Establishing the relative positions of objects is critical for various collaborative applications, including robot movement tracking, virtual/augmented reality (VR/AR), line following, and autonomous vehicles. Establishing the relative positioning between two objects is usually dependent on the deployment of fixed or mobile anchors based on Bluetooth [1], Wi-Fi [2], Global Positioning System (GPS) [3], or ultra-wideband (UWB) radio technology [4]. Most of the solutions applied in relative-position systems use range-measurement techniques. The most common range-measurement techniques are two-way ranging (TWR), time of arrival, time difference of arrival (TDOA), and angle of arrival (AOA). These range-measurement techniques use radiofrequency and acoustic signals to calculate the range between the two devices [5]. Range-measurement devices are especially appealing because they are often affordable, lightweight, computationally simple, and may be used in settings in which GPS is unavailable. This minimizes architecture and processing needs, allowing for the deployment of huge swarms of tiny, low-cost tracking devices in indoor or subterranean locations.

There are numerous existing approaches that seek to integrate range measurements into positioning systems. Most techniques for indoor localization have typically assumed the availability of an infrastructure consisting of four or more anchors with defined coordinates [6,7]. In [8], relative positioning was accomplished using a single anchor under the assumption of fixed motion; in other research, measurements of relative positioning have been accomplished using a range-based simultaneous localization and mapping (SLAM) technique. Other techniques use displacement data obtained from optical sensors, including infrared (IR) and visible-light communication (VLC) devices, to calculate the relative positioning of two objects. However, these methods do not provide a precise position, as IR methods suffer from interference from fluorescent light and sunlight [9], and VLC requires an environment with a clear line of sight (LOS) [10]. Moreover, the hardware and maintenance costs of these solutions are very high. Therefore, researchers have commonly opted for a radio-signal-based range-measurement approach for positioning due to the wide availability of inexpensive and lightweight sensors.

Most range-measurement techniques require constant relative movement between an anchor and an agent to acquire their relative positions [11–14]. Many studies have been conducted in robotics examining relative-location measurement using vision or laser-based sensors. These techniques are restricted in their use in complex scenarios due to field-of-view problems, sensor data association, and ambient illumination issues [14]. Other researchers have used radio signal strength (RSS) techniques with wireless devices through a variety of model-based or fingerprint-based solutions to estimate an object’s location. In contrast to the above-mentioned visual-based sensors, RSS may be used even when there is no LOS. However, the accuracy of RSS-based techniques may vary because radio propagation in an indoor environment can be affected by severe multipath and other site-specific characteristics, and fingerprinting methods require the dataset to be updated if the environment changes [15,16].

Recently, researchers have proposed UWB-based positioning systems that can provide very precise range measurements for both LOS and non-LOS (NLOS) environments. UWB-based positioning employs an approach using TWR to determine the range between two objects and can provide positioning precision within a few centimeters, yielding better results than RSS-based location-tracking methods. UWB-based range-measurement devices use two tags to calculate the relative positioning of objects, such as unmanned aerial vehicles (UAVs) [17] and autonomous vehicles [18].

Some researchers have proposed single range measurement methods to enable localization between two devices [19,20]. These single range measurement based methods involve initiating range measurement between a single anchor and a tag device and calculating the relative position using the acquired single range measurement information. However, such methods require continuous relative motion between two objects, and the relative position accuracy can deteriorate due to parallel motion [21]. Other studies have used three tags to calculate relative positions [22,23]. Both strategies retrieve two-dimensional data about the objects’ relative positions. Only a few studies have been conducted examining three-dimensional (3D) relative-positioning schemes using UWB and other complementary measurement units [24,25]. However, these solutions require the UWB anchors to be placed at fixed sites to enable real-time positioning, and massive installation of UWB anchors is costly and complicated.

Some researchers have proposed on-board UWB-based relative-position systems to solve the above-mentioned issue [26,27]. Although their solutions were found to achieve higher accuracy, they only considered mobile machinery in which the objects move slowly, and they did not consider standard-deviation mitigation in the range measurement, which is one of the main sources of error in UWB-based relative-position systems. Moreover, a UWB-based positioning system can only provide relative position information and not any attitude information, which is a very important factor in most collaborative tasks. An inertial navigation system (INS) can provide attitude information and compensate for positioning errors due to an NLOS environment. Inertial measurement units (IMUs) are generally used in INS-based solutions to provide positioning. However, the data from IMU sensors may be inaccurate due to the accumulation of errors; this must be mitigated or reduced by other sources, such as UWB, to enable precise positioning.

Therefore, a robust relative positioning system must be proposed by incorporating the UWB and IMU sensors to enable precise positioning. The range measurement between two objects is the primary means of calculating the relative position between the two devices. The UWB device can be used as a range measurement sensor because it can provide cm level accuracy unlike other devices such as Wi-Fi, Bluetooth, and Zigbee. Moreover, the recently developed UWB devices are cost effective compared to previously developed devices. The available UWB devices use different ranging methods such as TWR, TDOA, and AOA to enable range measurement between two devices. However, it is found that TWR can provide more precise range measurement in a dynamic environment as it can mitigate the clock drift and time synchronization issues found in UWB based range measurement methods. Therefore, TWR range measurements can be used for UWB devices. One of the limitations of the UWB device is the lack of pose estimation and deterioration of range accuracy in NLOS, which can be solved by using an IMU sensor. The IMU sensors can provide information about the displacement of the objects, which can be integrated with UWB devices to reduce the standard deviation of the relative positioning error. Moreover, the IMU sensor can also provide pose estimation, and the pose estimation information from both objects can be integrated to enable relative pose estimation between two objects. Therefore, this study integrates the UWB and IMU devices to propose a relative positioning system for wearable IoT devices. The UWB-based range measurement technique is used to estimate the range between two devices. The estimated range is then filtered using the moving average and min-max filtering methods prior to calculating the 3D relative position between the two devices. UWB antennas are distributed in a squared mobile structure with the Euler angle orientation method. The distributed Euler angle orientation is responsible for acquiring 3D relative position with precise accuracy. The multilateration method is modified according to the structural requirement of the proposed relative positioning system. Moreover, a novel UWB and IMU fusion method is proposed to reduce position error and increase the update rate of the system. The main contributions of this study are as follows:

A Distributed Euler antenna orientation is proposed to enable 3D relative positioning using a mobile structure.

The rest of the paper is divided as follows: Section 2 discusses the related literature, preliminaries are discussed in Section 3, Section 4 is dedicated to the materials and methods of the proposed solution, experimental results are analyzed in Section 5, discussion about the proposed solution in contrast to existing solutions is done in Section 6, and finally, a conclusion is drawn in Section 7.

Due to the increasing need for location-aware services, there has been a rise in research examining indoor localization over the past few years. Numerous studies have concentrated on indoor positioning using a static infrastructure. Wireless-network-based infrastructures, for instance, often include many wireless access points to provide full network coverage. Numerous off-the-shelf technologies are capable of providing RSS indicators, which can be used to estimate the position of a mobile node [28,29]. Obtaining a priori information about a structure is impractical in various situations, such as when workers are exploring disaster zones, during collaborative tasks, and for VR/AR agents. Therefore, researchers are now concentrating on relative positioning as opposed to indoor positioning. The authors of [30] described a placement technique for static sensor nodes in a sensor network. During placement, location uncertainty occurs in some nodes [31,32], and this will spread to neighboring nodes, resulting in inaccurate positioning.

To address these issues, a UWB-based relative-positioning scheme can be deployed, which can concurrently perform positioning and transmission with low latency. In comparison to the aforementioned conventional positioning technologies, UWB-based relative-positioning technology is much more flexible to complex scenarios and possesses all of the benefits of collaborative positioning applications. Although UWB is a kind of wireless-based positioning system, its greater temporal resolution allows it to deliver significantly more precise locations than other wireless-based solutions. UWB-based approaches have been extensively employed in transportation in recent years, but in most situations, UWB anchors must be placed beside pathways to determine the exact location of a vehicle [33,34]. However, the cost of placing UWB anchors on a large scale is high, and their installation can be very complex.

Table 1 shows the comparison between the existing solution and the proposed method. The comparison shows that most of the works only considered relative range measurement as relative positioning. Other works lack precise accuracy, mobile structure, and cost effective solutions. Therefore, it is evident from this literature review that the relative position accuracy for both 2D and 3D applications of these approaches is still not suitable for real-time implementation in scenarios such as VR and collaborative tasks. Moreover, the approaches used by most studies do not provide relative attitude information between two mobile nodes, which is crucial for life-critical collaborative tasks. Therefore, we propose a UWB–IMU fusion-based relative-position system to accurately calculate the relative position between two objects with a small mobile structure. The relative attitude is also calculated using a low-cost on-board IMU sensor.

The proposed system uses an IoT platform to transfer the data from the remote device to the Unity software. Fig. 2 shows the overall system architecture of the UWB–IMU-based relative-position system. The UWB and IMU sensors collect data and send it to a microcontroller device using the Serial Peripheral Interface and I²C protocols. The Qorvo DWS1000 UWB module and the InvenSense MPU-9250 IMU module were selected, as they are inexpensive and provide high accuracy when compared to other modules available at a similar price. The microcontroller collects the data and performs TWR to determine the distance between two objects. Data processing is also carried out prior to the calculation of the relative position. The STM32-based Nucleo F429ZI microcontroller development board was used as per the instructions of Decawave. Then, the acquired range measurement is sent to a Raspberry Pi development board using the universal asynchronous receiver-transmitter method to calculate the relative position using a fusion of the UWB and IMU sensors. The relative-position data is then sent to the base station via the hypertext transfer protocol (HTTP) and the Unity software as a VR platform to represent the relative position between the two objects in an indoor environment. In this work, a laptop was used as a base station to collect the relative-position data and represent it in the software. The UWB–IMU fusion-based relative-position system can be divided into two parts: a UWB-based relative-position system and a UWB–IMU fusion-based relative-position system. Detailed descriptions of these parts are presented in this section.

Fig. 3 shows the proposed UWB–IMU fusion method that is used to calculate the relative positioning of the two mobile nodes. The range measurement from the UWB devices and the IMU information from the two nodes are fused to perform this calculation. Then, an extended Kalman filter is used to process the calculated relative position, and a filtered relative position is obtained.

The IMU can provide displacement information about a device without the need for other devices. However, as noted, IMU measurements suffer from errors that must be minimized before fusing the IMU information with that from the UWB devices. The extended Kalman filter is used to mitigate the Euler angle and gyro-bias errors from the IMU device. The filtered values are then used to calculate the acquired relative position from the UWB system, and the attitude from the IMU module is sent to the relative position and attitude estimation unit to fuse the data. The device’s attitude (ϕ, θ, and ψ) is calculated according to the north-east-down standard.

An extensive experimental study was conducted to evaluate the performance of the proposed UWB–IMU fusion-based relative-position scheme. This section presents experimental results and relevant plots to show the potential of fusing UWB and IMU to provide a smooth relative position.

The average RMSE of the proposed system was compared with other relative-position systems in the literature. The purpose of this comparison was to determine the performance of different hardware and algorithm implementations. From Table 7, it can be seen that the performance varies due to the use of different algorithms and devices. As the number of UWB devices is increased, the accuracy is also improved due to the additional range measurements that are provided. The data preprocessing methods also help to improve the accuracy of the relative-position systems by reducing bias and standard deviation. We can see from the comparison that the proposed method has an RMSE of 0.31 m, which is lower than the RMSE values of the other solutions found in the literature. Therefore, it can be said that the proposed relative-position system has high accuracy and can thus be implemented for collaborative tasks such as VR/AR applications.

This paper presents a UWB–IMU fusion-based method for acquiring the relative positions of two mobile nodes. The anchor placement and modified multilateration methods were modified to enable mobile infrastructure-based measurements of relative position. In the present method, measurements from an IMU are fused with UWB measurements to mitigate the error caused by the variance characteristics of the UWB range measurements. The data from the proposed method were also sent to a VR platform to demonstrate its potential for use in VR/AR scenarios. An RMSE relative position accuracy of 0.31 m was achieved in three dimensions. The proposed method yields better results than previous methods; thus, it could be deployed in collaborative robotics tasks and VR/AR applications.

The UWB-IMU fusion-based relative position system is also prone to variations of the position due to the standard deviation of the range measurement. Standard deviation can be mitigated using different filters such as complementary filter, moving average filter, and min-max removal, but these filters decrease the measurement rate of the sensor. The measurement rate of the UWB and IMU devices is very important to enable real-time location-aware services for VR/AR applications. Moreover, more complex scenarios need to be proposed to evaluate the performance of the proposed relative position system. Deep learning methods can be explored to mitigate the range error for both LOS and NLOS environments.