A smart city used low-latency seamless positioning system based on inverse global navigation satellite system technology

Abstract

People have to move between indoor and outdoor frequently in city scenarios. The global navigation satellite system signal cannot provide reliable indoor positioning services. To solve the problem, this article proposes a seamless positioning system based on an inverse global navigation satellite system signal, which can extend the global navigation satellite system service into the indoor scenario. In this method, a signal source is arranged at a key position in the room, and the inverse global navigation satellite system signal is transmitted to the global navigation satellite system receiver to obtain a preset positioning result. The indoor positioning service is continued with the inertial navigation system after leaving the key position. The inverse global navigation satellite system seamless positioning system proposed in this article can unify indoor and outdoor positioning using the same receiver. The receiver does not need to re-receive navigation information when the scene changes, which avoids the switching process. Through the design of signal layer coverage, the receiver is in a warm start state, and the users can quickly fix the position when the scenario changes, realizing quick access in a true sense. This enables the ordinary commercial global navigation satellite system receiver to obtain indoor positioning capability without modification, and the algorithm can perform accurate positioning indoors and outdoors without switching.

Keywords

Global navigation satellite system indoor positioning low latency seamless positioning

Introduction

Global navigation satellite system (GNSS) signals are commonly used for outdoor positioning.¹ GNSS achieves accurate navigation and positioning when four or more satellites are visible.^2–4 In the field of open outdoor positioning, GNSS-based location services have been widely used in various applications, that is, in economic development, social development, and national security.^5–8

However, when GNSS signals are applied to city and indoor positioning,^9,10 the available GNSS satellite signals are severely occluded or even completely ineffective due to the closed or semi-enclosed indoor environment.¹¹ GNSS positioning cannot work smoothly, which seriously hinders the expansion and application of GNSS signals in indoor positioning.¹² Nowadays, the demand for indoor positioning has become increasingly prominent,^13–16 and people stay in indoor environments the most where they often cannot receive GNSS signals. Therefore, providing seamless positioning services connecting indoor and outdoor environments has become a critical issue. There are many indoor positioning technologies, such as integrated navigation,¹⁷ ultra wideband (UWB) positioning,^18–20 assisted global navigation satellite system (AGNSS),^21,22 high-sensitivity GNSS,²³ and WIFI positioning,^24–27 but these positioning methods all have their limitations.^28,29 AGNSS and high-sensitivity GNSS technology are extremely complex, and they can only solve the positioning problem of “shallow indoor environment”; some researches use pseudolites to provide indoor time of arrival (TOA) positioning, but they are still limited by non-line-of-sight (NLOS) and multi-path problems. Radio frequency identification (RFID) positioning^30,31 technologies use tags to identify users, while multiple card readers are needed in indoor scenarios. From commercial perspective, such a complex structure with multiple card readers costs too much. The UWB-based positioning system in theory has good positioning accuracy, but the frequency domain characteristics of the signal interfere with the surrounding wireless communication equipment, limiting its application.

Furthermore, its application also requires users to purchase UWB positioning receivers. Fingerprint positioning technologies, such as WIFI positioning and Bluetooth positioning,^32,33 have limitations including low accuracy and incompatibility with GNSS signals.

So far, there are two major ways to achieve seamless positioning. One is to propose a new positioning mechanism that can be used in both indoor and outdoor environments, and the other is to combine different indoor and outdoor positioning technologies through switching algorithms.^34–37 However, due to the significant difference between indoor and outdoor channel conditions, the former one always has relatively low positioning accuracy. The latter one requires users to equip different receivers for multiple systems, and in reality, it is difficult to achieve a smooth handover. Thus, it is challenging to find a positioning method, which performs well in both open areas and complex environments connecting both indoor and outdoor systems. Moreover, new positioning systems also require users to update their receivers. Considering the number of commercial users, such an update process is prohibitively costly, both for users and operators. A compromise is to use the outdoor positioning system signal in the indoor environment but extend it through various means. Thus, a GNSS receiver, such as in the indoor messaging system (IMES) system,^38–40 the early LOCATA system, and the GNSS fingerprint positioning system, could be used both in the indoor and outdoor environment. However, each of them has shortcomings: the IMES system^41,42 and the LOCATA system cannot guarantee the consistency of the positioning algorithm with the outdoor GNSS, and their pseudo-noise (PN) code and navigation data are different from GNSS; GNSS fingerprint positioning^43–45 has a large workload. For example, in IMES, the positioning algorithm of GNSS fingerprint positioning is different from GNSS. None of them, in reality, can achieve real seamless positioning.

According to the abovementioned situation, this article proposes a new indoor positioning method based on simulated GNSS signals that use traditional GNSS signals in indoor positioning. Unlike the traditional pseudo-satellite method, this method integrates the signals from multiple satellites on the same transmission antenna to avoid the complicated synchronization problem. Similar to the IMES system, the proposed system also provides position correction at discrete points, but unlike the IMES system, the system does not need to redesign the navigation signal nor need to change the positioning calculation method. The system deceives the GNSS receiver by arranging the inverse GNSS sources and transmitting the inversely derived GNSS signal. This technology is used to provide calibration for the inertial navigation system (INS)/magnetometer⁴⁶ which is commonly equipped in smartphones and provides continuous positioning.⁴⁷ The subsequent structure of this article is organized as follows: section “Overview” gives a general introduction to the inverse GNSS positioning method and briefly describes the positioning process and the composition of the system. Section “Signal design” describes the design of the signal layer of the system. Section “RF design” analyzes system requirements for radio frequency (RF) equipment. Section “Low-latency design” introduces the system’s quick access design. Section “Performance analysis” is an analysis and verification of system functions. Sections “Methods/experiments” and “Results and discussion” introduce the methods and the results, respectively. Section “Conclusion” gives the conclusion.

Overview

Working principle of inverse GNSS

In inverse GNSS technology, some GNSS signal sources are deployed in the building to provide positioning services at certain calibration points. The track of the user would be calibrated by GNSS service when the user passes a calibration point. When the user is away from the calibration point, the positioning service would be maintained by INS equipment until the user arrives at another calibration point. The positioning process of inverse GNSS is shown in Figure 1.

Figure 1.

The positioning process of inverse GNSS: GNSS service is available only near the calibration point, and the INS is used to maintain the positioning continuously.

Due to the complex structures of indoor environments, users often pass “position limited” locations like doors, corners, elevators, workstations, and restrooms. When users pass through a “position limited” location or use “position limited” related equipment, the position of the user is fixed, which turns the “position limited” location into a calibration point, denoted as $R$ . The absolute position of $R$ can be determined by the geo-spatial mapping method, denoted as $(X_{R}, Y_{R}, Z_{R})$ . A signal source, which is placed on the roof directly above the calibration point, is the inverse GNSS signal source. The inverse GNSS signal source uses a directional antenna with a very narrow beam. Thus, the signal coverage could be fixed within a small range near the calibration point $R$ . The signal source simultaneously simulates and broadcasts the signals of multiple GNSS satellites. By reasonably arranging the time delay relationship between the virtual satellite signals, the receiver can be deceived as working in an open environment, as shown in Figure 2, and the positioning result is at the calibration point $(X_{R}, Y_{R}, Z_{R})$ . Thus, the positioning equation of the calibration point is illustrated in equation (1)

\sqrt{{(X_{R} - X_{s'}^{(i)})}^{2} + {(Y_{R} - Y_{s'}^{(i)})}^{2} + {(Z_{R} - Z_{s'}^{(i)})}^{2}} = r'_{i}

(1)

where $X_{s'}^{(i)}$ , $Y_{s'}^{(i)}$ , and $Z_{s'}^{(i)}$ represent the location of the virtual satellite; $r'_{i}$ represents the virtual distance between the virtual satellite and the receiver.

Figure 2.

The deceive phenomenon of GNSS receiver: $S_{i}$ represents the information of real satellites, such as ephemeris information and various correction parameters, and $S'$ represents the corresponding information of the virtual satellites.

When a user passes by the calibration point, the receiver would calculate the preset position according to the virtual satellite signal located at the calibration point. The signal beam is tiny, which makes the localization service only available in a small area. Therefore, the receiver works only if the user remains in this “limited space,” which ensures the calculation result is accurate. In this technology, inertial navigation technology and mapping methods are needed as an aid. Since both of them are mature technologies, they are not analyzed in this article.

System components

To achieve the above positioning functions, the signal needs to be specially designed on both the signal layer and the information layer to maintain versatility with the GNSS system while ensuring the positioning capability. Therefore, the system should consist of the following parts.

RF par

Since each inverse GNSS signal source simulates a virtual signal according to the corresponding calibration point position, the GNSS receiver must be located at the calibration point when the signal is available. Therefore, the system needs to ensure that the user gets the location service only at the calibration point. This requires that each source must be equipped with a directional antenna that has excellent directivity. This limits the range of broadcast and prevents affecting other users.

The system will not make any modifications to existing receivers. Therefore, within the signal coverage of the correction point, the strength of the inverse GNSS signal should also be similar to that of the outdoor GNSS system, thus ensuring reliable operation of the receiver.

Inverse GNSS signal generator

To ensure the compatibility of the receiver, the signals generated by the inverse GNSS nodes must conform to the interface control document (ICD) of the GNSS. Moreover, the positioning result must be the preset position of the calibration point. It can be seen that a signal-generating device capable of performing the complex operation is necessary. In addition, to ensure a continuous positioning, navigation, and timing (PNT) service between indoor and outdoor scenes, the signal generation process of the inverse GNSS system should be based on real-time GNSS satellite constellation conditions and GNSS time.

GNSS signal monitor

To obtain the abovementioned real-time GNSS satellite constellation situation and GNSS time, the inverse GNSS positioning system needs a GNSS receiver to monitor the satellite operation in real time. The monitoring receiver can be equipped with each building, or each block, or can be achieved virtually by interconnecting with the GNSS augmentation system and downloading the corresponding information.

Signal design

Signal delay setting

Like GNSS, this proposed inverse GNSS is also a TOA system; the delay setting of each virtual satellite signal becomes the key point of the system design. Moreover, the unsynchronized problem also exists in inverse GNSS technology; the pseudorange of the corresponding satellite (equation (2)) can be written as

\begin{matrix} \sqrt{{(X_{u} - X_{s}^{(i)})}^{2} + {(Y_{u} - Y_{s}^{(i)})}^{2} + {(Z_{u} - Z_{s}^{(i)})}^{2}} \\ + δ t_{u} \times c = ρ_{c}^{(i)} \end{matrix}

(2)

where $δ t_{u}$ is the receiver clock bias, $c$ is the speed of light, and $ρ_{c}^{(i)}$ is the pseudorange of the corresponding satellite. $ρ_{c}^{(i)}$ is calculated based on the receiver local time $t_{u}$ and the satellite signal transmission time $t_{s}^{(i)}$ , as shown in equation (3)

ρ_{c}^{(i)} = c \times (t_{u} - t_{s})

(3)

Considering the existence of various errors in the signal propagation path, the satellite pseudorange needs to be corrected according to the corresponding information, including satellite clock error, ionospheric delay correction $I$ , and tropospheric delay correction $T$ . Accordingly, the above formula is corrected to equation (4)

ρ_{c}^{(i)} = c \times (t_{u} - t_{s}) + δ t \times c - I - T

(4)

$t_{s}$ is not directly demodulated from the information, but is assembled by the time relationship between the chip currently received and the time of week (TOW). Take the global positioning system (GPS) as an example

\begin{matrix} t_{s} = T_{TOW} + (30 w + b) \times 0.02 + (C_{c} + \frac{C_{CP}}{1023}) \\ \times 0.001 \end{matrix}

(5)

In equation (5), $w$ and $b$ represent the number of navigation words and the number of bits received after the arrival of the previous $T_{TOW}$ , respectively, and the values are between 0–9 and 0–29, respectively. $C_{C}$ and $C_{CP}$ represent the number of pseudo-noise (PN) code periods and the code phase in the current period, respectively, after the arrival of the previous bit, and the values are between 0–19 and 0–1022, respectively. Bringing the equations (3)–(5) into equation (2), the following relationship can be obtained

\begin{matrix} T_{TOW} + (30 w + b) \times 0.02 + (C_{C} + \frac{C_{CP}}{1023}) \times 0.001 \\ = δ t_{s}^{(i)} + t_{u} - δ t_{u} - \frac{I + T + \sqrt{{(X_{u} - X_{s}^{(i)})}^{2} + {(Y_{u} - Y_{s}^{(i)})}^{2} + {(Z_{u} - Z_{s}^{(i)})}^{2}}}{c} \end{matrix}

(6)

For the inverse GNSS technique, the receiver positioning result can be fixed, and the position of the virtual satellite can be calculated by the signal transmission time $t_{s}$ , so they are all known characters. Atmospheric correction parameters and satellite clock differences have been given in the navigation message and are also considered known. In order to balance the timing function of the GNSS system, the inverse GNSS signal source should make the receiver positioning equations obtain the correct time information, and this time information can also be obtained through the monitoring receiver, so it is regarded as the known GPS time $t$ . In addition, the receiver clock is not desirable; it should be 0. The evolution in inverse GNSS technology is shown in equation (6)

\begin{matrix} T_{TOW} (t) + (30 w (t) + b (t)) \times 0.02 + (C_{C} (t) + \frac{C_{CP} (t)}{1023}) \times 0.001 \\ = δ t_{s}^{(i)} (t_{s}) + t - \frac{I (t_{s}) + T (t_{s}) + \sqrt{{(X_{R} - X_{s'}^{(i)} (t_{s}))}^{2} + {(Y_{R} - Y_{s'}^{(i)} (t_{s}))}^{2} + {(Z_{R} - Z_{s'}^{(i)} (t_{s}))}^{2}}}{c} \\ = t_{s} \end{matrix}

(7)

It can be seen from equation (7) that to determine the timing parameters, it is necessary to know the transmission time $t_{s}$ , and $t_{s}$ is a function of itself. The signal path is determined by the satellite position at the time of $t_{s}$ , while the $t_{s}$ can only be calculated when the navigation data are received. Therefore, this equation does not directly yield analytical solutions. The only method is to determine the parameters iteratively, which is done as follows.

First, splitting the equation into two parts, as shown in equations (8) and (9)

{r^{'}}_{i} (t_{s}) = \sqrt{{(X_{R} - X_{s^{'}}^{(i)} (t_{s}))}^{2} + {(Y_{R} - Y_{s^{'}}^{(i)} (t_{s}))}^{2} + {(Z_{R} - Z_{s^{'}}^{(i)} (t_{s}))}^{2}}

(8)

t_{s} = δ t_{s}^{(i)} (t_{s}) + t - \frac{I (t_{s}) + T (t_{s}) + {r'}_{i} (t_{s})}{c}

(9)

When the iterative process starts, as shown in equations (10) and (11)

r'_{i (0)} = r'_{i} (t)

(10)

t_{s (0)} = δ t_{s}^{(i)} (t) + t - \frac{I (t) + T (t) + {r'}_{i (0)}}{c}

(11)

The formula of each iteration step is shown in equations (12) and (13)

r'_{i (j)} = r'_{i} (t_{s (j - 1)})

(12)

t_{s (j)} = δ t_{s}^{(i)} (t_{s (j - 1)}) + t - \frac{I (t_{s (j - 1)}) + T (t_{s (j - 1)}) + {r'}_{i (j - 1)}}{c}

(13)

Iteration stops when formula equation (14) is satisfied

| {r'}_{i (j)} - {r'}_{i (j - 1)} | < ε

(14)

where $ε$ is the expected accuracy, usually $10^{- 10}$ .

After determining the signal transmission time by the above method, equation (7) can be used to determine the time of week $T_{TOW}$ , number of words, number of bits $b$ , number of PN code periods $C_{C}$ , and code phase $C_{CP}$ , corresponding to the currently transmitted signal

T_{TOW} (t) = ⌊ t_{s} ⌋

(15)

w (t) = ⌊ \frac{t_{s} - T_{TOW} (t)}{0.6} ⌋

(16)

b (t) = ⌊ \frac{t_{s} - T_{TOW} (t) - 0.6 w (t)}{0.02} ⌋

(17)

C_{C} (t) = ⌊ \frac{t_{s} - T_{TOW} (t) - 0.6 w (t) - 0.02 b (t)}{0.001} ⌋

(18)

\begin{matrix} C_{CP} (t) = ⌊ 1, 023, 000 (t_{s} - T_{TOW} (t) - 0.6 w (t) \\ - 0.02 b (t) - 0.001 C_{C} (t)) ⌋ \end{matrix}

(19)

The timing of the baseband signal can be obtained by the rounding operation of equations (15)–(19), and the remaining numbers can be used to determine the current carrier phase $R_{F}$ , as shown in equation (20)

R_{F} (t) = \cos (f_{c} (t_{s} - T_{TOW} (t) - 0.6 w (t) - 0.02 b (t) - 0.001 C_{C} (t) - \frac{C_{CP} (t)}{1, 023, 000}))

(20)

where $f_{c}$ is the carrier frequency, which is 1.57542 GHz in the L1 signal of the GPS system and the E1 signal of the Galileo system. In other widely used GNSS systems, such as the B1 signal of the BeiDou system, the value is 1561.098 MHz. In addition, binary offset carrier (BOC) modulation is needed in the Galileo system, and the N-H code is required in the BeiDou system. For most receivers, carrier phase information is not used for positioning, but for special receivers, the carrier phase information is used to enhance the positioning accuracy.

Frequency correction

In order to reproduce the satellite signal more perfectly, the Doppler shift also needs to be corrected. Since the influence of Doppler shift on the carrier and baseband signals is the same, changing the oscillator frequency of the system is the most efficient way to achieve frequency correction, in terms of both system complexity and effectiveness. Because the inverse GNSS signal source simulates the signal that was received by a stationary receiver, the Doppler shift is completely caused by satellite motion, as shown in Figure 3.

Figure 3.

The Doppler effect of GNSS signal: the Doppler frequency caused by the movement of the satellite should be calibrated.

The speed of the satellite is v, and the Doppler phenomenon is caused by its component $v_{d}$ , which is the velocity toward the user direction. The satellite speed can be calculated by satellite ephemeris, but it is computationally intensive. In the inverse GNSS technique, since the real-time position of the satellite is known, the system can obtain the motion velocity vector v of the satellite by means of differentiation, as shown in equation (21)

v = \frac{(X_{s'}^{(i)} (t_{s} + Δ t) - X_{s'}^{(i)} (t_{s}), Y_{s'}^{(i)} (t_{s} + Δ t) - Y_{s'}^{(i)} (t_{s}), Z_{s'}^{(i)} (t_{s} + Δ t) - Z_{s'}^{(i)} (t_{s}))}{Δ t}

(21)

In the formula, $Δ t$ is an extremely short period of time, such as the sample period. Since this time is extremely short, the movement of the satellite can be regarded as along the orbital tangent. The component $v_{d}$ can be derived from the inner product of the velocity v and the satellite-to-user vector, as shown in equation (22)

v_{d} = v • ((X_{s^{'}}^{(i)} (t_{s}) - X_{R}), (Y_{s^{'}}^{(i)} (t_{s}) - Y_{R}), (Z_{s^{'}}^{(i)} (t_{s}) - Z_{R}))

(22)

Then, the oscillator frequency correction should be carried out according to the following equation (23)

O'_{clock} = O_{clock} \times (1 + \frac{v_{d}}{c})

(23)

The $O'_{clock}$ in the equation is the corrected clock frequency, and the $O_{clock}$ is the nominal oscillator frequency.

Processing delay correction

In addition to the frequency Doppler phenomenon, the system delay $t_{delay}$ is also a correction that needs to be considered. Processing delay happens during data processing, signal generation, and signal transmission. To correct these delays, the system time needs to be adjusted.

The solution equation for the GNSS receiver is shown in equation (24). Considering the existence of the system delay, the signal will arrive at the receiver $t_{delay}$ later than expected, so the equation should be rewritten as

\begin{matrix} \sqrt{{(X_{u} - X_{s}^{(i)})}^{2} + {(Y_{u} - Y_{s}^{(i)})}^{2} + {(Z_{u} - Z_{s}^{(i)})}^{2}} \\ + δ t_{u} \times c = ρ_{c}^{(i)} + t_{delay} \times c \end{matrix}

(24)

It can be seen from the equation that for the same inverse GNSS source, the newly added delay term $t_{delay}$ is the same for any satellite, and it can be combined with clock deviation $δ t_{u}$ . It can be found that this delay does not affect the positioning accuracy of the system but changes the timing accuracy of the system. Therefore, in the system design, it should be compensated in advance, and the receiving time $t$ is compensated to $t - t_{delay}$ in the calculation process. $t_{delay}$ includes two parts: transmission delay and processing delay. Transmission delay is caused by the distance between the transmission cable and the antenna, and it can be obtained or estimated by measurement. Because the speed of light is extremely fast, this part can be ignored. Processing delay is uncertain and depends on the processing complexity. To solve abovementioned problem, the system could wait a number of clock cycles before signal transmitting, leaving enough time for processing, thereby simplifying operations and avoiding the problem.

RF design

To improve the accuracy of the system and limit the available service area to a tiny square just below the inverse GNSS source, the transmit power of the GNSS signal source should be low and the directional antenna should be used with a very narrow beam. Furthermore, the placement direction of the antenna should theoretically maximize the antenna gain in the downward direction, that is, the main lobe antenna is downward and $G (0) = G_{\max}$ . Within the preset positioning range, the strength of the inverse GNSS signal is strong enough for the receiver, but outside the preset positioning range, the user’s GNSS receiver could not receive an effective inverse GNSS signal. Figure 4 serves as an example calibration point.

Figure 4.

Indoor calibration point receives signals: the height of the doorframe is $h$ ; the height of the user receiver is $h'$ ; the preset location area range of indoor nodes is a circle with radius $r$ .

The size of $h$ can be measured. And the size of $h'$ can be estimated according to the height of the human hand-held GNSS receiver. The maximum error of location will be $r$ , and the size of $r$ can be set manually in advance. Thus, it can be obtained that the angle between the GNSS signal source of the calibration point and the edge of the localizable area is shown in equation (25)

θ = \arctan (\frac{r}{h - h'})

(25)

To receive the inverse GNSS signal within the positioning area, signal strength must be greater than the sensitivity of the receiver. Outside this positioning area, the signal strength must be too low for the receiver. Therefore, the gain of the antenna should be large in the range of 0–θ angle and as small as possible outside this range. Therefore, the gain of the antenna suitable for this system should be changed at the angle $θ$ , that is, the derivative of $G$ should be as large as possible at the direction of $θ$ . The above is the basic condition for judging whether an antenna is suitable for an inverse GNSS indoor system.

We also need to consider the automatic gain control (AGC) of the receiver. In general, the AGC gain $Δ G$ of GNSS receivers is about 30 dB. Since this system does not require any improvement to the user’s commercial GNSS receiver, the strength of the inverse GNSS signal sent by the indoor node is the same as that of the conventional GNSS signal, which is −127 dBm. Therefore, according to the inverse GNSS signal strength received by the receiver directly below the node, equation (26) can be obtained

P_{0} + G_{\max} - P_{l} (0) \leq - 127 dBm + Δ G

(26)

In equation (26), $P_{0}$ is the input power of the antenna, $G_{\max}$ is the maximum gain of the antenna, that is, the antenna gain directly below the node, and $P_{l} (0)$ is the path loss when the receiver is directly below the signal source.

Low-latency design

Even if the inverse GNSS signal is designed according to the outdoor satellite signal, the GNSS signal changes when the user exits or enters a building, which leads to large positioning delays. Similarly, when the user moves indoors, the signal will only be available for a short time when passing through the calibration point, which is insufficient to complete GNSS positioning. These are the two main problems of the information layer in the inverse GNSS technology.

The problem of signal discontinuity that happens when entering or leaving a building can actually be regarded as a switching problem. To connect the indoor and outdoor positioning services, the navigation messages broadcast by indoor and outdoor signal sources should be as consistent as possible. For the inverse GNSS technology, the information transmitted by the space segment of the GNSS system is determined by the injection station. If the navigation information is changed, it is not only costly for the satellites but also needs to change the conventional receivers, which losses the advantages of inverse GNSS technology. Therefore, the signal advertised by the inverse GNSS source must be designed to be consistent with the current satellite signal in terms of ephemeris, almanac, correction parameters, and reliability parameters. The above information can be obtained by means of the monitoring receiver or downloaded from the network.

The startup mode of the receiver is divided into cold startup, warm startup, hot startup, and the “lost lock–reacquisition” process, which is much faster. The positioning speed, that is, the time to first fix (TTFF), is shown as follows:

Cold startup. No prior information is available. TTFF is 60 s all so.

Warm startup. No valid ephemeris, but the current time error is less than 5 min, the position error is less than 100 km, effective almanac. TTFF is 45 s all so.

Hot startup. A valid ephemeris is available under warm start conditions. TTFF is less than 12 s.

Lost lock–reacquisition. Enough prior information for the three-dimensional search of the acquisition process and the signal channel is still effective. TTFF is only a few seconds.

It can be seen that to enable the receiver to locate within just a few seconds when passing the small area below the inverted GNSS calibration point, it is necessary to keep the receiver in the state of “lost lock–reacquisition” process at all times.

To ensure the above conditions, a widely covered signal can be introduced into the system, called “maintaining signal,” as shown in Figure 5. This signal only broadcasts the data of three or fewer satellites to keep the receiver operating but cannot get fixed. This enables immediate access when the user is changing scenarios.

Figure 5.

The maintaining signal: the green fans indicate the maintaining signal, and the red ones stand for the positioning signal. Only a set of signal sources are broadcasting the maintaining signal and the positioning, while the rest sources only send positioning signal.

Performance analysis

Positioning accuracy analysis in antenna matching scenario

This analysis will use a door as the calibration point. The calibration point is considered as the coordinate origin. When the antenna satisfies the ideal condition, mentioned in section “RF design,” the preset calibration domain is a circular area with a radius $r$ , that is, the maximum positioning error is limited by $r$ .

Assume that the user tends to walk through the door in the middle at a constant speed and the position refresh rate of the GNSS receiver is fixed, then it can be approximated that the abscissa $x$ of the user position obeys the normal distribution $N$ (0, $δ$ ), and the user’s ordinate $y$ is uniformly distributed, as shown in Figure 6.

Figure 6.

The positioning samples in the service area in antenna matching scenario: the colored dots indicate the position sample of the users, and different colors correspond to different users.

Then, the cumulative distribution function (CDF) of the positioning error s can be calculated by equation (27)

\begin{matrix} P (\sqrt{x^{2} + y^{2}} \leq s) = \int_{- s}^{s} \frac{1}{\sqrt{2 π} σ} e^{- \frac{x^{2}}{2 σ^{2}}} dx \\ \int_{- \sqrt{s^{2} - x^{2}}}^{\sqrt{s^{2} - x^{2}}} \frac{1}{2 \sqrt{r^{2} - y^{2}}} dy \end{matrix}

(27)

Positioning accuracy analysis in antenna mismatching scenario

When the antenna is over directional or the input power of the antenna is too large, the antenna cannot satisfy equation (26). The received signal strength near the positioning center exceeds the AGC range of the receiver. Therefore, the locatable area turns to be an annular, as shown in Figure 7. Assume the positioning area is a ring with the inner circle radius $r_{n}$ and outer radius $r$ .

Figure 7.

The positioning samples in the service area in antenna mismatching scenario: the colored dots indicate the position sample of the users, and different colors correspond to different users.

Then, the CDF of the positioning error $s$ of the user can be calculated, as shown in equation (28)

\begin{matrix} P (\sqrt{x^{2} + y^{2}} \leq s) = 4 \int_{0}^{r_{n}} \frac{1}{\sqrt{2 π} σ} e^{- \frac{x^{2}}{2 σ^{2}}} dx \int_{- \sqrt{r_{n}^{2} - x^{2}}}^{\sqrt{s^{2} - x^{2}}} \frac{1}{2 \sqrt{r^{2} - y^{2}}} dy \\ + 2 \int_{r_{n}}^{s} \frac{1}{\sqrt{2 π} σ} e^{- \frac{x^{2}}{2 σ^{2}}} dx \int_{- \sqrt{s^{2} - x^{2}}}^{\sqrt{s^{2} - x^{2}}} \frac{1}{2 \sqrt{r^{2} - y^{2}}} dy \end{matrix}

(28)

Methods/experiments

To verify the effectiveness of the system, an accuracy simulation is provided. In the stationary positioning simulation, the GNSS signal source used in the simulation is generated by a GPS L1 signal simulator provided by Beijing Epoo Technology Company (bj-epoo). The GNSS software receiver given in Tsui⁴⁸ is used. The IF frequency and sampling rate of the signal are 1.405 MHz and 5.714 Msps, respectively. The $C / N_{0}$ is 45 dB-Hz. The user is located at the calibration point. In the simulation, a set of neighbor positioning samples are combined as a cluster; the mean value of the cluster is calculated as the final location, in order to enhance the positioning accuracy.

In terms of coverage simulation, the scenario is generated by MATLAB, as shown in Figure 8. The COST231 propagation model was used in the simulation. Six rooms are symmetrically distributed on both sides, and the six signal sources are distributed in the middle of the six doorframes.

Figure 8.

Room layout and signal source distribution: in this model, each room is set to 6 m long and 4 m wide, the corridor is 4 m wide, the door is 1.5 m wide and 2 m high, and the height of the GNSS receiver carried by the user is 1 m.

The positioning accuracy of the positioning system is directly related to the signal coverage, and the signal coverage depends on the signal transmission power and the antenna pattern. The pattern of the antenna used in the simulation is shown in Figure 9.

Figure 9.

Antenna pattern: the gain of the antenna is up to 4.391 dB in the direction of latitude $θ = 105^{°}$ and longitude $φ = 165^{°}$ . In the direction of latitude $θ = 75^{°}$ and longitude $φ = 340^{°}$ , the antenna gain gets its minimum of −12.04 dB.

It can be seen from Figure 9 that the antenna has strong directivity. The gain difference satisfies the automatic gain control range of most of the receivers. Therefore, this antenna can be applied to the GNSS indoor positioning system. Combined with the antenna pattern and the COST231 model, the signal transmission power is −83 dBm.

Results and discussion

The results of the stationary positioning simulation are shown in Figure 10. The basically refresh rate of inverse GNSS is 1 kHz, like that of GNSS.

Figure 10.

The CDF of the stationary positioning simulation: the different colors of the lines indicate different refreshing rates of the system, which are determined by the cluster lengths.

It can be seen that as the sample number of each cluster increases, the variance value gradually decreases. When 1000 samples are included in one cluster, the refresh frequency is 1 Hz, and the positioning accuracy to 2 m level. This accuracy and speed are acceptable for indoor positioning. The results of signal coverage simulation are shown in Figure 11.

Figure 11.

Location service domains of each calibration point: each cell is 0.2 m × 0.2 m, and the signal intensity of the marked area is between −127 and −97 dBm.

It can be observed from the figure that the radius of the positioning area at each signal source is about 1 m, which is in accordance with the theoretically estimated value. In summary, the indoor positioning method adopted in this article satisfies the positioning requirements in the case of error in the experimental simulation. The positioning accuracy of this system reaches meters’ level, which is compatible with most of the fingerprint positioning systems.^49–52 In contrast, the accuracy of IMES, which is the most similar one with the proposed system, is about 5 m, as reported recently.⁵³

Such system is less accurate than UWB-based positioning systems or RFID-based positioning systems, but its compatibility with GNSS reduces the handover latency and archives seamless localization. For example, the ideal tag distance of RFID positioning system is [1.50–2.50] m,⁵⁴ and it costs a lot for aforementioned 12 m × 16 m room. And for UWB positioning, a complicate algorithm is needed to distinguish the NLOS signal.⁵⁵ Furthermore, for both UWB- and RFID-based systems, users need to buy a set of new receivers, which cost a lot. The inverse GNSS system proposed in this article is device compatible with classical commercial positioning end; ordinary smartphones can be used as the receivers of the system.

Conclusion

This article proposes a seamless positioning system based on inverse GNSS technology, which makes conventional GNSS receivers useful for both indoor and outdoor scenarios. This technology is easy to promote as user terminal is backward compatible. Because most of the navigation systems equip both GNSS and INS. The proposed scheme utilizes the complex structure of the building and inverse GNSS signals to provide calibration services for INS at special calibration points. The inverse GNSS signal transmitted by the system is consistent with the outdoor GNSS constellation signal at the physical layer and the information layer. Only the delay relationship is changed. This benefits the handover process of the receiver, ensures the low-latency ability of the system, and allows seamless positioning.

Footnotes

Acknowledgements

The authors thank Dr Di Yang, Dr Yihe Fan, and Mr Craig Noles who provided language assistance for this article.

Handling Editor: Xi Chen

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Natural Science Foundation of China (no. 61701072).

ORCID iD

Deyue Zou

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