LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications.

Download Full-text

An Improved Multipath Mitigation Method and Its Application in Real-Time Bridge Deformation Monitoring

Remote Sensing ◽

10.3390/rs13122259 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2259

Author(s):

Ruicheng Zhang ◽

Chengfa Gao ◽

Qing Zhao ◽

Zihan Peng ◽

Rui Shang

Keyword(s):

Real Time ◽

Sampling Rate ◽

Threshold Value ◽

Deformation Monitoring ◽

Success Rates ◽

Multipath Mitigation ◽

Mode Decomposition ◽

Observation Noise ◽

Original Observation ◽

Better Than

A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to the influence of observation noise and the multipath differences between different satellites. Aiming at the insufficiency of MHM in dealing with the adverse impact of observation noise, we proposed the MHM_V model, based on Variational Mode Decomposition (VMD) and the MHM algorithm. Utilizing the VMD algorithm to extract the multipath from single-difference (SD) residuals, and according to the principle of the closest elevation and azimuth, the original observation of carrier phase in the few days following the implementation are corrected to mitigate the influence of the multipath. The MHM_V model proposed in this paper is verified and compared with the traditional MHM algorithm by using the observed data of the Forth Road Bridge with a seven day and 10 s sampling rate. The results show that the correlation coefficient of the multipath on two adjacent days was increased by about 10% after residual denoising with the VMD algorithm; the standard deviations of residual error in the L1/L2 frequencies were improved by 37.8% and 40.7%, respectively, which were better than the scores of 26.1% and 31.0% for the MHM algorithm. Taking a ratio equal to three as the threshold value, the fixed success rates of ambiguity were 88.0% without multipath mitigation and 99.4% after mitigating the multipath with MHM_V. The MHM_V algorithm can effectively improve the success rate, reliability, and convergence rate of ambiguity resolution in a bridge multipath environment and perform better than the MHM algorithm.

Download Full-text

Impact of robot antenna calibration on dual-frequency smartphone-based high-accuracy positioning: a case study using the Huawei Mate20X

GPS Solutions ◽

10.1007/s10291-020-01048-0 ◽

2020 ◽

Vol 25 (1) ◽

Author(s):

Francesco Darugna ◽

Jannes B. Wübbena ◽

Gerhard Wübbena ◽

Martin Schmitz ◽

Steffen Schön ◽

...

Keyword(s):

Ambiguity Resolution ◽

High Accuracy ◽

Global Navigation Satellite Systems ◽

Test Case ◽

Dual Frequency ◽

Main Site ◽

Satellite Systems ◽

The Individual ◽

The Impact ◽

Antenna Calibration

Abstract The access to Android-based Global Navigation Satellite Systems (GNSS) raw measurements has become a strong motivation to investigate the feasibility of smartphone-based positioning. Since the beginning of this research, the smartphone GNSS antenna has been recognized as one of the main limitations. Besides multipath (MP), the radiation pattern of the antenna is the main site-dependent error source of GNSS observations. An absolute antenna calibration has been performed for the dual-frequency Huawei Mate20X. Antenna phase center offset (PCO) and variations (PCV) have been estimated to correct for antenna impact on the L1 and L5 phase observations. Accordingly, we show the relevance of considering the individual PCO and PCV for the two frequencies. The PCV patterns indicate absolute values up to 2 cm and 4 cm for L1 and L5, respectively. The impact of antenna corrections has been assessed in different multipath environments using a high-accuracy positioning algorithm employing an undifferenced observation model and applying ambiguity resolution. Successful ambiguity resolution is shown for a smartphone placed in a low multipath environment on the ground of a soccer field. For a rooftop open-sky test case with large multipath, ambiguity resolution was successful in 19 out of 35 data sets. Overall, the antenna calibration is demonstrated being an asset for smartphone-based positioning with ambiguity resolution, showing cm-level 2D root mean square error (RMSE).

Download Full-text

First Preliminary Fast Static Ambiguity Resolution Results of Medium-Baseline with Triple-Frequency Beidou Wavebands

Journal of Navigation ◽

10.1017/s0373463314000332 ◽

2014 ◽

Vol 67 (6) ◽

pp. 1109-1119 ◽

Cited By ~ 6

Author(s):

Shengyue Ji ◽

Xiaolong Wang ◽

Ying Xu ◽

Zhenjie Wang ◽

Wu Chen ◽

...

Keyword(s):

Frequency Band ◽

Ambiguity Resolution ◽

Past Research ◽

Satellite System ◽

Tropospheric Delay ◽

Dual Frequency ◽

Long Distance ◽

Triple Frequency ◽

Global Navigation Satellite ◽

Better Than

Fast high precision relative Global Navigation Satellite System (GNSS) positioning is very important to various applications and ambiguity resolution is a key requirement. It has been a continuing challenge to determine and fix GNSS carrier-phase ambiguity, especially for medium- and long-distance baselines. In past research, with dual-frequency band Global Positioning System (GPS), it is almost impossible for fast ambiguity resolution of medium- and long-distance baselines mainly due to the ionospheric and tropospheric effects. With the launch of the BeiDou system, triple-frequency band GNSS observations are available for the first time. This research aims to test the ambiguity resolution performance with BeiDou triple-frequency band observations. In this research, two mathematical models are compared: zenith tropospheric delay as an unknown parameter versus corrected tropospheric delay. The ambiguity resolution performance is investigated in detail with BeiDou observations. Different distance baselines are tested: 45 km, 70 km and 100 km and the performances are investigated with different elevation cut-off angles. Also the performance with BeiDou alone and combined BeiDou and GPS are compared. Experimental results clearly show that with practical observations of triple-frequency bands, ambiguity of medium- or long-distance baselines can be fixed. The results also show that: the performance of ambiguity resolution with an elevation cutoff angle of 20° is much better than that of 15°; The performance with tropospheric effect corrected is slightly better than that with tropospheric effect as an estimated parameter; Dual-frequency band GPS observations will benefit ambiguity resolution of integrated BeiDou and GPS.

Download Full-text

Real-Time PPP-RTK Performance Analysis Using Ionospheric Corrections from Multi-Scale Network Configurations

Sensors ◽

10.3390/s20113012 ◽

2020 ◽

Vol 20 (11) ◽

pp. 3012 ◽

Cited By ~ 3

Author(s):

Dimitrios Psychas ◽

Sandra Verhagen

Keyword(s):

Real Time ◽

Ambiguity Resolution ◽

Ionospheric Disturbance ◽

The United States ◽

Integer Ambiguity ◽

Convergence Time ◽

Dual Frequency ◽

Multi Scale ◽

Time Required ◽

The Impact

The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially reduce the time required to achieve centimeter-level accuracy. In this study, we present and analyze the real-time PPP-RTK user performance using ionospheric corrections from multi-scale regional networks during a day with medium ionospheric disturbance. It is the goal of this contribution to measure the impact the network dimension has on the ambiguity-resolved user position through the predicted ionospheric corrections. The user-specific undifferenced ionospheric corrections are computed at the network side, along with the satellite phase biases needed for single-receiver ambiguity resolution, using the best linear unbiased predictor. Such corrections necessitate the parameterization of an estimable user receiver code bias, on which emphasis is given in this study. To this end, we process GPS dual-frequency data from four four-station evenly distributed CORS networks in the United States with varying station spacings in order to evaluate if and to what extent the ionospheric corrections from multi-scale networks can improve the user convergence times. Based on a large number of samples, our experimental results showed that sub-10 cm horizontal accuracy can be achieved almost instantaneously in the ionosphere-weighted partially-ambiguity-fixed kinematic PPP-RTK solutions based on corrections from a network with 68 km spacing. Most of the solutions (90%) were shown to require less than 6.0 min, compared to the ionosphere-float PPP solutions that needed 68.5 min. In case of sparser networks with 115, 174 and 237 km spacing, 50% of the horizontal positioning errors are shown to become less than one decimeter after 1.5, 4.0 and 7.0 min, respectively, while 90% of them require 10.5, 16.5 and 20.0 min. We also numerically demonstrated that the user’s convergence times bear a linear relationship with the network density and get shorter as the density increases, for both full and partial ambiguity resolution.

Download Full-text

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Artificial Satellites ◽

10.2478/arsa-2014-0001 ◽

2014 ◽

Vol 49 (1) ◽

pp. 1-19 ◽

Cited By ~ 3

Author(s):

Dominik Próchniewicz

Keyword(s):

Stochastic Model ◽

Ambiguity Resolution ◽

Degrees Of Freedom ◽

Correction Term ◽

Optimal Estimation ◽

Mountain Area ◽

Network Rtk ◽

High Level ◽

The Impact ◽

Correction Terms

ABSTRACT The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

Download Full-text

Advertising Media Impact in Consumer Buying Behavior

Journal of Balkumari College ◽

10.3126/jbkc.v8i0.29310 ◽

2019 ◽

Vol 8 ◽

pp. 54-56

Author(s):

Ashmita Dahal Chhetri

Keyword(s):

Consumer Behavior ◽

Young Male ◽

Electronic Media ◽

Buying Behavior ◽

Media Impact ◽

High Degree ◽

The Impact ◽

Buying Behaviors ◽

The Relationship ◽

Better Than

Advertisements have been used for many years to influence the buying behaviors of the consumers. Advertisements are helpful in creating the awareness and perception among the customers of a product. This particular research was conducted on the 100 young male and female who use different brands of product to check the influence of advertisement on their buying behavior while creating the awareness and building the perceptions. Correlation, regression and other statistical tools were used to identify the relationship between these variables. The results revealed that the relationship between media and consumer behavior is positive. The adve1tising impact on sales and there is positive and high degree relationship between advertising and consumer behavior. The impact on advertising of a product of electronic media is better than non-electronic media.

Download Full-text

Empirical Stochastic Model of Multi-GNSS Measurements

Sensors ◽

10.3390/s21134566 ◽

2021 ◽

Vol 21 (13) ◽

pp. 4566

Author(s):

Dominik Prochniewicz ◽

Kinga Wezka ◽

Joanna Kozuchowska

Keyword(s):

Stochastic Model ◽

Density Ratio ◽

Functional Model ◽

Optimal Solution ◽

Global Navigation Satellite Systems ◽

Unknown Parameters ◽

Short Baseline ◽

Stochastic Parameters ◽

Dependent Model ◽

The Impact

The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

Download Full-text

Locking down the Impact of New Zealand’s COVID-19 Alert Level Changes on Pets

Animals ◽

10.3390/ani11030758 ◽

2021 ◽

Vol 11 (3) ◽

pp. 758

Author(s):

Fiona Esam ◽

Rachel Forrest ◽

Natalie Waran

Keyword(s):

New Zealand ◽

Separation Anxiety ◽

National Surveys ◽

Normal Life ◽

Pet Owners ◽

Level 1 ◽

The Impact ◽

Better Than

The influence of the COVID-19 pandemic on human-pet interactions within New Zealand, particularly during lockdown, was investigated via two national surveys. In Survey 1, pet owners (n = 686) responded during the final week of the five-week Alert Level 4 lockdown (highest level of restrictions—April 2020), and survey 2 involved 498 respondents during July 2020 whilst at Alert Level 1 (lowest level of restrictions). During the lockdown, 54.7% of owners felt that their pets’ wellbeing was better than usual, while only 7.4% felt that it was worse. Most respondents (84.0%) could list at least one benefit of lockdown for their pets, and they noted pets were engaged with more play (61.7%) and exercise (49.7%) than pre-lockdown. Many respondents (40.3%) expressed that they were concerned about their pet’s wellbeing after lockdown, with pets missing company/attention and separation anxiety being major themes. In Survey 2, 27.9% of respondents reported that they continued to engage in increased rates of play with their pets after lockdown, however, the higher levels of pet exercise were not maintained. Just over one-third (35.9%) of owners took steps to prepare their pets to transition out of lockdown. The results indicate that pets may have enjoyed improved welfare during lockdown due to the possibility of increased human-pet interaction. The steps taken by owners to prepare animals for a return to normal life may enhance pet wellbeing long-term if maintained.

Download Full-text

Improving the Stochastic Model of Ionospheric Delays for BDS Long-Range Real-Time Kinematic Positioning

Remote Sensing ◽

10.3390/rs13142739 ◽

2021 ◽

Vol 13 (14) ◽

pp. 2739

Author(s):

Huizhong Zhu ◽

Jun Li ◽

Longjiang Tang ◽

Maorong Ge ◽

Aigong Xu

Keyword(s):

Real Time ◽

Long Range ◽

Ionospheric Delay ◽

Time Interval ◽

Short Time Interval ◽

Dual Frequency ◽

Triple Frequency ◽

Ambiguity Fixing ◽

Power Spectral ◽

Observation Noise

Although ionosphere-free (IF) combination is usually employed in long-range precise positioning, in order to employ the knowledge of the spatiotemporal ionospheric delays variations and avoid the difficulty in choosing the IF combinations in case of triple-frequency data processing, using uncombined observations with proper ionospheric constraints is more beneficial. Yet, determining the appropriate power spectral density (PSD) of ionospheric delays is one of the most important issues in the uncombined processing, as the empirical methods cannot consider the actual ionosphere activities. The ionospheric delays derived from actual dual-frequency phase observations contain not only the real-time ionospheric delays variations, but also the observation noise which could be much larger than ionospheric delays changes over a very short time interval, so that the statistics of the ionospheric delays cannot be retrieved properly. Fortunately, the ionospheric delays variations and the observation noise behave in different ways, i.e., can be represented by random-walk and white noise process, respectively, so that they can be separated statistically. In this paper, we proposed an approach to determine the PSD of ionospheric delays for each satellite in real-time by denoising the ionospheric delay observations. Based on the relationship between the PSD, observation noise and the ionospheric observations, several aspects impacting the PSD calculation are investigated numerically and the optimal values are suggested. The proposed approach with the suggested optimal parameters is applied to the processing of three long-range baselines of 103 km, 175 km and 200 km with triple-frequency BDS data in both static and kinematic mode. The improvement in the first ambiguity fixing time (FAFT), the positioning accuracy and the estimated ionospheric delays are analysed and compared with that using empirical PSD. The results show that the FAFT can be shortened by at least 8% compared with using a unique empirical PSD for all satellites although it is even fine-tuned according to the actual observations and improved by 34% compared with that using PSD derived from ionospheric delay observations without denoising. Finally, the positioning performance of BDS three-frequency observations shows that the averaged FAFT is 226 s and 270 s, and the positioning accuracies after ambiguity fixing are 1 cm, 1 cm and 3 cm in the East, North and Up directions for static and 3 cm, 3 cm and 6 cm for kinematic mode, respectively.

Download Full-text

Characterization of Carrier Phase-Based Positioning in Real-World Jamming Conditions

Remote Sensing ◽

10.3390/rs13142680 ◽

2021 ◽

Vol 13 (14) ◽

pp. 2680

Author(s):

Søren Skaarup Larsen ◽

Anna B. O. Jensen ◽

Daniel H. Olesen

Keyword(s):

Real World ◽

Carrier Phase ◽

Reference Station ◽

Baseline Length ◽

Dual Frequency ◽

Positioning Accuracy ◽

The Impact ◽

Single Versus ◽

Selection Of

GNSS signals arriving at receivers at the surface of the Earth are weak and easily susceptible to interference and jamming. In this paper, the impact of jamming on the reference station in carrier phase-based relative baseline solutions is examined. Several scenarios are investigated in order to assess the robustness of carrier phase-based positioning towards jamming. Among others, these scenarios include a varying baseline length, the use of single- versus dual-frequency observations, and the inclusion of the Galileo and GLONASS constellations to a GPS only solution. The investigations are based on observations recorded at physical reference stations in the Danish TAPAS network during actual jamming incidents, in order to realistically evaluate the impact of real-world jamming on carrier phase-based positioning accuracy. The analyses performed show that, while there are benefits of using observations from several frequencies and constellations in positioning solutions, special care must be taken in solution processing. The selection of which GNSS constellations and observations to include, as well as when they are included, is essential, as blindly adding more jamming-affected observations may lead to worse positioning accuracy.

Download Full-text