Position Dilution Of Precision Research Articles

Environmental spatial data within dense tree cover: exploiting multi-frequency GNSS signals to improve positional accuracy

Environmental monitoring tasks over large spatial coverage often necessitate acquiring sample/reference positions using the global navigation satellite systems in order to optimise operational costs. Often, such tasks occur within dense tree coverage where the navigation signals are blocked. For tasks requiring accurate positions under limited resources, this becomes undesirable, especially if the operation is to be carried out while in motion, i.e. “on the fly” or “real-time kinematic”. Even with this realisation, numerous studies investigating the potential of combining the constellations of these navigation systems mostly focus on their structural aspects, leaving the exploitation of the multi-signal constellation under dense tree cover largely untested. Using a test experiment of a station declared unusable due to dense tree cover at Curtin University (Australia), this study evaluates whether sample positions can be improved using multi-constellation global navigation satellite systems where poor sky visibility exist due to tree coverage. Positioning improvement measures are (1) geometrical gain measured by position dilution of precision, (2) horizontal and vertical uncertainty estimates and (3) positional accuracies determined through the comparison of the obtained control positions and their known values. The results indicate significant positioning improvement when all constellations are utilised in comparison with using Global Positioning System alone in dense tree cover environments, i.e. geometrical gain of as much as 72%, horizontal precisions by about 40%, vertical precisions of up to 50% and 94% accuracy improvement. This study thus opines that utilising full global navigation satellite’s constellation would benefit environmental monitoring tasks carried out under dense tree cover.

Sensor Position Estimation Method for IoT Using Mobile Reference Node

The paper proposes an innovative method of locating objects for the Internet of Things (IoT). The proposed method allows the position of a fixed measuring sensor (MS) to be estimated using one mobile base station with a known position moving around the MS. The mathematical analysis of the method, and three algorithms - Newton's (NA), gradient descent (GD) and genetic (GA) - for solving the system of non-linear positional equations are presented. Next, the analysis of the position dilution of precision (PDoP) parameter for the proposed method, and the Cramér-Rao lower bound (CRLB), limiting the accuracy of the method, are presented. Finally, the results of complex simulation studies on the efficiency of the proposed method for various selected system parameters of the sensor network and convergence of the algorithms used to solve the system of non-linear equations are described.

Пространственный геометрический фактор и развитие ГЛОНАСС

Пространственный геометрический фактор и развитие ГЛОНАСС

A Novel Localization Technique Using Luminous Flux

As global navigation satellite system (GNNS) signals are unable to enter indoor spaces, substitute methods such as indoor localization-based visible light communication (VLC) are gaining the attention of researchers. In this paper, the systematic investigation of a VLC channel is performed for both direct and indirect line of sight (LoS) by utilizing the impulse response of indoor optical wireless channels. In order to examine the localization scenario, two light-emitting diode (LED) grid patterns are used. The received signal strength (RSS) is observed based on the positional dilution of precision (PDoP), a subset of the dilution of precision (DoP) used in global navigation satellite system (GNSS) positioning. In total, 31 × 31 possible positional tags are set for a given PDoP configuration. The values for positional error in terms of root mean square error (RMSE) and the sum of squared errors (SSE) are taken into consideration. The performance of the proposed approach is validated by simulation results according to the selected indoor space. The results show that the position accuracy enhanced is at short range by 24% by utilizing the PDoP metric. As confirmation, the modeled accuracy is compared with perceived accuracy results. This study determines the application and design of future optical wireless systems specifically for indoor localization.

Modeling and Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution

Multi-frequency and multi-GNSS integration is currently becoming an important trend in the development of satellite navigation and positioning technology. In this paper, GPS/Galileo/BeiDou (BDS) precise point positioning (PPP) with ambiguity resolution (AR) are discussed in detail. The mathematical model of triple-system PPP AR and the principle of fractional cycle bias (FCB) estimation are firstly described. With the data of 160 stations in Multi-GNSS Experiment (MGEX) from day of year (DOY) 321-350, 2018, the FCBs of the three systems are estimated and the experimental results show that the range of most GPS wide-lane (WL) FCB is within 0.1 cycles during one month, while that of Galileo WL FCB is 0.05 cycles. For BDS FCB, the classification estimation method is used to estimate the BDS FCB and divide it into GEO and non-GEO (IGSO and MEO) FCB. The variation range of BDS GEO WL FCB can reach 0.5 cycles, while BDS non-GEO WL FCB does not exceed 0.1 cycles within a month. However, the accuracies of GPS, Galileo, and BDS non-GEO narrow-lane (NL) FCB are basically the same. In addition, the number of visible satellites and Position Dilution of Precision (PDOP) values of different combined systems are analyzed and evaluated in this paper. It shows that the triple-system combination can significantly increase the number of observable satellites, optimize the spatial distribution structure of satellites, and is significantly superior to the dual-system and single-system. Finally, the positioning characteristics of single-, dual-, and triple-systems are analyzed. The results of the single station positioning experiment show that the accuracy and convergence speed of the fixed solutions for each system are better than those of the corresponding float solutions. The average root mean squares (RMSs) of the float and the fixed solution in the east and north direction for GPS/Galileo/BDS combined system are the smallest, being 0.92 cm, 0.52 cm and 0.50 cm, 0.46 cm respectively, while the accuracy of the GPS in the up direction is the highest, which is 1.44 cm and 1.27 cm, respectively. Therefore, the combined system can accelerate the convergence speed and greatly enhance the stability of the positioning results.

Improving the GRACE Kinematic Precise Orbit Determination Through Modified Clock Estimating.

Utilizing global positioning system (GPS) to determine the precise kinematic orbits for the twin satellites of the Gravity Recovery and Climate Experiment (GRACE) plays a very important role in the earth’s gravitational and other scientific fields. However, the orbit quality is highly depended on the geometry of observed GPS satellites. In this study, we propose a kinematic orbit determination method for improving the GRACE orbit quality especially when the geometry of observed GPS satellites is weak, where an appropriate random walk clock constraint between adjacent epochs is recommended according to the stability of on-board GPS receiver clocks. GRACE data over one month were adopted in the experimental validation. Results show that the proposed method could improve the root mean square (RMS) by 20–40% in radial component and 5–20% in along and cross components. For those epochs with position dilution of precision (PDOP) larger than 4, the orbits were improved by 50–70% in radial component and 17–50% in along and cross components. Meanwhile, the Allan deviation of clock estimates in the proposed method was much closer to the reported Allan deviation of GRACE on-board oscillator. All the results confirmed the improvement of the proposed method.

Evaluating PDOP in Multi-GNSS Environment

Hybrid operation with two or more Global Navigation Satellite Systems (GNSS) together with (Multi-GNSS) is now popular in the enhanced Signal-in-Space (SiS) scenario that is expected to provide several advantages. The accuracy of solution using GNSS is affected by satellite geometry, quantitatively expressed in terms of Dilution of Precision (DOP) parameters. DOP values indicate the impact of the spatial distribution of the satellites on the final accuracy of the position solution. Evaluation of Position Dilution of Precision (PDOP) is important for the optimum selection of visible satellites of an individual or combined constellation to obtain good accuracy in 3-dimensioanl (3d) position fix. A proposed formulation, to evaluate PDOP in GPS-only environment with 4 satellites using the knowledge of elevation and azimuth of satellites, has been modified here to accommodate Multi-GNSS satellite availability without having any restriction on the number of satellites used for the calculation. Computed PDOP values using this algorithm match well with the data from the GNSS receivers that suggests the appropriate applicability of the algorithm for any constellation combination. Results on the optimum number of satellites for the best satellite geometry are also presented here that shows 23–25 GNSS satellites provide saturated PDOP values below 1, the addition of more satellites does not improve PDOP much.

Kinematic PPP Using Mixed GPS/Glonass Single-Frequency Observations

Abstract Nowadays, Precise Point Positioning (PPP) is a very popular technique for Global Navigation Satellite System (GNSS) positioning. The advantage of PPP is its low cost as well as no distance limitation when compared with the differential technique. Single-frequency receivers have the advantage of cost effectiveness when compared with the expensive dual-frequency receivers, but the ionosphere error makes a difficulty to be completely mitigated. This research aims to assess the effect of using observations from both GPS and GLONASS constellations in comparison with GPS only for kinematic purposes using single-frequency observations. Six days of the year 2018 with single-frequency data for the Ethiopian IGS station named “ADIS” were processed epoch by epoch for 24 hours once with GPS-only observations and another with GPS/GLONASS observations. In addition to “ADIS” station, a kinematic track in the New Aswan City, Aswan, Egypt, has been observed using Leica GS15, geodetic type, dual-frequency, GPS/GLONASS GNSS receiver and single-frequency data have been processed. Net_Diff software was used for processing all the data. The results have been compared with a reference solution. Adding GLONASS satellites significantly improved the satellite number and Position Dilution Of Precision (PDOP) value and accordingly improved the accuracy of positioning. In the case of “ADIS” data, the 3D Root Mean Square Error (RMSE) ranged between 0.273 and 0.816 m for GPS only and improved to a range from 0.256 to 0.550 m for GPS/GLONASS for the 6 processed days. An average improvement ratio of 24%, 29%, 30%, and 29% in the east, north, height, and 3D position components, respectively, was achieved. For the kinematic trajectory, the 3D position RMSE improved from 0.733 m for GPS only to 0.638 m for GPS/GLONASS. The improvement ratios were 7%, 5%, 28%, and 13% in the east, north, height, and 3D position components, respectively, for the kinematic trajectory data. This opens the way to add observations from the other two constellations (Galileo and BeiDou) for more accuracy in future research.

Analytical optimization on GNSS buoy array for underwater positioning

Global navigation satellite system (GNSS)/acoustic positioning precision is determined by the positioning geometry and the ranging precision; thus optimizing GNSS buoys array is meaningful to improve the positioning accuracy and reliability. An analytical method is proposed for optimizing the GNSS buoys array with regard to the cutoff angle constraints for underwater acoustic observations. For the practical limitation of coplanarity of GNSS buoys and the cutoff angle, an algorithm is proposed to analytically minimize the position dilution of precision (PDOP). The proposed method is validated to give complete solutions of PDOP minimization with five GNSS buoys. At last, in order to search a best configuration among the PDOP solution set, we propose a search algorithm to get the solution with the smallest geometric dilution of precision (GDOP). It indicates that within a given region, the GDOP minimization at the center of a region is equivalent to the PDOP mean minimization over the region. The relation between the positioning accuracy and the positioning geometry with five known points is illustrated in an experiment performed in South China Sea.

Triple-frequency carrier phase precise time and frequency transfer models for BDS-3

The third-generation BeiDou navigation satellite system (BDS-3) began providing global positioning, navigation and timing service on December 27, 2018. We present three triple-frequency carrier phase (CP) precise time and frequency transfer models using the BDS-3 B1I/B3I/B2a signals, named IF-PPP1, IF-PPP2 and UC-PPP models, respectively. The BDS B1I/B3I dual-frequency ionospheric-free (IF) model is also introduced, known as IF-PPP0 model. The corresponding mathematical and stochastic models are developed. Two stations located at time laboratories and connected to a high-precision atomic clock are utilized to assess the performances of the proposed CP precise time and frequency transfer models. In addition, the number of visible satellites, position dilution of precision, time dilution of precision, estimated positioning errors, zenith tropospheric delay and inter-frequency bias for two stations are also analyzed. The results show that BDS CP precise time and frequency transfer can achieve better performances with increasing number of BDS-3 observations. The proposed models all can be applied for precise time and frequency transfer with the BDS-3 triple-frequency signals, with stability and accuracy identical to the BDS IF-PPP0 solution. The stability of 10,000 s for the proposed BDS CP precise time and frequency models is better than 1.5 × 10−14.

Initial Positioning Assessment of BDS New Satellites and New Signals

With the official announcement of open service since the end of 2018, the BeiDou navigation satellite system (BDS) has started to provide global positioning, navigation and timing (PNT) services. Thus, it is worth assessing the positioning service of new BDS satellites and signals. In this paper, we comprehensively assess the system status and the global positioning performance of BDS regarding single point positioning (SPP) and real-time kinematic (RTK) performance. Results show that the signal in space range error (SISRE) of BDS-3 satellites is superior to that of BDS-2 satellites, showing an overall accuracy of 0.71 m versus 0.97 m, which is competitive with GPS and Galileo. With the contribution of BDS-3, the number of global average visible satellites has increased from 5.1 to 10.7, which provides a mean global position dilution of precision (PDOP) value better than 6 at 99.88% and the mean availability of basic PNT performance is also improved from 35.25% to 98.84%. One week of statistical results from 54 globally distributed international GNSS service (IGS) stations show that the root mean square (RMS) of SPP accuracy is 1.1 m in horizontal and 2.2 m in vertical, which is at the same level of GPS. The new B1c and B2a signals show a smaller observation noise than B1I, and SPP performance of B1c is similar to that of B1I. However, the positioning precision is slightly worse at the B2a frequency, which may be due to the inaccurate BDS ionosphere correction. As for short baseline RTK, baseline accuracy is also improved due to the increased number of new BDS satellites.

Assessment of BeiDou-3 and Multi-GNSS Precise Point Positioning Performance.

With the launch of BDS-3 and Galileo new satellites, the BeiDou navigation satellite system (BDS) has developed from the regional to global system, and the Galileo constellation will consist of 26 satellites in space. Thus, BDS, GPS, GLONASS, and Galileo all have the capability of global positioning services. It is meaningful to evaluate the ability of global precise point positioning (PPP) of the GPS, BDS, GLONASS, and Galileo. This paper mainly contributes to the assessment of BDS-2, BDS-2/BDS-3, GPS, GLONASS, and Galileo PPP with the observations that were provided by the international Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS). The Position Dilution of Precision (PDOP) value was utilized to research the global coverage of GPS, BDS-2, BDS-2/BDS-3, GLONASS, and Galileo. In particular, GPS-only, BDS-2-only, BDS-2/BDS-3, GLONASS-only, Galileo-only, and multi-GNSS combined PPP solutions were analyzed to verify the capacity of the PPP performances in terms of positioning accuracy, convergence time, and zenith troposphere delay (ZTD) accuracy. In view of PDOP, the current BDS and Galileo are capable of global coverage. The BDS-2/BDS-3 and Galileo PDOP values are fairly evenly distributed around the world similar to GPS and GLONASS. The root mean square (RMS) of positioning errors for static BDS-2/BDS-3 PPP and Galileo-only PPP are 10.7, 19.5, 20.4 mm, and 6.9, 18.6, 19.6 mm, respectively, in the geographic area of the selected station, which is the same level as GPS and GLONASS. It is worth mentioning that, by adding BDS-3 observations, the positioning accuracy of static BDS PPP is improved by 17.05%, 24.42%, and 35.65%, and the convergence time is reduced by 27.15%, 27.87%, and 35.76% in three coordinate components, respectively. Similar to the static positioning, GPS, BDS-2/BDS-3, GLONASS, and Galileo have the basically same kinematic positioning accuracy. Multi-GNSS PPP significantly improves the positioning performances in both static and kinematic positioning. In terms of ZTD accuracy, the difference between GPS, BDS-2/BDS-3, GLONASS, and Galileo is less than 1 mm, and the BDS-2/BDS-3 improves ZTD accuracy by 20.48% over the BDS-2. The assessment of GPS, BDS-2, BDS-2/BDS-3, GLONASS, Galileo, and multi-GNSS global PPP performance are shown to make comments for the development of multi-GNSS integration, global precise positioning, and the construction of iGMAS.

A Low-Cost Underground Garage Navigation Switching Algorithm Based on Kalman Filtering.

Modern parking lots have gradually developed into underground garages to improve the efficient use of space. However, the complex design of parking lots also increases the demands on vehicle navigation. The traditional method of navigation switching only uses satellite signals. After the Position Dilution Of Precision (PDOP) of satellite signals is over the limit, vehicle navigation will enter indoor mode. It is not suitable for vehicles in underground garages to switch modes with a fast-response system. Therefore, this paper chooses satellite navigation, inertial navigation, and the car system to combine navigation. With the condition that the vehicle can freely travel through indoor and outdoor environments, high-precision outdoor environment navigation is used to provide the initial state of underground navigation. The position of the vehicle underground is calculated by the Dead Reckoning (DR) navigation system. This paper takes advantage of the Extended Kalman Filter (EKF) algorithm to provide two freely switchable navigation modes for vehicles in ground and underground garages. The continuity, robustness, fast response, and low cost of the indoor and outdoor switching navigation methods are verified in real-time systems.

A Fuzzy-Innovation-Based Adaptive Kalman Filterfor Enhanced Vehicle Positioning in DenseUrban Environments.

In this paper, a fuzzy-innovation based adaptive extended Kalman filter (FI-AKF) is proposed to improve the performance of the GNSS/INS fusion system, which is degraded due to satellite signal cutoff and attenuation and inaccurate modeling in dense urban environments. The information used for sensor fusion is obtained from real-time kinematic (RTK), micro-electro-mechanical system based inertial measumrement unit (MEMS-IMU), and on-board diagnostics (OBD). The fuzzy logic system is proposed to adaptively update the measurement covariance matrix of the RTK according to the position dilution of precision (PDOP), the number of receivable satellites, and the innovation of the extended Kalman filter (EKF). In addition, the driving state of the vehicle is defined as stop, straight run, left/right turn, and the like. To reduce the heading estimation error of the Kalman filter, the estimated heading is corrected according to the driving state. Also, the measurement covariance matrices of IMU and OBD are applied adaptively considering the characteristics of each sensor according to the driving state. In order to analyze the performance of the proposed FI-AKF positioning system in a dense urban environment, a computer simulation is performed. The proposed FI-AKF is compared to the performance of the existing extended Kalman filter and the innovation-based adaptive extended Kalman filter. In addition, we conduct a performance comparison experiment with a commercial positioning system in the field test. Through each experiment, it is confirmed that the proposed FI-AKF system has higher positioning performance than the comparison positioning systems in a dense urban environment.

GNSS RTK Positioning Augmented with Large LEO Constellation

It is widely known that in real-time kinematic (RTK) solution, the convergence and ambiguity-fixed speeds are critical requirements to achieve centimeter-level positioning, especially in medium-to-long baselines. Recently, the current status of the global navigation satellite systems (GNSS) can be improved by employing low earth orbit (LEO) satellites. In this study, an initial assessment is applied for LEO constellations augmented GNSS RTK positioning, where four designed LEO constellations with different satellite numbers, as well as the nominal GPS constellation, are simulated and adopted for analysis. In terms of aforementioned constellations solutions, the statistical results of a 68.7-km baseline show that when introducing 60, 96, 192, and 288 polar-orbiting LEO constellations, the RTK convergence time can be shortened from 4.94 to 2.73, 1.47, 0.92, and 0.73 min, respectively. In addition, the average time to first fix (TTFF) can be decreased from 7.28 to 3.33, 2.38, 1.22, and 0.87 min, respectively. Meanwhile, further improvements could be satisfied in several elements such as corresponding fixing ratio, number of visible satellites, position dilution of precision (PDOP) and baseline solution precision. Furthermore, the performance of the combined GPS/LEO RTK is evaluated over various-length baselines, based on convergence time and TTFF. The research findings show that the medium-to-long baseline schemes confirm that LEO satellites do helpfully obtain faster convergence and fixing, especially in the case of long baselines, using large LEO constellations, subsequently, the average TTFF for long baselines has a substantial shortened about 90%, in other words from 12 to 2 min approximately by combining with the larger LEO constellation of 192 or 288 satellites. It is interesting to denote that similar improvements can be observed from the convergence time.

BeiDou Augmented Navigation from Low Earth Orbit Satellites.

Currently, the Global Navigation Satellite System (GNSS) mainly uses the satellites in Medium Earth Orbit (MEO) to provide position, navigation, and timing (PNT) service. The weak navigation signals limit its usage in deep attenuation environments, and make it easy to interference and counterfeit by jammers or spoofers. Moreover, being far away to the Earth results in relatively slow motion of the satellites in the sky and geometric change, making long time needed for achieved centimeter positioning accuracy. By using the satellites in Lower Earth Orbit (LEO) as the navigation satellites, these disadvantages can be addressed. In this contribution, the advantages of navigation from LEO constellation has been investigated and analyzed theoretically. The space segment of global Chinese BeiDou Navigation Satellite System consisting of three GEO, three IGSO, and 24 MEO satellites has been simulated with a LEO constellation with 120 satellites in 10 orbit planes with inclination of 55 degrees in a nearly circular orbit (eccentricity about 0.000001) at an approximate altitude of 975 km. With simulated data, the performance of LEO constellation to augment the global Chinese BeiDou Navigation Satellite System (BeiDou-3) has been assessed, as one of the example to show the promising of using LEO as navigation system. The results demonstrate that the satellite visibility and position dilution of precision have been significantly improved, particularly in mid-latitude region of Asia-Pacific region, once the LEO data were combined with BeiDou-3 for navigation. Most importantly, the convergence time for Precise Point Positioning (PPP) can be shorted from about 30 min to 1 min, which is essential and promising for real-time PPP application. Considering there are a plenty of commercial LEO communication constellation with hundreds or thousands of satellites, navigation from LEO will be an economic and promising way to change the heavily relay on GNSS systems.

Уточнение геометрической интерпретации пространственного геометрического фактора в ГНСС

Уточнение геометрической интерпретации пространственного геометрического фактора в ГНСС

Node‐pair selection scheme based on modified PDOP for cooperative triangulation

This Letter proposes a scheme to select a pair of nodes for cooperative triangulation-based localisation. The authors select the pair of nodes by considering the position dilution of precision (PDOP) and the noise power of the measured distance error. The proposed scheme reduces the localisation error by considering the measured distance errors of the positioning user equipment (UE) and the cooperative UE at the same time in calculating PDOP. The simulation results show that the proposed scheme provides higher positioning accuracy than the conventional triangulation schemes.

THE USE OF FUZZY RULE-BASED SYSTEMS IN DETERMINING HORIZONTAL PCO PARAMETERS OF GNSS ANTENNAS

Abstract Knowledge concerning Phase Center Offset (PCO) is an important aspect in the calibration of GNSS antennas and has a direct influence on the quality of high precision positioning. Studies show that there is a correlation between meteorological variables when determining the north (N), east (E) and vertical Up (H) components of PCO. This article presents results for the application of Fuzzy Rule-Based Systems (FRBS) for determining the position of these components. The function Adaptive Neuro-Fuzzy Inference Systems (ANFIS) was used to generate FRBS, with the PCO components as output variables. As input data, the environmental variables such as temperature, relative humidity and precipitation were used; along with variables obtained from the antenna calibration process such as Positional Dilution of Precision and the multipath effect. An FRBS was constructed for each planimetric N and E components from the carriers L1 and L2, using a training data set by means of ANFIS. Once the FRBS were defined, the verification data set was applied, the components obtained by the FRBS and Antenna Calibration Base at the Federal University of Paraná were compared. For planimetric components, the difference was less than 1.00 mm, which shows the applicability of the method for horizontal components.

How much can we trust GPS wildlife tracking? An assessment in semi-free-ranging Crested Ibis Nipponia nippon.

GPS tracking has been increasingly used for wildlife studies in recent decades, but its performance has not been fully assessed, especially for newly developed lightweight transmitters. We assessed the performance of eight GPS transmitters developed in China by attaching them to Crested Ibises Nipponia nippon confined to two acclimation cages mimicking real habitats. We calculated the distance between GPS locations and the centroid of the cages as the positioning error, and used the 95% (95th percentile) positioning errors to define the accuracy. The positioning success averaged 92.0%, which is much higher than that of previous studies. Locations were not evenly distributed by Location Class (LC), with the LC A and B locations accounting for 88.7%. The observed 95% positioning error in the locations of LC A (9–39 m) and B (11–41 m) was quite accurate, while up to 6.9–8.8% of poor-quality locations were detected in LC C and D with >100 m or even >1, 000 m positioning error. Positioning success and accuracy were different between the test sites, probably due to the difference in vegetation structure. Thus, we argue that the tested transmitters could provide a large proportion of high-quality data for fine-scale studies, and a number of poor-quality locations that need attention. We suggest that the HPOD (horizontal dilution of precision) or PDOP (positional dilution of precision) be reported instead of the LC as a measurement of location accuracy for each location to ensure identification and filtering of implausible locations.