2.1 Selecting a primary positioning method

Unless in exceptional cases, multilateration and fingerprinting are the two positioning methods generally selected for indoor positioning applications. Each has benefits and disadvantages in its application. Multilateration is suitable for a relatively open space, usually with a LOS condition between APs and the end user's smartphone. Research has shown that fingerprinting is a better choice for a stable complex space in which the multipath effect and NLOS condition occur (Pathak et al., Reference Pathak, Palaskar, Palaskar and Tawari2014; Bai, Reference Bai2016; Van Haute et al., Reference Van Haute, De Poorter, Crombez, Lemic, Handziski, Wirström and Moreman2016; Yaro et al., Reference Yaro, Sha'ameri and Kamel2018). In this research, multilateration was selected as the positioning method due to the following reasons:

1. a) relatively open spaces are often available in city canyon areas, which are more suitable for multilateration applications, although the NLOS condition exists for satellite signals detection;

2. b) it is hard to conduct the training phase of the fingerprinting method in irregular and large outdoor spaces;

3. c) there is a lack of variation of signal transmission in most outdoor spaces for adequately implementing a fingerprinting-based positioning system.

In practice, different strategic positioning methods and technologies are involved for different positioning scenarios. For example, Wi-Fi RTT-based trilateration is designated for indoor positioning in this project. For outdoors, either GPS alone, Wi-Fi alone or a combination of Wi-Fi and GPS can be involved for positioning. Figure 1 describes this strategy. As the figure shows, the determination of IOD assessment criteria is the main focus of this paper. Some fingerprinting concepts are also used to make the IOD assessment more robust.

2.2 Ranging with Wi-Fi RTT

Wi-Fi RTT technology provides a simple and accurate way of ranging calculation, especially in an open space. The round-trip-time and estimated range between a Wi-Fi AP and the end user's smartphone (D _est) for a period of mean RTT can be obtained through Equations (1) and (2) (Yu et al., Reference Yu, Chen, Chen, Guo, Ye and Liu2019):

(1)\begin{align}{t_{RTT}} & = \frac{1}{N} \left( {\mathop \sum \limits_{i = 1}^N {t_{4\_i}} - \mathop \sum \limits_{i = 1}^N {t_{1\_i}}} \right) - \frac{1}{N} \left( {\mathop \sum \limits_{i = 1}^N {t_{3{\_ _i}}} - \mathop \sum \limits_{i = 1}^N {t_{2{\_ _i}}}} \right)\end{align}

(2)\begin{align}{D_{\textrm{est}}} & = \frac{1}{2}\mathrm{\ast }{t_{RTT}}\mathrm{\ast }c\end{align}

where ${t_{RTT}}$ is the round-trip-time of the signal transmitted between the smartphone and an AP; $c$ is the signal transmission speed; ${t_{1\_i}}$ is the timestamp when the FTM framework was first sent by a Wi-Fi AP; ${t_{2\_i}}$ is the timestamp when the FTM signal arrives at the smartphone; ${t_{3\_i}}$ is the timestamp when the smartphone returns the acknowledgement signal to the AP; ${t_{4\_i}}$ is the timestamp when the acknowledgement signal is received by the AP; $N$ is the successful burst number (where $N > 0,N< B$) and B is the total burst number (i.e., burst size, B = 8 as the default value in the Android operating system (OS).

Generally, an Android Pie (Android P) or higher Android operating system is required for running the FTM. Other smartphone default settings such as the ACCESS_FINE_LOCATION, location tracking and Wi-Fi scanning permissions need to be enabled on the end-user device (Okamoto and Chen, Reference Okamoto and Chen2015). All the estimated ranges are simplified to horizontal distances in this research. No vertical distance between an access point (AP) and a user is considered in this research (Gao et al., Reference Gao, Tang and Bai2019).

2.3 Combination of the indoor and outdoor coordinate systems

A standard local coordinate system needs to be established for integrating both indoor and outdoor positioning processes seamlessly. First, an East, North and Up (ENU) local coordinate system is defined based on the universal Cartesian system. The ENU coordinates are formed from a plane tangent to the Earth surface fixed to a specific location, and hence it is sometimes known as a local tangent or local geodetic plane (see Figures 2 and 8).

Figure 2. Relationships between the local ENU and the ECEF coordinate systems

For any point (e.g., $P(\phi,\lambda,h))$ received by a smartphone, its local ENU coordinates can be obtained from the point's known latitude $(\phi )$, longitude $(\lambda )$ and height (h). A local XYZ coordinate system is defined using the same initial point of the ENU system, which is for both indoors and outdoors. To simplify the testing process, only ‘EN’ and ‘XY’ coordinates are selected, while ‘Up’ and ‘Z’ coordinates are ignored. Assuming point $P(E^{\prime},\;N^{\prime})$ is a point with known universal Cartesian coordinates $E^{\prime}$ and $N^{\prime}$ (see Figure 2), then the coordinates can be converted geometrically to the local ENU and the local XYZ coordinate systems through Equations (4) and (5).

(3)\begin{equation}(\phi ,\; \lambda ,\; h)\; = > ({X_{ecef}},\; {Y_{ecef}},\; {Z_{ecef}})\; = > (E^{\prime},\; N^{\prime},\; U^{\prime})\; = > (E,\; N,\; U)\end{equation}

The above coordinate transformations are accomplished by Equations (4)–(6); more details can be found in (Deakin and Hunter, Reference Deakin and Hunter2013; PCG, P.C.o.G. and I.C.o.S.a.M.(ICSM), 2018; A Guide to Coordinate Systems in Great Britain Geodesy & Positioning, 2020)):

(4)\begin{align}&\left[ {\begin{array}{@{}c@{}} {{X_{ecef}}}\\ {{Y_{ecef}}}\\ {{Z_{ecef}}} \end{array}} \right] = \left[ {\begin{array}{@{}c@{}} {({v + h} )\textrm{cos}\phi \; \textrm{cos}\lambda }\\ {({v + h} )\textrm{cos}\phi \; \textrm{sin}\lambda }\\ {[{v({1 - {e^2}} )+ h} ]\textrm{sin}\phi } \end{array}} \right]\end{align}

(5)\begin{align}&\left[ {\begin{array}{@{}c@{}} {E^{\prime}}\\ {N^{\prime}}\\ {U^{\prime}} \end{array}} \right] = \left[ {\begin{array}{@{}ccc@{}} { - \textrm{sin}\lambda }& {\textrm{cos}\lambda }& 0\\ { - \textrm{sin}\phi \; \textrm{cos}\lambda }& { - \textrm{sin}\phi \; \textrm{sin}\lambda }& {\textrm{cos}\phi }\\ {\textrm{cos}\phi \; \textrm{cos}\lambda }& {\textrm{cos}\phi \; \textrm{sin}\lambda }& {\textrm{sin}\phi } \end{array}} \right]\left[ {\begin{array}{@{}c@{}} {{X_{ecef}} - {X_{ref}}}\\ {{Y_{ecef}} - {Y_{ref}}}\\ {{Z_{ecef}} - {Z_{ref}}} \end{array}} \right]\end{align}

where $v = \; (a/\sqrt {(1 - {e^2}\textrm{si}{\textrm{n}^2}\phi )} )$, $\; {e^2} = 2f - {f^2}$ and $a = 6378137.0\;\textrm{m}$ is the semi-major axis of the earth based on the World Geodetic System 1984 (WGS84); f is the flattening and 1/f = 298⋅257223563; $({{X_{ecef}},\; {Y_{ecef}},\; {Z_{ecef}}} )$ are the coordinates in the Earth-Centred, Earth-Fixed (ECEF) Cartesian coordinate system; $({{X_{ref}},\; {Y_{ref}},\; {Z_{ref}}} )$ are the ECEF coordinates of the origin of $E^{\prime}N^{\prime}U^{\prime}$ coordinate system. Assuming the coordinates of the origin of the ENU coordinate system is $({E^{\prime}_0},\; {N_0},\; {U^{\prime}_0})$ in the $E^{\prime}N^{\prime}U^{\prime}$ coordinate system, then

(6)\begin{align}\left[ {\begin{array}{@{}c@{}} E\\ N\\ U \end{array}} \right] & = \left[ {\begin{array}{@{}c@{}} {E^{\prime} - {{E^{\prime}_0}}}\\ {N^{\prime} - {N^{\prime}_0}}\\ {U^{\prime} - {{U^{\prime}_0}}} \end{array}} \right]\end{align}

(7)\begin{align}\left[ {\begin{array}{@{}c@{}} {{x_G}}\\ {{y_G}} \end{array}} \right] & = \left[ {\begin{array}{@{}cc@{}} {\textrm{cos}\theta }& {\textrm{sin}\theta }\\ { - \textrm{sin}\theta }& {\textrm{cos}\theta } \end{array}} \right]\left[ {\begin{array}{@{}c@{}} E\\ N \end{array}} \right]\end{align}

where ${x_G}\;\textrm{and}\;{y_G}$ are the smartphone's GPS location measurements under the local XY coordinate system; E and N is the smartphone's GPS location measurement under the local EN coordinate system.

2.4 LS-based trilateration positioning process

Least-squares (LS) is a commonly used method for trilateration-based positioning, especially when a user is in motion or the motion parameters are untraceable. The coordinates obtained through the LS method are generally more accurate than those obtained by solving all equations algebraically (Gavin, Reference Gavin2020). Apart from the general LS application to Wi-Fi- and smartphone-based multilateration (see its implementation details in (Bai, Reference Bai2016)), it can also be used in the multilateration positioning process combining both GPS and Wi-Fi measurements. When such a combination is involved in the multilateration process, for example the combination of two Wi-Fi and one GPS measurements, the specific LS model becomes (with the assistance of Taylor series to the first-order expansion):

(8)\begin{equation}\left[ {\begin{array}{@{}cc@{}} {{x_G} - x_G^0}& {{y_G} - y_G^0}\\ {\begin{array}{@{}cc@{}} {\dfrac{{{x_{W\!1}} - {x_0}}}{{d_{W\!1}^0}}}\\ {\begin{array}{@{}cc@{}} \vdots \\ {\dfrac{{{x_{wn}} - {x_0}}}{{d_{W\!n}^0}}} \end{array}} \end{array}}& {\begin{array}{@{}cc@{}} {\dfrac{{{y_{W\!1}} - {y_0}}}{{d_{W\!1}^0}}}\\ {\begin{array}{@{}cc@{}} \vdots \\ {\dfrac{{{y_{w\!n}} - {y_0}}}{{d_{W\!n}^0}}} \end{array}} \end{array}} \end{array}}\!\! \right] \left[ {\begin{array}{@{}c@{}} {\Delta x}\\ {\Delta y} \end{array}} \right]\; = \left[ {\begin{array}{@{}c@{}} {\begin{array}{@{}c@{}} {{d_G} - d_G^0}\\ {{d_{W\!1}} - d_{W\!1}^0} \end{array}}\\ \vdots \\ {{d_{wn}} - d_{wn}^0} \end{array}} \right]\end{equation}

where

• $d_{Wi}^0 = \sqrt {{{({{x_{wi}} - {x_0}} )}^2} + {{({{y_{wi}} - {y_0}} )}^2}}$; $i = 1, \ldots ,n$,

• $\Delta x = x - {x_0}$;

• $\Delta y = y - {y_0}$;

where $x\textrm{ and }y$ are the smartphone's coordinates in the local XY coordinate system, ${d_{wi}}({i = 1, \ldots ,n} )$ is the measured distance between the ${i^{th}}$ Wi-Fi AP and the smartphone, ${x_G}$ and ${y_G}$ are the smartphone's GPS location measurements in the local XY coordinate system, and ${x_{wi}}$ and ${y_{wi}}$ $({i = 1, \ldots ,n} )$ are the coordinates of the ${i^{th}}$ Wi-Fi AP in the local XY coordinate system. The initial values of ${x_0}\textrm{ and }{y_0}$ can be obtained from other methods such as simplified LS, as described by Bai et al. (Reference Bai, Kealy, Retscher and Holden2020). The initial pair of $x_G^0\textrm{ and }y_G^0$ values can be assigned to ${x_0}\textrm{ and }{y_0}$ during the first round of iteration for a particular end user's location.

Based on Equation (8), we define

\[\textrm{d}X = \left[ {\begin{array}{@{}c@{}} {\Delta x}\\ {\Delta y} \end{array}} \right];\;B = \left[ {\begin{array}{@{}cc@{}} {{x_G} - x_G^0}& {{y_G} - y_G^0}\\ {\begin{array}{@{}cc@{}} {\dfrac{{{x_{W\!1}} - {x_0}}}{{d_{W\!1}^0}}}\\ {\begin{array}{@{}c@{}} \vdots \\ {\dfrac{{{x_{wn}} - {x_0}}}{{d_{W\!n}^0}}} \end{array}} \end{array}}& {\begin{array}{@{}c@{}} {\dfrac{{{y_{W\!1}} - {y_0}}}{{d_{W\!1}^0}}}\\ {\begin{array}{@{}c@{}} \vdots \\ {\dfrac{{{y_{wn}} - {y_0}}}{{d_{W\!n}^0}}} \end{array}} \end{array}} \end{array}} \right];\;L = \left[ {\begin{array}{@{}c@{}} {\begin{array}{@{}c@{}} {{d_G} - d_G^0}\\ {{d_{W\!1}} - d_{W\!1}^0} \end{array}}\\ \vdots \\ {{d_{wn}} - d_{wn}^0} \end{array}} \right]\]

The vector $\textrm{d}X$ can be estimated using the LS method through Equation (9):

(9)\begin{equation}dX = {({B^T}B)^{ - 1}}{B^T}L\end{equation}

The final estimated end user's coordinates $(\hat{x},\hat{y})$ can then be obtained from Equation (10) when the iteration is not required:

(10)\begin{equation}\left\{ {\begin{array}{@{}c@{}} {\hat{x} = \; {x_0} + \; \Delta x}\\ {\hat{y} = \; {y_0} + \; \Delta y} \end{array}} \right.\end{equation}

2.5 Hybrid indoor and outdoor detection approach

As mentioned previously, successful IOD is critical for seamless smartphone-based positioning systems. This section proposes and describes an HIOD approach, which includes a combined use of Wi-Fi RSSI, Wi-Fi RTT-based range measurements, number of connected APs and number of interconnected satellites, as well as the SNR measurements and some valuable ideas from fingerprinting and machine learning. The hybrid approach includes three main rules ordered according to their reliability and effectiveness. The ultimate goal for all these rules is to find whether the smartphone user is located indoors or outdoors by evaluating the following:

• • Rule 1 – evaluating Wi-Fi-based ranges and RSSI values;

• • Rule 2 – evaluating the number of connected satellites and their SNR values;

• • Rule 3 – evaluating the number of connected APs, the numbers of available satellites and their corresponding SNR values, and comparing the current machine learning model (CML) and the latest machine-learning pattern (MLP).

Each of the rules has its own emphasis, and they are processed orderly during the IOD process. Rule 1 is the most straightforward rule, and it is processed first, followed by Rule 2, then Rule 3 (see Figure 3). Three critical parameters in the HIOD model need to be determined for successful IOD. One is a valid AP selection criterion, and the other two are the threshold values of SNR_I and SNR_O. Other parameters received from the end user's smartphone are also used during the IOD process, such as:

• • the estimated Wi-Fi ranges, RSSI values and AP IDs from all connected APs, including the data received from those FTM-unsupported APs, which can be used for updating the MLP;

• • the SNR values and IDs of all connected satellites;

• • the number of connected APs and satellites (only GPS considered in this research).

A value of −71 dB is selected to be the RSSI threshold (RSS_T) for validating an AP as referred in (Bai, Reference Bai2016). The MLP database is updated each time after Rule 1 or Rule 2 is processed. Previous research has also considered using the combination of SNR and elevation (i.e., SNR_Ele) values as an IOD criterion (Okamoto and Chen, Reference Okamoto and Chen2015). In this research, the elevation was not selected for the following reasons:

• • the orders of the SNR values and elevation values are not perfectly matched, and this leads to three confusing SNR, elevation and SNR*Elevation options for satellite selection;

• • generally, a satellite with a higher elevation value also has a higher SNR value, although exceptional cases exist sometimes. Therefore, the SNR values already reflect the characteristics of signals from different satellite elevations;

• • higher computational efficiency due to the reduced complexity with the usage of SNR only.

These scenarios are explained through the three testing results listed in Table 1, where the orders for SNR, Elevation and SNR*Elevation are not exactly matched.

Figure 3. Principle of the HIOD approach

Table 1. Examples of the SNR values and their corresponding elevation values

Thus, only SNR is selected for the HIOD model. Figure 4 shows an example of the SNR values received by a smartphone, where nine satellites are detected and one SNR value per second is recorded for each satellite. Seven SNR curves are stable and have higher average values (the average SNR values are between 25 and 40 dB), whereas the other two are unstable and have lower average values (the average SNR values are between 21 and 25 dB). The testing results in Figure 4 match the real testing condition, where two satellites are partly blocked by the surrounding buildings; meanwhile, the top seven SNR curves demonstrate a smooth and stable trend even in a short period. These characteristics make the SNR values attractive for end-user's IO detection.

Figure 4. An example of SNR values received by a smartphone (approximately one-minute data collection period with nine satellites connected)

As presented in Figure 3, a unique code for each type of detection path is necessary to represent a specific IOD result. The format of the unique code pattern is R#*_I/O, where ‘R’ represents ‘Rule’; ‘#’ represents rule number; ‘*’ represents a subtype of a particular rule; ‘I’ means ‘indoor result’ and ‘O’ means ‘outdoor result’. Furthermore, two SNR threshold parameters (i.e., SNR_I and SNR_O) for IOD have been designated rather than one SNR threshold. One reason for defining two thresholds is that it is challenging for a single threshold parameter for successful IOD operation in semi-outdoor and semi-indoor environments (Gao and Groves, Reference Gao and Groves2018; Zhu et al., Reference Zhu, Luo, Wang, Zhao, Ning, Ke and Zhang2019). Also, two SNR thresholds allow identification and removal of ambiguous cases and better clarify the whole IOD process. Another reason is to improve the detection rate. Two levels of thresholds practically provide more robust IOD results by using SNR_I as the ‘indoor threshold’ and SNR_O as the ‘outdoor threshold’. Based on the above clarification, a core issue for the success of the HIOD approach is how to determine appropriate SNR_I and SNR_O values. As a novel approach and without sufficient evidence for proving and assigning a specific value to each threshold, it was decided to obtain the SNR_I and SNR_O values through a range of empirical tests (introduced in Section III).

The main principle of the MLP model is derived from pattern recognition. A number of MLP elements are stored in the database and updated continuously during the HIOD process. A comparative analysis is undertaken when an unknown IO case occurs. Each MLP element includes a set of features extracted from the previous IOD process (see Figure 5). The following prerequisite conditions are applied for the feature of MLP element selection:

1. 1) threshold – RSSI value $\ge - 81\; \textrm{dBm}$ (Bai, Reference Bai2016);

2. 2) a maximum of six RTT-supported APs and six other normal AP's are collected. The range value is the selection criteria for RTT-supported APs, and the RSSI value is the criteria for normal APs.

Figure 5. Key components of an MLP element

4.1 Experimental IOD test

An experimental test was designated to examine the HIOD approach. The test site was selected from more than six different candidates of venues. The final test site was set up in the roof garden of Building 10, at the city campus of RMIT University, not typical but belonging to a mixed area of both semi-indoor and semi-outdoor. The test site is surrounded by tall buildings on three sides and also contains furniture and parterres here and there. The outdoor garden is under a semi-outdoor condition with parterres, benches and coffee tables. There is also an indoor room connected to the outdoor garden through a corridor. In Figure 8, T1, T2, … T10 represent the ten outdoor TPs, and P1, P2, … P10 represent the ten indoor TPs. The major hardware devices used were six CompuLab WILD routers and a Pixel 3 smartphone. The duration of data collected at each TP was approximately 1 min using an Android-based APP developed in-house. All the APs and the smartphone were placed at a vertical distance of 1⋅72 m above the ground with known X and Y coordinates for each TP. The AP1, 2 and 3 were placed outdoors, and AP 4, 5 and 6 were mounted indoors. Referring to Figure 8, all TPs were located in a semi-outdoor space; T1 through T7 were under a more complex environment, and T2 and T3 were in the worst outdoor condition for signal transmission. P3, P4, P5 and P6 can be considered to be in an indoor space, and the other indoor TPs were all in a semi-indoor space. Among those indoor TPs, as P1 and P7 were located very close to the open entrances, they were considered the hardest points for IO detection.

Figure 8. Sitemap of the test site and indoor and outdoor TPs

The SNR and Wi-Fi-based measurement results are summarised in Tables 5 and 6, respectively. For the indoor TPs, the user's IO locations at P01, 03, 04, 06, 07, 08 and 10 were recognised by Rule 1, and at P02, 05 and 09 were recognised by Rule 2; for the outdoor TPs, the user's IO locations at T01, 04–09 were recognised by Rule 2, and at T02 and T03 were recognised by Rule 3, the IO location at T10 was recognised by Rule 1. All IO detection results from the 20 TPs are shown in Table 7, and the correct detection rate was 100%.

Table 5. SNR measurement results received from the 20 TPs

Table 6. Measurement results of the estimated distances and RSSI values from the 20 TPs

Table 7. The final test results from HIOD