₃ and AP₃MSAP₁). Based on the above assumptions and Fig. 3, we can propose the following approach:

r₁ = d₁cosθ₁₂

d₂² = (D − r₁)² + (d₁² − r₁²) ⟹

d₂² = (D − d₁cosθ₁₂)² + (d₁² − d₁cosθ₁₂² )⟹

d₂² = D² + d₁² − 2Dd₁cosθ₁₂ = D² + d₁² − 2Dr₁ ⟹

\(r_{1}=\frac{D^{2}+d_{1}^{2}-d_{2}^{2}}{2 D}\)       (1)

We define here the first factor q₁ as follows:

\(\mathrm{q}_{1}=\frac{\mathrm{r}_{1}}{\mathrm{D}}=\frac{\mathrm{D}^{2}+\mathrm{d}_{1}^{2}-\mathrm{d}_{2}^{2}}{2 \mathrm{D}^{2}}\)       (2)

The range of parameter can determine the shape of the triangle AP₁MSAP₂(Table 2).

Table 2. Different forms of the triangle (AP1MSAP2).

We propose to narrow the size of the triangle containing the MS location. In this context, we orthogonally project the MS location on the (AP₁ , AP₂), (AP₂ , AP₃), and (AP₃ AP₁) sides, which results in triangles A₀ , B₀ , and C₀ respectively. Consequently, the triangle (A₀ , B₀ , C₀) is smaller than (AP₁ , AP₂ , AP₃). In other terms, we have just created three new virtual APs, placed at A₀ , B₀ , and C₀. Based on [49], the coordinates (x₁₂ , y₁₂) of the point A₀ are given as follows:

x ₁₂ = q₁X₂ + (1 − q₁ )X₁

y ₁₂ = q₁Y₂ + (1 − q₁ )Y₁

Where (X₁ , Y₁) and (X₂, Y₂) are the coordinates of AP₁ and AP₂ , respectively.

Let r₂ be the distance between AP2 and B0 and r3 be the distance between AP3 and C0. As described previously, we can obtain the coordinates of the points B₀ and C₀ as follows:

x₂₃ = q₂X₃ + (1 − q₂ )X₂

y₂₃ = q₂Y₃ + (1 − q₂ )Y₂

x₃₁ = q₃X₁ + (1 − q₃ )X ₃

y₃₁ = q₃Y₁ + (1 − q₃ )Y₃

Where:

\(\mathrm{q}_{2}=\frac{\mathrm{r}_{2}}{\mathrm{D}}=\frac{\mathrm{D}^{2}+\mathrm{d}_{2}^{2}-\mathrm{d}_{3}^{2}}{2 \mathrm{D}^{2}} \quad \mathrm{q}_{3}=\frac{\mathrm{r}_{3}}{\mathrm{D}}=\frac{\mathrm{D}^{2}+\mathrm{d}_{3}^{2}-\mathrm{d}_{1}^{2}}{2 \mathrm{D}^{2}}\)

Using the Pythagorean Theorem, we can calculate the distances between the MS and the new points A₀ , B₀ , and C₀ :

\(\mathrm{d}\left(\mathrm{MS}, \mathrm{A}_{0}\right)=\sqrt{\mathrm{d}_{1}^{2}-\mathrm{r}_{1}^{2}} \quad \mathrm{~d}\left(\mathrm{MS}, \mathrm{B}_{0}\right)=\sqrt{\mathrm{d}_{2}^{2}-\mathrm{r}_{2}^{2}} \quad \mathrm{~d}\left(\mathrm{MS}, \mathrm{C}_{0}\right)=\sqrt{\mathrm{d}_{3}^{2}-\mathrm{r}_{3}^{2}}\)       (3)

Now, the MS exists inside a smaller triangle defined by three new virtual APs located at A₀ , B₀ , and C₀ . As a result, we return to the first step of the computational process for a new iteration using the distances between the MS and each access point as well as the location of those APs. During the second iteration, the orthogonal projections of the MS on the (A₀B₀ ), (B₀C₀ ), and (C₀A₀) sides lead to three new points, A₁ , B₁ , and C₁ (i.e., their coordinates) as well as their distances from the MS. Moreover, the area of A₁B₁C₁ is smaller than that of A₀B₀C₀ .

At the i^th iteration, the MS will be located in a triangle A_iB_iC_i that is smaller than A_i-1B_i-1C_i-1 . The triangle A_iB_iC_i allows the designing of the next triangle A_i+1B_i+1C_i+1 . After a few iterations, the coordinates of the three vertices of the triangle (A, B, and C) converge to the actual MS coordinates. At this stage, the triangle A conv B conv C conv with vertices A_conv , B_conv , and C_conv is considered a point. It is therefore possible to write the following:

x_Aconv ≈ xB_conv ≈ xC_conv and y_Aconv ≈ y_Bconv ≈ y_Cconv

We suppose that the MS coordinates can be obtained by the average, as given in Eq. 4. The division by 3 assumes that the MS exists at the center of gravity of the triangle A_conv B_conv C_conv.

\(\mathrm{x}_{\mathrm{MS}}=\frac{\mathrm{x}_{\mathrm{Aconv}}+\mathrm{x}_{\mathrm{Bconv}}+\mathrm{x}_{\mathrm{Cconv}}}{3}, \quad \mathrm{y}_{\mathrm{MS}}=\frac{\mathrm{y}_{\mathrm{Aconv}}+\mathrm{y}_{\mathrm{Bconv}}+\mathrm{y}_{\mathrm{Cconv}}}{3}\)       (4)

3.4 CORDIC-based localization (COL)

Location-based services are the most significant characteristic of 3G/4G wireless communication systems, which enables support for several new types of applications. The ToA localization technique is most frequently used for MS position estimation. This technique uses standard methods based on complex computing processes that are generally implemented with software tools [1,50]. The main challenge of ToA resides in the power limitations of MSes, which requires optimization combined with the ability to be used in an indoor environment.

To overcome these limitations, we propose a CORDIC approach based on our previous contributions [47, 48, 16] considering two technical aspects. Firstly, the proposal is expected to simplify the intensive and recursive computation of the localization process by reducing the execution time, cost, and power consumption. Secondly, a suitable topological architecture including only two APs has been considered to adapt to indoor environment localization.

Fig. 4 represents the basic architecture of the network topology considered for the COL algorithm. We assume that the coordinates (X_j , Y_j) (j = 1, 2) of two APs are predefined. For signal propagation, we consider two path-loss models: free space and noisy. Using these models, d_j (j = 1, 2) values are calculated based on the measured received signal strength indicator (RSSI), as outlined in Eq. 5. These parameters are illustrated in a local coordinate system, as shown in Fig. 4.

Fig. 4. Basic network architecture of COL deployment.

Pr = Pt.Gt.Gr.[λ/4πd]²       (5)

Consider the following:

• (X₁ , Y₁ ) = (0, 0) and (X₂ , Y₂ ) = (D, 0)

• 𝛉 = \((\mathrm{AP1}-\widehat{\mathrm{MS}, \mathrm{AP1}}-\mathrm{AP2})\)

• 𝛃 = \((\mathrm{AP2}-\widehat{\mathrm{MS}, \mathrm{AP2}}-\mathrm{AP1})\)

• D is the distance between AP₁ and AP₂ .

• d is obtained in the convergence state (i.e., when MS location is identified).

The question now is how do we calculate the coordinates of the MS from these two angles and the parameters mentioned above?

The proposed technique is based on using two vectors \(\overrightarrow{\mathrm{V}}_{1}\) and \(\overrightarrow{\mathrm{V}}_{2}\) whose origins are located at the positions of the APs and ends on the circle ζ i (AP_i , d_i ). The principle of this technique is rotating these two vectors \(\overrightarrow{\mathrm{V}}_{1}\) and \(\overrightarrow{\mathrm{V}}_{2}\) until they cross at a focal point, denoted by (x_c , y_c ) (Fig. 5).

Fig. 5. Localization principle of COL.

The initial positions (x₁ ,y₁ ) and (x₂ ,y₂ ) of the ends of the vectors \(\overrightarrow{\mathrm{V}}_{1}\) and \(\overrightarrow{\mathrm{V}}_{2}\) are (d₁ ,0) and (D - d₂,0), respectively. The initial and final positions of the first vector \(\overrightarrow{\mathrm{V}}_{1}\) are the following, respectively:

\(\overrightarrow{\mathrm{V}_{1}}\left(\begin{array}{l} \mathrm{x}_{1} \\ \mathrm{y}_{1} \end{array}\right)=\left(\begin{array}{c} \mathrm{d}_{1} \\ 0 \end{array}\right) \text { and }\left(\begin{array}{l} \mathrm{x}_{1}^{\mathrm{n}} \\ \mathrm{y}_{1}^{\mathrm{n}} \end{array}\right)=\left(\begin{array}{l} \mathrm{xc} \\ \mathrm{yc} \end{array}\right)\)

This vector undergoes a global rotation with an angle θ, which we propose here to study its complete evolution. Elementary rotations with angles θ i were performed on the vector # to reach the final position and therefore calculate the MS position with a given accuracy. To simplify the computing complexity, an iterative process has been developed by following these steps:

1. Applying CORDIC process to θ and β variations,

2. Checking/testing vector convergence condition,

3. Optimizing for more accuracy,

4. Computing MS coordinates.

Applying CORDIC process to θ and β variations

From Fig. 5(b), the angles θ and β can be defined using Eq. 6:

θ = sin^-1(d₁₁/d₁), β = sin^-1(d₂₂ /d₂)       (6)

where θ and β are managed by the CORDIC process within the rotation interval [-π/2,π/2]. The convergence conditions on vectors # and # must be checked and verified constantly. Two conditions are required to satisfy vector convergence (Eqs. 7 and 8). Only one condition is useful but not sufficient for the convergence state.

d₁₁ = d₂₂ → d₁sinθ = d₂sinβ       (7)

d₁cosθ + d₂cosβ = D       (8)

If the MS is located in area 1, defined by θ∈[0, π/2], θ and β are assigned the middle value (θ = β = π/4). Then, θ and β are adjusted according to three different cases of the vectors \(\overrightarrow{\mathrm{V}}_{1}\) and \(\overrightarrow{\mathrm{V}}_{2}\)(Table 3). In case (a), θ and β are increased by a certain fraction (ε) of their values. However, in cases (b) or (c), only one angle θ or β has to be adjusted by decreasing its value by a certain fraction (ε). This fraction decreases with the iteration number.

Table 3. Three cases for adjusting θ and β.

Checking/testing vector convergence condition

However, the equalities in Eqs. 7 and 8 represent a strict requirement/condition that may not be satisfied due to the estimation error when measuring d 1 and d 2 from signal strength. Therefore, these conditions should be satisfied within a certain range that reflects the accuracy level with which we are computing the convergence conditions. In other terms, the convergence conditions are now given by Eqs. 9 and 10, using a predefined accuracy level α.

α ≤ d₁sinθ / d₂sinβ ≤ 1/a       (9)

Where α is the accuracy level.

α ≤ ^{(d₁cosθ + d₂cosβ)} / _D ≤ 1/a       (10)

Optimizing for more accuracy

Within the optimization phase, θ and β are adjusted in order to improve their localization accuracy. Once the convergence conditions are justified/verified, additional iterations are performed with finer variations to obtain coordinates close to the ideal case, as defined in Eqs. 7 and 8. The optimization process continues adjusting θ and β while the convergence conditions are limited within a narrow interval.

Computing MS coordinates

The optimization phase outlines the most suitable values of θ and β that represent the most accurate values of the convergence conditions of vectors \(\overrightarrow{\mathrm{V}}_{1}\) and \(\overrightarrow{\mathrm{V}}_{2}\). As a result, the mobile station coordinates are expressed by Eqs. 11 and 12, based on the representation in Fig. 4.

X_MS = d₁cosθ ≈ d₂cosβ       (11)

Y_MS = d₁sinθ ≈ d₂sinβ       (12)

Fig. 6 shows the COL localization flowchart, primarily consisting of processes and conditions responsible for computing MS coordinates. COL constitutes an efficient geolocation method able to estimate MS coordinates based on fundamental vector rotation functions in a 2D space.

Fig. 6. COL flowchart.

4. Simulation results and performance evaluation

In an effort to design two new localization techniques, this framework was thoroughly focused on the utilization and employment of Matlab-based platform coding, for a sophisticated simulation of an MS and two or three APs. Matlab was selected as the most suitable tool for the design of the TCL and COL algorithms, since they are mainly based on computational algorithms ranging from elementary functions to more sophisticated ones. Matlab is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features and is fit for our purpose.

4.1 Performance metrics

The performance criteria associated with localization systems can be classified into the following areas:

Accuracy or location estimation error (LEE). This measures the Euclidean distance between the real and estimated positions of the MS (13).

\(\mathrm{LEE}=\sqrt{(X r-X e)^{2}+(Y r-Y e)^{2}}\)       (13)

r: real, e: estimated

Responsiveness. Responsiveness is how fast the geolocation technique/system is able to determine the location of a certain target (or to update the location of a moving target). In our results, responsiveness corresponds to the number of iterations useful for localization. It reflects the amount of time in which the location is determined.

Scalability. Scalability measures the performance of the location system/technique when it operates with a larger number of location requests and coverage. In this regard, several simulations have been performed with various coverage areas.

Adaptiveness. Adaptiveness is the ability of the localization system to cope with environmental changes. Better adaptiveness reduces the need for repeated calibration.

Cost and complexity. Cost may include extra infrastructure, additional bandwidth, lifetime, weight, energy, and nature of deployed technology. Complexity is related to the signal processing and algorithms used to estimate the location.

In this study, performance is measured in terms of accuracy, responsiveness, and scalability.

4.2 Simulation parameters

In this section, we illustrate the validity of the proposed methods for wireless device localization in indoor environment using Bluetooth technology. The simulation parameters employed to evaluate the performance of our algorithms are shown in Table 4.

Table 4. Parameters of the simulation system.

4.3 Comparative study

A comparative study is conducted in this section between different localization approaches found in the literature. The major metrics featuring localization techniques reside on: complexity (cost), accuracy and responsiveness. These metrics allow evaluating the localization performances and outlining the targeted applications.

Complexity of a system can be attributed to hardware, software or computational processes. The key idea of “mathematical programming” based approaches is to formulate the position estimation problem as a constraint optimization problem, which can be solved by iterative (e.g. [16-21, 32, 36, 42]) or direct methods (e.g., [23, 25, 28, 31]). Direct methods are generally based on factorization of the matrix where this operation is absent in iterative methods. Such operations can accomplish/perform execution efficiency on advanced computer architectures, but are the major factor for high computational complexity (Table 5). However, iterative methods are usually simpler to implement than direct methods since no full factorization has to be stored.

Table 5. Comparison of indoor localization techniques.

Furthermore, the basic operations in our proposed iterative method relies on an effective combination between (a) simplifying the trigonometric operators and (b) optimizing the iterative process. This combination implies low computational complexity and reduces the total solution time for the positioning system. The recent iterative localization techniques [16-21, 32, 36, 42] are based on very complex computational aspect in terms of operators, matrices, long iterative processes and components (broadband ultrasound, filters, correlators etc…) which impact their implementation cost (Table 5).

Accuracy is the key factor to describe how close the estimation from a positioning technique is to match the actual position of devices for indoor areas. It is usually determined by the location estimation error (13). Table 5 shows the results of comparison between the state of the art and the proposed approaches TCL and COL. Table 4 compares Dolphin [18], Cricket [19,20], TDoA-based VLP [27], ELM-Gauss filtering [25], PSO-Gauss filtering [25] and Geometric localization [47] approaches with the proposed approaches. To do that, we used unified conditions under which the simulations have been performed for both existing and proposed algorithms. In other terms, the accuracy of our proposed algorithms are extracted/collected within the same condition under which each existing algorithm has been applied.

It is very clear from this table that our approaches TCL and COL performs well not only in terms of accuracy but as well in terms of computational complexity. It also reflects that the accuracy requirements depend on the scale of the transmission; hence, it will impact the type of application supported by the corresponding localization technique. Furthermore, TCL and COL perform localization process within a reduced delay which allows to support realtime tracking applications (section 4.4 - responsiveness).

4.4 Performance evaluation and analysis

Two different localization scenarios are created and analyzed for the proposed localization techniques COL and TCL. In the first scenario, a grid of stationary APs in an indoor environment is maintained and an MS is randomly placed in an area with variable size. In the second scenario, measurements are generated by adding white Gaussian noise introducing a certain deviation in the range domain from the true values. For TCL, simulation is performed with three stationary APs. However, only two APs are sufficient for simulating COL. The performance evaluation compares these algorithms in terms of accuracy, scalability, and responsiveness.

Accuracy

The LEE represents the Euclidian distance between the estimated and real target locations. The MS locations have been selected randomly in an area defined by the APs' positions. This area forms a triangle ABC for TCL and a square for COL. Figs. 7 and 8 illustrate the performance of the TCL and COL algorithms in terms of localization accuracy for different channel models.

Fig. 7. Localization accuracy: LEE for free space channel.

Fig. 8. Localization accuracy: LEE for noisy channel.

In a free channel model, TCL provides a very high accuracy level of around 10 –14 m. TCL is also capable of determining the position of any MS located outside the triangle ABC. However, the accuracy level increases significantly when moving away from the triangle ABC, as shown in Fig. 9. On the other hand, COL provides an acceptable accuracy level, averaging at 10 –2 m based on several scenarios. This result is very interesting since in a Bluetooth environment with a range 10 m, the positioning error is around 10 cm, which is considered a reasonable error for various types of Bluetooth-based applications.

Fig. 9. LEE for MS located outside the triangle ABC (LEE in meter for TCL).

In the noisy channel model, the TCL and COL algorithms provide similar performances with LEE slightly lower than 10 cm (Fig. 8).

These types of results have been averaged over N random MS positions (N=30), and then re-extracted for various coverage area sizes in order to provide more credibility to both algorithms. These results provide, in the following section, the scalability effectiveness of TCL and COL.

Scalability

In order to measure the scalability performance of the proposed localization techniques, several simulations have been performed with various coverage areas. The coverage area is determined by the APs locations in a rectangular form. For the first scenario, where the pathloss model is deployed in free space, Fig. 10(a) shows that TCL is capable of identifying the location of the MS with a negligible LEE of around 10^–15 m. As expected, LEE increases slightly with coverage area. For the second scenario, the LEE is around 10^-2 m and increases almost linearly with the coverage area (Fig. 10(b)).

Fig. 10. TCL: location estimation error vs. coverage in (a) noiseless and (b) noisy environments.

Similar simulations have been performed with COL, where Figs. 11(a) and 11(b) show the LEE obtained for several coverage areas. In Fig. 11(a), the COL technique has an LEE of around 10^-2 m in the free space path-loss model. COL maintains almost the same accuracy level in the noisy channel model (Fig. 11(b)) compared to the free space. This result proves that COL is less sensitive to noise and multipath compared to TCL. Moreover, similar variations in LEE for the same area is a common feature of TCL and COL (Figs. 10 and 11).

Fig. 11. COL: location estimation error vs. coverage for (a) noiseless and (b) noisy environments.

Responsiveness

Fig. 12 shows how coordinates (X,Y) of the triangle vertices (A,B,C) converge on the MS coordinates. It shows the number of iterations required to determine the MS position. By running TCL and based on several simulations performed for random positions of the MS, around 10 iterations are required to determine the coordinates of the MS. This result reflects a high responsiveness level of the TCL algorithm, especially when operating on fast hardware. It is an indication of the usefulness of TCL for tracking applications, where the localization process must recompute and update the MS position within a restricted period. In a noisy channel, the responsiveness is almost similar, and the number of iterations is around 11 (Fig. 13).

Fig. 12. Number of iterations useful for locating the MS (TCL noiseless).

Fig. 13. Number of iterations useful for locating the MS (TCL noisy).

Fig. 14 shows the number of iterations useful to determine MS position based on COL technique. The number of iterations is mainly affected by (a) the predefined accuracy level and (b) the elementary angle value used for rotating vectors # and # during the optimization phase. The responsiveness is slightly lower with COL compared to TCL, which requires 7 iterations for MS positioning. This result has been averaged based on 30 different scenarios. Fig. 14 outlines the number of iterations and the real and estimated (x,y) coordinates of the MS for an accuracy level of α = 0.99. COL was also tested in a noisy channel, and the average number of iterations increased by 1.

Fig. 14. Number of iterations useful for locating the MS (COL noiseless).

5. Conclusion

This paper covers different technological solutions for wireless indoor positioning and outlines several trade-offs amongst them. It proposed COL and TCL, which are recent advances in wireless indoor localization. COL and TCL are based on 2D geometric approaches consisting of trigonometric computing models. The performance of both techniques was evaluated. Accuracy, responsiveness, and scalability were considered for comparison. TCL displayed better performance particularly in terms of accuracy and responsiveness. In addition, the implementation simplicity and low computational overhead are major advantages.

In future work, two alternatives will be investigated. (1) Propagation channel modeling already realized in [51] will be considered in order to improve localization for line of sight (LOS) and non-line of sight (NLOS) positions of the MS. (2) A hardware implementation of these techniques can be designed in order to reduce the cost, an area in which most positioning systems suffer. Localization speed is also a very interesting factor in evaluating an explicit hardware implementation and proving the efficiency of these techniques for tracking.