Accurate Relative Position Research Articles

DNN-Based Relative Localization Technique for Real-Time Positioning of Moving Unmanned Swarm Robots

The unmanned swarm robot system, which enables multiple robots to collaborate and perform a variety of tasks, is extensively researched for its potential applications. Accurate determination of the location of swarm robots during operation is of paramount importance, and various positioning algorithms are employed to achieve this. Specifically, in situations where global positioning system (GPS) signals are unavailable, fixed anchor nodes with known location information can be utilized for localization. However, in scenarios where fixed anchor nodes are not present, and the robots operate in a swarm, applying this technology poses challenges, necessitating a localization technique that relies solely on distance information between the robots. This paper proposes a deep neural network (DNN) technique that utilizes only the distance information between moving nodes to predict the real-time relative coordinates of each node. It is assumed that the distances between nodes are updated sequentially and periodically according to a predetermined measurement cycle. A grid-based localization technique is used as the existing method for performance comparison. Computer simulation results demonstrate that the proposed DNN-based relative Localization technique exhibits superior localization performance compared to the existing Grid-based method. Furthermore, the proposed technique shows similar performance regardless of the distance measurement cycle, indicating that it is not significantly affected by the cycle. Therefore, applying the proposed relative Localization algorithm to swarm robots could enable real-time and accurate relative positioning, facilitating precise location tracking of the swarm.

Determining the Antenna Phase Center for the High-Precision Positioning of Smartphones.

In recent years, smartphones have emerged as the primary terminal for navigation and location services among mass users, owing to their universality, portability, and affordability. However, the highly integrated antenna design within smartphones inevitably introduces interference from internal signal sources, leading to a misalignment between the antenna phase center (APC) and the antenna geometric center. Accurately determining a smartphone's APC can mitigate system errors and enhance positioning accuracy, thereby meeting the increasing demand for precise and reliable user positioning. This paper delves into a detailed analysis of the generation of Global Navigation Satellite System (GNSS) receiver antenna phase center errors and proposes a method for correcting the receiver antenna phase center. Subsequently, a smartphone positioning experiment was conducted by placing the smartphone on an observation column with known coordinates. The collected observations were processed in static relative positioning mode, referencing observations from geodetic-grade equipment, and the accuracy of the static relative positioning fixed solution was evaluated. Following weighted estimation, we determined the antenna phase center of the Xiaomi Mi8 and corrected the APC. A comparison of the positioning results of the Xiaomi Mi8 before and after APC correction revealed minimal impact on the standard deviations (STDs) but significant influence on the root mean square errors (RMSEs). Specifically, the RMSEs in the E/N/U direction were reduced by 59.6%, 58.5%, and 42.0%, respectively, after APC correction compared to before correction. Furthermore, the integer ambiguity fixing rate slightly improved after the APC correction. In conclusion, the determination of a smartphone's APC can effectively reduce system errors in the plane direction of GNSS positioning, thereby enhancing smartphone positioning accuracy. This research holds significant value for advancing high-precision positioning studies related to smartphones.

Real-time high-precision baseline measurement of satellite formation flying based on GNSS

With the establishment of the Chinese space station, a series of space science missions will be conducted in its vicinity. One of the extended tasks for the in-orbit service of space station is the formation flying of small satellites centered around the space station. Satellite formations can perform simultaneous three-dimensional observations of the space station, generating three-dimensional images and monitoring and assessing the status of critical components of the space station. The real-time and accurate relative position measurement is one of the key issues in formation flying. It is a fundamental prerequisite for maintaining and reconfiguring formation configurations, collision avoidance and safety assurance. GNSS-based relative positioning is a low-cost and high-precision measurement method, which is not constrained by light, weather, or relative attitude of satellites. This study introduces a novel approach to determine the relative position of satellites based on single-epoch Global Navigation Satellite System (GNSS) carrier phase difference measurements. Unlike traditional methods, the proposed technique eliminates the need for precise ephemeris and clock bias files and does not require historical observation data. The algorithm avoids the complexity associated with full cycle ambiguity jumps, facilitating real-time, high-precision calculations of relative position baseline vectors. Special attention is given to the influence of Geostationary Earth Orbit (GEO) satellites in the BeiDou Navigation Satellite System (BDS), and measures are taken to mitigate their impact on measurement accuracy by adjusting their observation weights. Our newly developed GNSS-based real-time measurement module, designed for high-quality GNSS signal reception and data communication, was tested on terrestrial and simulated low-orbit platforms. Remarkably, over baselines ranging from 10 m to 9.3 km, while traditional pseudorange differential measurements showed errors up to 1.5571 m, our proposed method consistently held errors under 5 cm and ensured computational speeds within 0.1 s per epoch. High-dynamic zero-baseline tests further validated its potential, with errors less than 1 cm. The innovations encapsulated in this work, resonating with the evolving trends of miniaturized and scalable satellites, present a cost-efficient and real-time solution for inter-satellite relative position measurement. This promises a new horizon in satellite formation technology, with future endeavors focusing on on-orbit experiments.

Study on high-precision three-dimensional reconstruction of pulmonary lesions and surrounding blood vessels based on CT images.

The adoption of computerized tomography (CT) technology has significantly elevated the role of pulmonary CT imaging in diagnosing and treating pulmonary diseases. However, challenges persist due to the complex relationship between lesions within pulmonary tissue and the surrounding blood vessels. These challenges involve achieving precise three-dimensional reconstruction while maintaining accurate relative positioning of these elements. To effectively address this issue, this study employs a semi-automatic precise labeling process for the target region. This procedure ensures a high level of consistency in the relative positions of lesions and the surrounding blood vessels. Additionally, a morphological gradient interpolation algorithm, combined with Gaussian filtering, is applied to facilitate high-precision three-dimensional reconstruction of both lesions and blood vessels. Furthermore, this technique enables post-reconstruction slicing at any layer, facilitating intuitive exploration of the correlation between blood vessels and lesion layers. Moreover, the study utilizes physiological knowledge to simulate real-world blood vessel intersections, determining the range of blood vessel branch angles and achieving seamless continuity at internal blood vessel branch points. The experimental results achieved a satisfactory reconstruction with an average Hausdorff distance of 1.5 mm and an average Dice coefficient of 92%, obtained by comparing the reconstructed shape with the original shape,the approach also achieves a high level of accuracy in three-dimensional reconstruction and visualization. In conclusion, this study is a valuable source of technical support for the diagnosis and treatment of pulmonary diseases and holds promising potential for widespread adoption in clinical practice.

Precise Relative Navigation in Medium Earth Orbits with Global Navigation Satellite Systems and Intersatellite Links for Black Hole Imaging

The Event Horizon Telescope (EHT) is a ground-based array of Very Long Baseline Interferometry (VLBI) telescopes designed to image the event horizon of black holes. To overcome its limitations, this study explores a mission concept involving a two-satellite constellation of VLBI telescopes deployed in Medium Earth Orbit (MEO). Achieving high-resolution black hole images requires precise baseline determination at the millimetre level. To address this challenge, each satellite in the constellation is equipped with two Global Navigation Satellite System (GNSS) receivers and an optical Intersatellite Link (ISL) to enhance orbit determination. The results highlight the importance of integer ambiguity resolution and reveal that the ISL primarily improves baseline estimation along the link direction, with minimal impact along the black hole direction. Large intersatellite distances lead to sub-optimal relative orbit accuracy, challenging the attainment of the 3.5 mm relative position accuracy goal along the black hole direction.

OBTAINING APPROXIMATIONS FOR RANGE-BASED FREE-NETWORK ADJUSTMENT

Abstract. Airborne and ground mobile mapping platforms are increasingly used in group formations to increase productivity or complement each other in terms of improving observation capacity and efficiency in the surveyed area. Similarly, the navigation of assisted and autonomous vehicles presents a similar problem of sharing a small place where, for example, accurate relative positioning is essential to avoid collisions. Estimating platform relative positions from inter-platform range measurements is important in these applications, as they can provide valuable information to improve individual platform navigation or can potentially detect anomalies in these solutions that could be caused by unintentional or intentional disturbances. Free-network adjustment based on ranges forms the baseline solution to obtain relative positions. The challenge is to provide adequate platform position approximations for the least squares adjustment to achieve both quick convergence and fast execution time. Here we propose a preprocessing method that creates suitable approximations based on range values.

A graph optimization approach to range-based relative location

With the development of multi-robot cluster system, the research of multi-node relative pose estimation is in the ascendant. However, for the environment without GNSS or fixed anchors, the problem of relative pose estimation is still challenging. In this paper, a general algorithm and system framework based on graph optimization algorithm is proposed to fuse inter- and intra-robot measurements, as well as mobility models with sliding windows for relative attitude estimation. In order to verify the feasibility and universality of the algorithm, the algorithm has used to design a relative positioning system based on UWB positioning with a “single-node multi-tags” system structure, which can simultaneously obtain reliable relative positions and directions. The design of multi-source fusion can further improve the accuracy and robustness of relative positioning. Experiment results shows that in the harsh environment without GNSS and fixed anchor points, the relative pose estimation accuracy of this system can reach centi-meter level, which may be the best potential choice for relative positioning of multi robot cluster in complex environment.

The enhanced search procedure in a coordinate domain for precise satellite positioning

Recently, there has been an increase in the availability of GNSS satellites for observation, which poses new challenges in the computational process of precise satellite positioning. Ambiguity resolution is a crucial step in achieving accurate relative positioning. In this regard, an improved version of a searching procedure in a three-dimensional coordinate domain has been proposed and tested. The method starts with a float solution, similar to classic methods like the LAMBDA. However, the subsequent step, the search procedure, is conducted in the coordinate space instead of the ambiguity space. This shift to a three-dimensional coordinate space leads to reduced computation time. A computational experiment was performed to validate the proposed method, which demonstrated a significant reduction in processing time. The advantages of this method are particularly prominent when dealing with a large number of satellites.

Field distortion correction in galvanometric scanning system by interpolation with symmetric polynomials

Due to its high precision and flexibility, laser process system is widely used in laser marking, drilling, cutting and projection. Laser scanning machines are usually equipped with high-speed galvanometric scanning systems, which are inevitably accompanied by field distortion. The error compensation method can help improve the marking quality that minimizes inherent and random errors. This paper introduces a facile software compensation method for this purpose. Based on symmetry of field distortion, the length of four characteristic lines is required to determine the polynomial compensation function. The experimental results verified that the technique could effectively reduce the field-distortion errors in the galvanometer laser-machining system, which verifies the feasibility and effectiveness of the compensation method. Within the processing range of the experiment (100 × 100 mm), the average relative position accuracy is 0.00068 (＜1‰). In the light of these results, high-quality laser processing is promising for achieving by the compensation method.

Peg-in-Hole Using Transient Information of Force Response

In precision assembly, a peg is guided into a hole with a tolerance smaller than the position accuracy. Although force/torque sensing can estimate the relative position between the peg and hole accurately, its performance is impaired because of the degradation of estimation accuracy caused by transient error at the time of the collision. We found in this study that if contact state transitions can be generated reproducibly, accurate relative positions can be derived from the transient responses, which were previously regarded as errors. We propose a method that focuses on this characteristic. The transition in the contact state is determined by force/torque responses. Then, the estimation accuracy of the direction of the hole improves by using only the force/torque responses of a specific contact state. Additionally, the time between the contact and estimation of the relative position is reduced by using the transient force information.

Study on Differential Phase Delay of Same‐Beam VLBI in Rendezvous and Docking of Chang'E‐5

AbstractThe Chang'E‐5 (CE5) ascender achieved lunar orbit autonomous rendezvous and docking with orbiter‐returner successfully on 5 December 2020. Same‐beam Very Long Baseline Interferometry (VLBI) (SBI) observations were performed for the first time for autonomous rendezvous and docking in lunar orbit. In this paper, by studying the CE5 rendezvous and docking data observed by the Chinese VLBI network and analyzing the residual differential phase delay of the autonomous control phase, we successfully captured the maneuver of the 5 km holding of the orbiter‐returner. The differential phase delay (DPD) data of the far‐range guidance phase were used to perform orbit determination of the ascender and orbiter‐returner successfully. The results of orbit determination show that the DPD data can improve the relative position accuracy between the ascender and the orbiter‐returner, and the residual root mean square of the DPD data is 5 ps. Furthermore, when one of the probes has only DPD data, its orbit can also be determined.

Geometry-free TDRTK: a new time-difference RTK model considering multi-frequency observations

The time difference RTK (TDRTK) of GNSS can obtain high-precision baseline constraints to control the cumulative error of dead reckoning technology. However, the availability of traditional TDRTK decreases sharply with the increase of time interval. A geometry-free TDRTK method with quality control using multi-frequency observations is proposed to solve this problem. Experimental shows that in the dynamic condition of a stand-alone GNSS receiver, the average and maximum relative position accuracy (10 min and 10 kilometres tests) of the proposed method are improved by 42.2% and 44.2% compared with the existing methods.

Robust UKF Relative Positioning Approach for Tightly Coupled Vehicle Ad Hoc Networks Based on Adaptive M-Estimation

Huber M-estimation, as an estimation method based on mixed norm as cost function, provides an effective method for robust filtering to deal with measurement outliers. Based on statistical linear regression model approximating nonlinear measurement model, M-estimation algorithm is used to realize measurement update of states. However, when the measurement noise pollution rate is high, the filtering performance will be seriously degraded. In order to further improve the actual performance of data fusion under abnormal measurement noise, a vehicle cooperative positioning scheme based on adaptive M-estimation robust unscented Kalman filter (AMRUKF) was proposed. This algorithm combines Huber’s linear regression problem with covariance matching method, and calculates the adaptive matrix through the innovation covariance estimator based on fading memory index weighting to adaptively adjust the measurement noise covariance used in Huber M estimation method. The analytical and experimental results of tightly-coupled vehicle relative positioning show that the proposed AMRUKF method can effectively improve the robustness and accuracy of relative positioning and provide a practical control scheme for vehicle cooperative positioning.

A ROS-based distributed multi-robot localization and orientation strategy for heterogeneous robots

The problem of estimating and tracking the location and orientation of a mobile robot by another in heterogeneous distributed multi-robots is studied in this paper. We propose a distributed multi-robot localization strategy (DMLS) that is Robotic Operating System (ROS) based. It consists of an algorithm that fuses data of diverse sensors from 2 heterogeneous robots that are not connected within their transform trees to localize and measure the relative position and orientation.The method exploits the robust detection of the Convolutional Neural Networks (CNN) and the accurate relative position measurements from the local costmap. The algorithm is composed of two parts: The localization part and the relative orientation measurement part. Localization is done by optimization and alignment calibration of the CNN output with the costmap in an individual robot. The relative orientation measurement is done by a collaborative multi-robot fusing of diverse sensor data to align and synchronize the transform frames of both robots in their costmaps. To illustrate the performance of this strategy, the proposed method is compared with a conventional object localization and orientation measuring method that uses computer vision and QR codes. The results show that this proposed method is robust and accurate while maintaining a degree of simplicity and efficiency in costs. The paper also presents various application experiments in laboratory and simulation environments. By using the proposed method, distributed multi-robots collaborate to achieve collective intelligence from individuals, which increases team performance.

Application of Saturn’s Rings to Spacecraft Optical Navigation

This work explores the feasibility of using images of Saturn’s ring system as a navigation resource for spacecraft. The perspective geometry of Saturn’s rings provides closed-form expressions for estimating a spacecraft’s relative position as well as its analytical covariance. Numerical simulations detail the performance and sensitivity of the position estimates. An extended Kalman filter fuses the relative position estimates with spacecraft dynamics for more accurate relative position and velocity estimates. An Enceladus sample collection mission serves as a case study where the proposed method seems viable. With filtering, simulation of an Enceladus sample-collection mission achieves maximum bounds of 7.19 km and for relative position and velocity estimates, respectively, during its Enceladus encounter. Autonomous navigation may reduce the cost of such a mission to the point where several small spacecraft can achieve the science objectives.

Study on angle-only relative navigation for unmanned aerial vehicle formation in GPS-denied environment

To satisfy the autonomous relative navigation demand of unmanned aerial vehicle (UAV) formation in a GPS-denied environment, an angle-only relative navigation algorithm is proposed. First, the relative states in 3-dimension space are decoupled into relative motion along the horizontal plane and altitude by applying the relative azimuth between the north-east-down global frame and the body-fixed horizontal frame belonging to UAVs. Second, a relative dynamic and measurement model considering the measurement deviation of sensors are established. This solves the problem of colored noise in a majority of sensors used in practical engineering. Third, a consensus constraint model of relative states is established by introducing a geometric constraint among formation members. Additionally, a consensus-extended Kalman filter is designed. Finally, the angle-only relative navigation method is validated using standard Monte Carlo simulations. The simulation results show that all the states of the system are observable when the observability criterion is satisfied. The relative position accuracy achieved using gyros with a drift rate of 50°/h, accelerometers with 1 mg deviation, and optical cameras with 1° Gaussian white noise is within 10 m (3σ). Additionally, the method proposed in this study can be used to estimate the sensor measurement deviations effectively. Furthermore, it can be potentially applied to improve the absolute navigation accuracy of UAVs.

Relative-Position Estimation Based on Loosely Coupled UWB–IMU Fusion for Wearable IoT Devices

Relative positioning is one of the important techniques in collaborative robotics, autonomous vehicles, and virtual/augmented reality (VR/AR) applications. Recently, ultra-wideband (UWB) has been utilized to calculate relative position as it does not require a line of sight compared to a camera to calculate the range between two objects with centimeter-level accuracy. However, the single UWB range measurement cannot provide the relative position and attitude of any device in three dimensions (3D) because of lacking bearing information. In this paper, we have proposed a UWB-IMU fusion-based relative position system to provide accurate relative position and attitude between wearable Internet of Things (IoT) devices in 3D. We introduce a distributed Euler angle antenna orientation which can be equipped with the mobile structure to enable relative positioning. Moving average and min-max removing preprocessing filters are introduced to reduce the standard deviation. The standard multilateration method is modified to calculate the relative position between mobile structures. We combine UWB and IMU measurements in a probabilistic framework that enables users to calculate the relative position between two nodes with less error. We have carried out different experiments to illustrate the advantages of fusing IMU and UWB ranges for relative positioning systems. We have achieved a mean accuracy of 0.31 m for 3D relative positioning in indoor line of sight conditions.

Prescribed precision for medical products obtained with additive manufacturing technologies

The paper highlights the importance of corelating the function of a medical product, with its’ design and manufacture stages within the global product design and development process. Dimensional accuracy, macro-geometric and micro-geometric shape accuracy, relative surface position accuracy and other prescribed characteristics of medical products should take into consideration a variety of factors, such as custom requirements, regulated by the product functions. In an ideal scenario, with unlimited resources, prescribed characteristics dictate the selection of the manufacturing technology and equipment. Nonetheless, in most cases the design stage takes into consideration capabilities of available technology, correlated with bespoke requirements. In this context, the authors propose a clear distinction between precision, accuracy, repeatability, and resolution, as to properly address each issue in the lifecycle of a medical product manufactured using additive technologies. Using a real application for an upper limb prosthesis, the nominal position precision is prescribed, based on size-dependent geometric tolerances, for a cylindrical surface in relation to three reference surfaces, with the application of the maximum and minimum material principles.

A distance calibration method for kinematic parameters of serial industrial robots considering the accuracy of relative position

This paper proposes a kinematic calibration method based on the optimized distance error function to improve the accuracy of the relative positions of industrial robots. For implementation, a three-dimensional measurement system with R-test is designed to measure the robot end-effector's distance, which is the first successful use of this system for robot calibration. Then, an optimization function of the distance errors is proposed without an approximation condition to identify the controller's modifiable parameter errors. In addition, the influence of the redundant parameter on the error of relative position is analyzed, which indicates it can further improve the relative position’s accuracy. Simulations prove the performance of the proposed solution by comparing it with the current distance and positioning error methods. The validation experiment shows the proposed method reduced the mean of distance error/distance and relative positioning error/relative positioning from 14.30 µm/mm to 4.4 µm/mm and from 20.15 µm/mm to 10.85 µm/mm.

Research on Android-odometry based on the estimation of GNSS temporal ambiguity variation with Xiaomi MI8

Following extant studies on temporal relative localization (TRL) methods, this study uses a doppler velocity constraint-based temporal ambiguity variation (TAV) detection method and a two-step TAV resolution method to obtain the high-precisiontemporal relative position variations over time based on raw GNSS observations of Android smartphones, commonly plagued by frequent half-cycle slips and lock-loss. Results show that the proportion of the detectable satellites over 0.65 reaches the 95.57% level and the fix rate of global TAV resolution reaches 82.93%. We then propose the Android-odometry method which is a real-time high-precision TRL method with time-differenced carrier-phase observations of Android smartphones. The experimental results show that the method achieves centimeter-level temporal relative position accuracy during the 13-min dynamic test with Xiaomi MI8, showing a dramatic improvement of over 90% compared to the traditional RTK method.