A Stochastic Model Based on Optimal Satellite Subset Selection Strategy for Smartphone Pseudorange Relative Positioning.

In order to overcome the limitations of traditional stochastic models for smartphones, we introduce a double-difference code pseudorange residual (DDPR)-dependent stochastic model based on an optimal satellite subset, with the goal of mitigating the constraints imposed by the quality of GNSS observations in smartphones on the accuracy and reliability of phone-based GNSS positioning. In our methodology, the satellite selection process involved considering the integrated carrier-to-noise density ratio (C/N0) index of both the reference station and the smartphone, enabling us to construct a satellite subset characterized by superior observation quality. Furthermore, by leveraging the optimal subset of satellites and incorporating the C/N0-dependent stochastic model, we could determine the approximate location of the terminal through pseudorange differential positioning. Subsequently, we estimated the DDPRs for all satellites and utilized these values as prior information to build a stochastic model of the observations. Our findings indicate that in occluded environments, the DDPR-dependent stochastic model significantly enhances positioning accuracy for both the Huawei Mate40 and P40 terminals compared to the C/N0-dependent model. Numerically, the improvements in the north (N), east (E), and up (U) directions were approximately 30%, 32%, and 34% for the Mate40, and 26%, 33%, and 24% for the P40 terminal. This suggests that the proposed DDPR-dependent stochastic model effectively identifies and mitigates large gross error signals caused by multipath and non-line-of-sight (NLOS) signals, thereby assigning lower weights to these problematic observations and ultimately enhancing positioning accuracy. Moreover, the weighting method involves minimal computations and is straightforward to implement, making it particularly suitable for GNSS positioning applications on smartphones in complex urban environments.

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.

A Novel Ranging and IMU-Based Method for Relative Positioning of Two-MAV Formation in GNSS-Denied Environments.

Global Navigation Satellite Systems (GNSS) with weak anti-jamming capability are vulnerable to intentional or unintentional interference, resulting in difficulty providing continuous, reliable, and accurate positioning information in complex environments. Especially in GNSS-denied environments, relying solely on the onboard Inertial Measurement Unit (IMU) of the Micro Aerial Vehicles (MAVs) for positioning is not practical. In this paper, we propose a novel cooperative relative positioning method for MAVs in GNSS-denied scenarios. Specifically, the system model framework is first constructed, and then the Extended Kalman Filter (EKF) algorithm, which is introduced for its ability to handle nonlinear systems, is employed to fuse inter-vehicle ranging and onboard IMU information, achieving joint position estimation of the MAVs. The proposed method mainly addresses the problem of error accumulation in the IMU and exhibits high accuracy and robustness. Additionally, the method is capable of achieving relative positioning without requiring an accurate reference anchor. The system observability conditions are theoretically derived, which means the system positioning accuracy can be guaranteed when the system satisfies the observability conditions. The results further demonstrate the validity of the system observability conditions and investigate the impact of varying ranging errors on the positioning accuracy and stability. The proposed method achieves a positioning accuracy of approximately 0.55 m, which is about 3.89 times higher than that of an existing positioning method.

Improving the Performance of Time-Relative GNSS Precise Positioning in Remote Areas.

Global navigation satellite systems (GNSS) can attain centimeter level positioning accuracy, which is conventionally provided by real-time precise point positioning (PPP) and real-time kinematic (RTK) techniques. Corrections from the data center or the reference stations are required in these techniques to reduce various GNSS errors. The time-relative positioning approach differs from the traditional PPP and RTK in the sense that it does not require external real-time corrections. It computes the differences in positions of a single receiver at different epochs using phase observations. As the code observations are not used in this approach, its performance is not affected by the noise and multipath of code observations. High reliability is another advantage of time-relative precise positioning because the ambiguity resolution is not needed in this approach. Since the data link is not required in the method, this approach has been widely used in remote areas where wireless data link is not available. The main limitation of time-relative positioning is that its accuracy degrades over time between epochs because of the temporal variation of various errors. The application of the approach is usually limited to be within a time interval of less than 20 min. The purpose of this study was to increase the time interval of time-relative positioning and to extend the use of this method to applications with a longer time requirement, especially in remote areas without wireless communication. In this paper, the main error sources of the time-relative method are first analyzed in detail, and then the approach to improve the accumulated time relative positioning method is proposed. The performance of the proposed method is assessed using both static and dynamic observations with a duration as long as several hours. The experiments presented in this paper show that, among the four scenarios tested (i.e., GPS, GPS/Galileo, GPS/Galileo/BeiDou, and GPS/Galileo/BeiDou/GLONASS), GPS/Galileo/BeiDou performed best and GPS/Galileo/BeiDou/GLONASS performed worst. The maximum positioning errors were mostly within 0.5 m in the horizontal direction, even after three hours with GPS/Galileo/BeiDou. It is expected that the method could be used for positioning and navigation for as long as several hours with decimeter level horizontal accuracy in remote areas without wireless communication.

Helmert Variance Component Estimation for Multi-GNSS Relative Positioning.

The Multi-constellation Global Navigation Satellite System (Multi-GNSS) has become the standard implementation of high accuracy positioning and navigation applications. It is well known that the noise of code and phase measurements depend on GNSS constellation. Then, Helmert variance component estimation (HVCE) is usually used to adjust the contributions of different GNSS constellations by determining their individual variances of unit weight. However, HVCE requires a heavy computation load. In this study, the HVCE posterior weighting was employed to carry out a kinematic relative Multi-GNSS positioning experiment with six short-baselines from day of year (DoY) 171 to 200 in 2019. As a result, the HVCE posterior weighting strategy improved Multi-GNSS positioning accuracy by 20.5%, 15.7% and 13.2% in east-north-up (ENU) components, compared to an elevation-dependent (ED) priori weighting strategy. We observed that the weight proportion of both code and phase observations for each GNSS constellation were consistent during the entire 30 days, which indicates that the weight proportions of both code and phase observations are stable over a long period of time. It was also found that the quality of a phase observation is almost equivalent in each baseline and GNSS constellation, whereas that of a code observation is different. In order to reduce the time consumption of the HVCE method without sacrificing positioning accuracy, the stable variances of unit weights of both phase and code observations obtained over 30 days were averaged and then frozen as a priori information in the positioning experiment. The result demonstrated similar ENU improvements of 20.0%, 14.1% and 11.1% with respect to the ED method but saving 88% of the computation time of the HCVE strategy. Our study concludes with the observations that the frozen variances of unit weight (FVUW) could be applied to the positioning experiment for the next 30 days, that is, from DoY 201 to 230 in 2019, improving the positioning ENU accuracy of the ED method by 18.1%, 13.2% and 10.6%, indicating the effectiveness of the FVUW.

An Improved Relative GNSS Tracking Method Utilizing Single Frequency Receivers.

The Global Navigation Satellite Systems (GNSS) becomes the primary choice for device localization in outdoor situations. At the same time, many applications do not require precise absolute Earth coordinates, but instead, inferring the geometric configuration information of the constituent nodes in the system by relative positioning. The Real-Time Kinematic (RTK) technique shows its efficiency and accuracy in calculating the relative position. However, when the cycle slips occur, the RTK method may take a long time to obtain a fixed ambiguity value, and the positioning result will be a "float" solution with a low meter accuracy. The novel method presented in this paper is based on the Relative GNSS Tracking Algorithm (Regtrack). It calculates the changes in the relative baseline between two receivers without an ambiguity estimation. The dead reckoning method is used to give out the relative baseline solution while a parallel running Extended Kalman Filter (EKF) method reinitiates the relative baseline when too many validation failures happen. We conducted both static and kinematic tests to assess the performance of the new methodology. The experimental results show that the proposed strategy can give accurate millimeter-scale solutions of relative motion vectors in adjacent two epochs. The relative baseline solution can be sub-decimeter level with or without the base station is holding static. In the meantime, when the initial tracking point and base station coordinates are precisely obtained, the tracking result error can be only 40 cm away from the ground truth after a 25 min drive test in an urban environment. The efficiency test shows that the proposed method can be a real-time method, the time that calculates one epoch of measurement data is no more than 80 ms and is less than 10 ms for best results. The novel method can be used as a more robust and accurate ambiguity free tracking approach for outdoor applications.

Characterisation of GNSS Carrier Phase Data on a Moving Zero-Baseline in Urban and Aerial Navigation.

We present analyses of Global Navigation Satellite System (GNSS) carrier phase observations in multiple kinematic scenarios for different receiver types. Multi-GNSS observations are recorded on high sensitivity and geodetic-grade receivers operating on a moving zero-baseline by conducting terrestrial urban and aerial flight experiments. The captured data is post-processed; carrier phase residuals are computed using the double difference (DD) concept. The estimated noise levels of carrier phases are analysed with respect to different parameters. We find DD noise levels for L1 carrier phase observations in the range of 1.4-2 mm (GPS, Global Positioning System), 2.8-4.6 mm (GLONASS, Global Navigation Satellite System), and 1.5-1.7 mm (Galileo) for geodetic receiver pairs. The noise level for high sensitivity receivers is at least higher by a factor of 2. For satellites elevating above 30 ∘ , the dominant noise process is white phase noise. For the flight experiment, the elevation dependency of the noise is well described by the exponential model, while for the terrestrial urban experiment, multipath and diffraction effects overlay; hence no elevation dependency is found. For both experiments, a carrier-to-noise density ratio (C/N 0 ) dependency for carrier phase DDs of GPS and Galileo is clearly visible with geodetic-grade receivers. In addition, C/N 0 dependency is also visible for carrier phase DDs of GLONASS with geodetic-grade receivers for the terrestrial urban experiment.

Validating InSAR-SBAS results by means of different GNSS analysis techniques in medium- and high-grade deformation areas.

This study aimed to validate the interferometric synthetic aperture radar (InSAR) method by using relative and absolute Global Navigation Satellite System (GNSS) techniques. In this context, two land subsidence areas, one high (Mexico City) and one medium (Aguascalientes), were monitored between 2014 and 2018 by using Sentinel 1A satellite data. The monitoring was carried out with the Small Baseline Subset (SBAS) technique using 46 images for Mexico City and 18 images for Aguascalientes. Concordantly, the GNSS Continuously Operating Reference Station (CORS) data in the regions were analyzed with relative and Precise Point Positioning (PPP) GNSS analysis techniques. The time series obtained from three different analyses were compared and the results were evaluated in light of statistical criteria. According to the results, it is determined that the InSAR-SBAS technique can vary up to ± 20 mm from the displacement values obtained from GNSS due to various noise sources. Such deviations were limited to a few samples, and in general the differentiations were reasonable in the range of 7-8 mm. The difference between the deformation velocity estimation results obtained from the three different methods varied between 3 and 10 mm/year. In this context, these findings suggest that the InSAR-SBAS technique is an effective method for monitoring land deformation with the accuracy of sub-centimeter decided. In addition, PPP which has become an increasingly popular technique showed fast and reliable results in the range of 5-10 mm for InSAR verification. Moreover, with this study, most current results for Mexico City, which is the world's fastest subsiding metropole, were achieved. In the central region of the city, the detected 300 mm/year of subsidence rate was updated as 370 mm/year. In addition, Aguascalientes was monitored by using the Sentinel 1A satellite mission for the first time in this study. The 60 mm/year subsidence rate obtained for Aguascalientes in previous studies was updated and it was estimated that there are zones where this rate reaches up to - 115 mm/year levels. In this regard, it was concluded that the deformation rate has increased for both regions since the previous monitoring studies.

The First Result of Relative Positioning and Velocity Estimation Based on CAPS.

The Chinese Area Positioning System (CAPS) is a new positioning system developed by the Chinese Academy of Sciences based on the communication satellites in geosynchronous orbit. The CAPS has been regarded as a pilot system to test the new technology for the design, construction and update of the BeiDou Navigation Satellite System (BDS). The system structure of CAPS, including the space, ground control station and user segments, is almost like the traditional Global Navigation Satellite Systems (GNSSs), but with the clock on the ground, the navigation signal in C waveband, and different principles of operation. The major difference is that the CAPS navigation signal is first generated at the ground control station, before being transmitted to the satellite in orbit and finally forwarded by the communication satellite transponder to the user. This design moves the clock from the satellite in orbit to the ground. The clock error can therefore be easily controlled and mitigated to improve the positioning accuracy. This paper will present the performance of CAPS-based relative positioning and velocity estimation as assessed in Beijing, China. The numerical results show that, (1) the accuracies of relative positioning, using only code measurements, are 1.25 and 1.8 m in the horizontal and vertical components, respectively; (2) meanwhile, they are about 2.83 and 3.15 cm in static mode and 6.31 and 10.78 cm in kinematic mode, respectively, when using the carrier-phase measurements with ambiguities fixed; and (3) the accuracy of the velocity estimation is about 0.04 and 0.11 m/s in static and kinematic modes, respectively. These results indicate the potential application of CAPS for high-precision positioning and velocity estimation and the availability of a new navigation mode based on communication satellites.

Combination of High- and Low-Rate GPS Receivers for Monitoring Wind-Induced Response of Tall Buildings.

High-rise buildings are susceptible to wind-induced displacements, which can be precisely monitored by using GPS technology. However, GPS monitoring applications may be subject to signal interference and high hardware costs. This study presents a new wind-induced vibration monitoring approach that is based on the mixed use of high-rate and low-rate GPS receivers. In the proposed approach, high-rate receivers are only required in the monitoring stations, where we apply time-differenced positioning to obtain position changes between adjacent epochs. The derived high-rate monitoring station position changes are then integrated with low-rate single epoch relative positioning results between the monitoring and reference stations. Experimental results with both simulated and real data show that the proposed method has a comparable performance with the traditional relative positioning approach, in terms of determining buildings' vibration frequency, displacement, and acceleration.

Impacts of Satellite Orbit and Clock on Real-Time GPS Point and Relative Positioning.

Satellite orbit and clock corrections are always treated as known quantities in GPS positioning models. Therefore, any error in the satellite orbit and clock products will probably cause significant consequences for GPS positioning, especially for real-time applications. Currently three types of satellite products have been made available for real-time positioning, including the broadcast ephemeris, the International GNSS Service (IGS) predicted ultra-rapid product, and the real-time product. In this study, these three predicted/real-time satellite orbit and clock products are first evaluated with respect to the post-mission IGS final product, which demonstrates cm to m level orbit accuracies and sub-ns to ns level clock accuracies. Impacts of real-time satellite orbit and clock products on GPS point and relative positioning are then investigated using the P3 and GAMIT software packages, respectively. Numerical results show that the real-time satellite clock corrections affect the point positioning more significantly than the orbit corrections. On the contrary, only the real-time orbit corrections impact the relative positioning. Compared with the positioning solution using the IGS final product with the nominal orbit accuracy of ~2.5 cm, the real-time broadcast ephemeris with ~2 m orbit accuracy provided <2 cm relative positioning error for baselines no longer than 216 km. As for the baselines ranging from 574 to 2982 km, the cm-dm level positioning error was identified for the relative positioning solution using the broadcast ephemeris. The real-time product could result in <5 mm relative positioning accuracy for baselines within 2982 km, slightly better than the predicted ultra-rapid product.

Survey on Ranging Sensors and Cooperative Techniques for Relative Positioning of Vehicles.

Future driver assistance systems will rely on accurate, reliable and continuous knowledge on the position of other road participants, including pedestrians, bicycles and other vehicles. The usual approach to tackle this requirement is to use on-board ranging sensors inside the vehicle. Radar, laser scanners or vision-based systems are able to detect objects in their line-of-sight. In contrast to these non-cooperative ranging sensors, cooperative approaches follow a strategy in which other road participants actively support the estimation of the relative position. The limitations of on-board ranging sensors regarding their detection range and angle of view and the facility of blockage can be approached by using a cooperative approach based on vehicle-to-vehicle communication. The fusion of both, cooperative and non-cooperative strategies, seems to offer the largest benefits regarding accuracy, availability and robustness. This survey offers the reader a comprehensive review on different techniques for vehicle relative positioning. The reader will learn the important performance indicators when it comes to relative positioning of vehicles, the different technologies that are both commercially available and currently under research, their expected performance and their intrinsic limitations. Moreover, the latest research in the area of vision-based systems for vehicle detection, as well as the latest work on GNSS-based vehicle localization and vehicular communication for relative positioning of vehicles, are reviewed. The survey also includes the research work on the fusion of cooperative and non-cooperative approaches to increase the reliability and the availability.

Indicators describing the tumor lesion aggregation and dissemination and their impact on the prognosis of patients with diffuse large B cell lymphoma receiving chimeric antigen receptor T cell therapy.

INTRODUCTION: Chimeric antigen receptor (CAR) T cell therapy has markedly improved the prognosis of patients with diffuse large B-cell lymphoma (DLBCL). The relative positioning of tumor lesions in lymphoma varies among patients, manifesting as either aggregation (clumped together) or dissemination (spread throughout the body). Prognostic significance of factors indicating the relative positioning of tumor lesions in CAR T cell therapy remains underexplored. For aggregation, prior research proposed the tumor volume surface ratio (TVSR), linking it to prognosis in chemotherapy. Regarding dissemination, indicators such as disease stage or extranodal involvement, commonly used in clinical practice, have not demonstrated prognostic significance in CAR T cell therapy. This study aims to analyze current indicators of tumor aggregation or dissemination and introduce a novel indicator to assess the prognostic value of tumor lesions' relative positioning in DLBCL patients undergoing CAR T cell therapy. METHODS: This retrospective study included 42 patients receiving CAR T cell therapy. Lesion image information was obtained from the last PET/CT scan prior to CAR T cell infusion, including total metabolic tumor volume, total tumor surface, diameter of lymphoma masses, and the sites of tumor lesions. We evaluated TVSR and bulky disease as descriptors of tumor aggregation. We refined existing indicators, stage III&IV and >1 site extranodal involvement, to distill a new indicator, termed 'extra stage', to better represent tumor dissemination. The study examined the prognostic significance of tumor aggregation and dissemination. RESULTS: Our findings indicate that TVSR, while prognostically valuable in chemotherapy, lacks practical prognostic value in CAR T cell therapy. Conversely, bulky disease emerged as an optimal prognostic indicator of tumor aggregation. Both bulky disease and extra stage were associated with poor prognosis and exhibiting synergistic prognostic impact in CAR T cell therapy. CONCLUSIONS: Overall, the relative positioning of tumor lesions significantly influences the prognosis of patients with DLBCL receiving CAR T cell therapy. The ideal scenario involves tumors with minimal dissemination and no aggregation.

Examination of running pattern consistency across speeds.

Duty factor (DF) and step frequency (SF) are key running pattern determinants. However, running patterns may change with speed if DF and SF changes are inconsistent across speeds. We examined whether the relative positioning of runners was consistent: 1) across five running speeds (10-18 km/h) for four temporal variables [DF, SF, and their subcomponents: contact (tc) and flight (tf) time]; and 2) across these four temporal variables at these five speeds. Three-dimensional whole-body kinematics were acquired from 52 runners, and deviations from the median for each variable (normalised to minimum-maximum values) were extracted. Across speeds for all variables, correlations on the relative positioning of individuals were high to very high for 2-4 km/h speed differences, and moderate to high for 6-8 km/h differences. Across variables for all speeds, correlations were low between DF-SF, very high between DF-tf, and low to high between DF-tc, SF-tc, and SF-tf. Hence, the consistency in running patterns decreased as speed differences increased, suggesting that running patterns be assessed using a range of speeds. Consistency in running patterns at a given speed was low between DF and SF, corroborating suggestions that using both variables can encapsulate the full running pattern spectrum.

Modeling the behavior of an underwater acoustic relative positioning system based on complementary set of sequences.

The great variability usually found in underwater media makes modeling a challenging task, but helpful for better understanding or predicting the performance of future deployed systems. In this work, an underwater acoustic propagation model is presented. This model obtains the multipath structure by means of the ray tracing technique. Using this model, the behavior of a relative positioning system is presented. One of the main advantages of relative positioning systems is that only the distances between all the buoys are needed to obtain their positions. In order to obtain the distances, the propagation times of acoustic signals coded by Complementary Set of Sequences (CSS) are used. In this case, the arrival instants are obtained by means of correlation processes. The distances are then used to obtain the position of the buoys by means of the Multidimensional Scaling Technique (MDS). As an early example of an application using this relative positioning system, a tracking of the position of the buoys at different times is performed. With this tracking, the surface current of a particular region could be studied. The performance of the system is evaluated in terms of the distance from the real position to the estimated one.

Performance improvement for GPS single frequency kinematic relative positioning under poor satellite visibility.

Reliable ambiguity resolution in difficult environments such as during setting/rising events of satellites or during limited satellite visibility is a significant challenge for GPS single frequency kinematic relative positioning. Here, a recursive estimation method combining both code and carrier phase measurements was developed that can tolerate recurrent satellite setting/rising and accelerate initialization in motion. We propose an ambiguity dimension expansion method by utilizing the partial ambiguity relevance of previous and current observations. In essence, this method attempts to integrate all useful information into the recursive estimation equation and performs a better least squares adjustment. Using this method, the success rate of the extended ambiguity estimation is independent of the satellite setting and shows robust performance despite poor satellite visibility. Our model allows integration of other useful information into the recursive process. Actual experiments in urban environments demonstrate that the proposed algorithm can improve the reliability and availability of relative positioning.