Global Positioning System Code Research Articles

Detection of global positioning system spoofing using fusion of signal quality monitoring metrics

This paper reports on the results of a detection performance analysis of a signal quality monitoring (SQM) method used to detect global positioning system (GPS) spoofing. The GPS code tracking was based on a correlation function evaluation of three replicas, namely early, prompt, and late. The receiver synchronized the received code with the local code generated by combining these replicas with a delay lock loop (DLL). In the presence of a GPS spoofer, the correlation was no longer the same because its shape was distorted, leading to a code tracking error. This error relied on the delay and relative phase of the spoofer, and could be used to detect it. In this context, an SQM method based on the fusion of metrics using an OR rule was investigated to detect the spoofer’s presence. Furthermore, closed forms of the optimal thresholds and the probability of detection were derived. The results obtained for different scenarios are presented and analyzed.

Minimum Error Entropy Based EKF for GPS Code Tracking Loop

This paper investigates the minimum error entropy based extended Kalman filter (MEEKF) for multipath parameter estimation of the Global Positioning System (GPS). The extended Kalman filter (EKF) is designed to give a preliminary estimation of the state. The scheme is designed by introducing an additional term, which is tuned according to the higher order moment of the estimation error. The minimum error entropy criterion is introduced for updating the entropy of the innovation at each time step. According to the stochastic information gradient method, an optimal filer gain matrix is obtained. The mean square error criterion is limited to the assumption of linearity and Gaussianity. However, non-Gaussian noise is often encountered in many practical environments and their performances degrade dramatically in non-Gaussian cases. Most of the existing multipath estimation algorithms are usually designed for Gaussian noise. The I (in-phase) and Q (quadrature) accumulator outputs from the GPS correlators are used as the observational measurements of the EKF to estimate the multipath parameters such as amplitude, code delay, phase, and carrier Doppler. One reasonable way to obtain an optimal estimation is based on the minimum error entropy criterion. The MEEKF algorithm provides better estimation accuracy since the error entropy involved can characterize all the randomness of the residual. Performance assessment is presented to evaluate the effectivity of the system designs for GPS code tracking loop with multipath parameter estimation using the minimum error entropy based extended Kalman filter.

Improving GPS Code Phase Positioning Accuracy in Urban Environments Using Machine Learning

The accuracy of location information, mainly provided by the global positioning system (GPS) sensor, is critical for Internet-of-Things applications in smart cities. However, built environments attenuate GPS signals by reflecting or blocking them resulting in some cases multipath and non-line-of-sight (NLOS) reception. These effects cause range errors that degrade GPS positioning accuracy. Enhancements in the design of antennae and receivers deliver a level of reduction of multipath. However, NLOS signal reception and residual effects of multipath are still to be mitigated sufficiently for improvements in range errors and positioning accuracy. Recent machine learning-based methods have shown promise in improving pseudorange-based position solutions by considering multiple variables from raw GPS measurements. However, positioning accuracy is limited by low accuracy signal reception classification. Unlike the existing methods, which use machine learning to directly predict the signal reception classification, we use a gradient boosting decision tree (GBDT)-based method to predict the pseudorange errors by considering the signal strength, satellite elevation angle and pseudorange residuals. With the predicted pseudorange errors, two variations of the algorithm are proposed to improve positioning accuracy. The first corrects pseudorange errors and the other either corrects or excludes the signals determined to contain the effects of multipath and NLOS signals. The results for a challenging urban environment characterized by high-rise buildings on one side, show that the 3-D positioning accuracy of the pseudorange error correction-based positioning measured in terms of the root mean square error is 23.3 m, an improvement of more than 70% over the conventional methods.

Performance Analysis of Static Precise Point Positioning Using Open-Source GAMP

Abstract In addition to Global Positioning System (GPS) constellation, the number of Global Navigation Satellite System (GLONASS) satellites is increasing; it is now possible to evaluate and analyze the position accuracy with both the GPS and GLONASS constellation. In this article, statistical analysis of static precise point positioning (PPP) using GPS-only, GLONASS-only, and combined GPS/GLONASS modes is evaluated. Observational data of 10 whole days from 10 International GNSS Service (IGS) stations are used for analysis. Position accuracy in east, north, up components, and carrier phase/code residuals is analyzed. Multi-GNSS PPP open-source package is used for the PPP performance analysis. The analysis also provides the GNSS researchers the understanding of the observational data processing algorithm. Calculation statistics reveal that standard deviation (STD) of horizontal component is 3.83, 13.80, and 3.33 cm for GPS-only, GLONASS-only, and combined GPS/GLONASS PPP solutions, respectively. Combined GPS/GLONASS PPP achieves better positioning accuracy in horizontal and three-dimensional (3D) accuracy compared with GPS-only and GLONASS-only PPP solutions. The results of the calculation show that combined GPS/GLONASS PPP improves, on an average, horizontal accuracy by 12.11% and 60.33% and 3D positioning accuracy by 10.39% and 66.78% compared with GPS-only and GLONASS-only solutions, respectively. In addition, the results also demonstrate that GPS-only solutions show an improvement of 54.23% and 62.54% compared with GLONASS-only PPP mode in horizontal and 3D components, respectively. Moreover, residuals of GLONASS ionosphere-free code observations are larger than the GPS code residuals. However, phase residuals of GPS and GLONASS phase observations are of the same magnitude.

Evaluation and Application of the GPS Code Observable in Precise Point Positioning

The accuracy of the Global Positioning System (GPS) observable, especially for the code observable, has improved with the development of Global Navigation Satellite System (GNSS) receiver technology. An evaluation of the GPS code observable is presented in this paper, together with a stochastic model for the code and phase observables in Precise Point Positioning (PPP), established using the evaluated results. The results show that the code observables of Leica GNSS receivers are generally better than those of some other brand receivers and the Root Mean Square (RMS) for the code observables of the Leica GRX1200PRO, which includes the multipath effect, reaches 0·71 m, although Coarse/Acquisition (C/A) code observables are tracked. The static positioning of the code observable can reach centimetre level and the convergence time for the JPLM station is just 2·5 hours. The positioning results show that it is difficult to converge the Up direction to the centimetre level, compared with the North and East directions. The results show that static positioning can be correlated with the accumulation characteristic of the error for the code observable, while that that of the kinematic mode can be correlated to the error value. The shortened PPP convergence times verify that the presented stochastic models are effective.

BeiDou Code Pseudorange Precision Estimation and Time Correlation Analysis from Trimble Net-R9 and ComNav 708 Receivers

Stochastic models describe the observation precisions and their correlations with each other and play an important role in reliable global navigation satellite system ambiguity resolution and precise positioning. However, the characteristics of BeiDou Navigation Satellite System (BDS) observations are still not clear at present. In general, the stochastic model used for BDS is based on empirical models from global positioning system (GPS) knowledge in most cases. In this paper, the zero-baseline dual-frequency GPS and BDS data with different sampling intervals are used to evaluate the precision and time correlation of the BDS code pseudorange observations. The results show that the precisions of BDS and GPS code measurements are almost of the same magnitude. However, the standard deviations of BDS measurements are larger than those of GPS measurements. Inclined geostationary orbit observations suffer from periodic error, which has been confirmed to be unaffected by multipath error in this paper. Traditional elevation-dependent models cannot work well for precise positioning for either GPS or BDS because the elevation dependencies of the two carrier frequencies’ pseudorange observations are not the same. Moreover, BDS observations have a significant time correlation, especially for geostationary orbit satellites. The time correlation coefficients are maintained at ~0.63–0.75 for different receiver types. Consequently, the BDS positioning residuals are significantly larger than those of GPS even if the observations have similar precision.

Decentralized Detection of GPS Spoofing in Vehicular Ad Hoc Networks

This letter proposes a decentralized scheme for the detection of global positioning system (GPS) spoofing in vehicular ad hoc networks. In this scheme, vehicles exchange their measured GPS code pseudo-ranges with neighboring vehicles using dedicated short-range communications. The vehicles then perform linear operations on the exchanged GPS data and derive independent statistics that are related to the measurements of each neighbor. Using these statistics, a vehicle implements a cumulative sum procedure to locally detect high correlations in the time of arrival of spoofed GPS signals. The vehicles report their local detection values to an elected head vehicle, which employs a min–max change-detection procedure to optimize the global-spoofing detection. Our experimental results show that: 1) the average detection delay decreases as the number of vehicles increase and 2) the proposed scheme converges to optimal as the probability of false-alarm reduces to zero.

Multipath interference cancelation in GPS time series under changing physical conditions by means of adaptive filtering

Multipath, a highly autocorrelated signal is observable phenomena during time periods longer than the sidereal period of Global Positioning System (GPS) satellites in their constellations. Multipath pattern and sidereal repeat time interaction are examined in terms of time series correlations of topocentric coordinates using GPS code and phase observations collected at high and low frequencies. The horizontal and vertical components at 5 and 30 s sampling rates are analyzed to detect and remove multipath classified by their M P 1 levels and baseline lengths. For the selected 11 stations that have 24-hour data from CORS stations in the USA and Turkey, the repeat times of the GPS constellation were identified as a function of maximum cross-correlation of adjacent time series. The multipath interference signal from two-day time series data is removed by an adaptive filter to improve time series of coordinate estimates. After the filtering process, an effective epoch based position tracking has been accomplished, especially in the height component. The position errors disappeared to maximum possible extent in the pseudo-range measurements. Up to 70% improvement for the phase derived coordinates in reflective environment has been achieved over the baselines ranging from 1 km to 175 km. For the phase observables, the filter success directly related to the multipath level which is specific to the station.

Impact of GPS antenna phase center and code residual variation maps on orbit and baseline determination of GRACE

Precision Orbit Determination (POD) is a prerequisite for the success of many Low Earth Orbiting (LEO) satellite missions. With high-quality, dual-frequency Global Positioning System (GPS) receivers, typically precisions of the order of a few cm are possible for single-satellite POD, and of a few mm for relative POD of formation flying spacecraft with baselines up to hundreds of km. To achieve the best precision, the use of Phase Center Variation (PCV) maps is indispensable. For LEO GPS receivers, often a-priori PCV maps are obtained by a pre-launch ground campaign, which is not able to represent the real space-borne environment of satellites. Therefore, in-flight calibration of the GPS antenna is more widely conducted.This paper shows that a further improvement is possible by including the so-called Code Residual Variation (CRV) maps in absolute/undifferenced and relative/Double-differenced (DD) POD schemes. Orbit solutions are produced for the GRACE satellite formation for a four months test period (August-November, 2014), demonstrating enhanced orbit precision after first using the in-flight PCV maps and a further improvement after including the CRV maps. The application of antenna maps leads to a better consistency with independent Satellite Laser Ranging (SLR) and K-band Ranging (KBR) low-low Satellite-to-Satellite Tracking (ll-SST) observations. The inclusion of the CRV maps results also in a much better consistency between reduced-dynamic and kinematic orbit solutions for especially the cross-track direction. The improvements are largest for GRACE-B, where a cross-talk between the GPS main antenna and the occultation antenna yields higher systematic observation residuals.For high-precision relative POD which necessitates DD carrier-phase ambiguity fixing, in principle frequency-dependent PCV maps would be required. To this aim, use is made of an Extended Kalman Filter (EKF) that is capable of optimizing relative spacecraft dynamics and iteratively fixing the DD carrier-phase ambiguities. It is found that PCV maps significantly improve the baseline solution. CRV maps slightly enhance the baseline precision, more significantly they lead to a much better initialization of the ambiguity fixing. The GRACE single-satellite orbit solutions compare to within a few cm 3-dimensionally with state-of-the-art external orbit solutions and SLR observations, whereas for the baseline a consistency of better than 0.7mm with KBR observations is achieved.

A performance improvement method for low-cost land vehicle GPS/MEMS-INS attitude determination.

Global positioning system (GPS) technology is well suited for attitude determination. However, in land vehicle application, low-cost single frequency GPS receivers which have low measurement quality are often used, and external factors such as multipath and low satellite visibility in the densely built-up urban environment further degrade the quality of the GPS measurements. Due to the low-quality receivers used and the challenging urban environment, the success rate of the single epoch ambiguity resolution for dynamic attitude determination is usually quite low. In this paper, a micro-electro-mechanical system (MEMS)—inertial navigation system (INS)-aided ambiguity resolution method is proposed to improve the GPS attitude determination performance, which is particularly suitable for land vehicle attitude determination. First, the INS calculated baseline vector is augmented with the GPS carrier phase and code measurements. This improves the ambiguity dilution of precision (ADOP), resulting in better quality of the unconstrained float solution. Second, the undesirable float solutions caused by large measurement errors are further filtered and replaced using the INS-aided ambiguity function method (AFM). The fixed solutions are then obtained by the constrained least squares ambiguity decorrelation (CLAMBDA) algorithm. Finally, the GPS/MEMS-INS integration is realized by the use of a Kalman filter. Theoretical analysis of the ADOP is given and experimental results demonstrate that our proposed method can significantly improve the quality of the float ambiguity solution, leading to high success rate and better accuracy of attitude determination.

A multipath mitigation discriminator for GPS receiver

A novel technique for mitigating the multipath-induced code delay estimation error in Global Positioning System (GPS) is proposed. In contrast to conventional methods that aim to eliminate multipath signals, the proposed method exploits them to enhance the direct signal without affecting the accuracy of GPS code delay estimates. To achieve this, coherent accumulation of the received GPS signals is first done by transforming the received data into frequency domain and the parameters of multipath signals are then estimated by sparse reconstruction algorithm. Subsequently, a modified local reference signal is employed in delay lock loop (DLL) of the GPS receiver, which mitigates the pseudo-range estimation error and increases the correlation value of direct GPS signal. Simulation results demonstrate the performance and robustness of the proposed method.

Reduced complexity crosscorrelation interference mitigation in GPS-enabled collaborative ad-hoc wireless networks – Theory

Localization based services rely on Global Positioning System (GPS) receivers embedded in the network nodes, but the satellite signal availability is often limited in indoors environment. Collaborative network-assisted GPS algorithms addressed this issue by communicating various assistance data between the nodes or transforming open-sky nodes into virtual GPS satellite transmitters (pseudolites). Even though such approach improves the coverage, the crosscorrelation problem surfaces due to masking of relatively weak available satellite signals by stronger pseudolites. This paper proposes reduced complexity algorithms to mitigate such a self-jamming (near/far) effect in ad hoc networks. The idea is based on adaptive modifications of dispreading GPS codes in receiver nodes to minimize interference caused by strong pseudolite signals. An optimization problem is formulated for the minimization of interference using mean squared error (MSE) as a cost function. Then computational optimization is achieved through adaptive implementation and parameterized dimension reduction of the optimization problem.

Statistical Analysis of Urban GPS Multipaths and Pseudo-Range Measurement Errors

In urban environments one of the causes of pseudo-range measurement error in Global Positioning System (GPS) is short-delay multipaths due to the scatterers around the receiver. Therefore knowledge of the temporal distribution of GPS multipaths based on a statistical scatterer distribution in an urban environment is essential to estimating the positioning performance and to developing an efficient multipath mitigation technique for urban GPS applications. The work presented here introduces a scatterer distribution model for the urban environment, derives analytical expressions of the consequent time-of-arrival (TOA) probability density function (pdf) with respect to satellite elevation angles, and analyzes the effect of short-delay multipaths on the pseudo-range measurement errors. The expressions derived provide insights into the statistical properties of GPS multipaths and pseudo-range measurement errors in GPS code phase measurement functions due to the short-delay multipaths.

Space Weather and the Global Positioning System

Space Weather and the Global Positioning System

Interferometric Baseline Performance Estimations for Multistatic Synthetic Aperture Radar Configurations Derived from GRACE GPS Observations

Recent studies have demonstrated the usefulness of global positioning system (GPS) receivers for relative positioning of formation-flying satellites using dual-frequency carrier-phase observations. The accurate determination of distances or baselines between satellites flying in formation can provide significant benefits to a wide area of geodetic studies. For spaceborne radar interferometry in particular, such measurements will improve the accuracy of interferometric products such as digital elevation models (DEM) or surface deformation maps. The aim of this study is to analyze the impact of relative position errors on the interferometric baseline performance of multistatic synthetic aperture radar (SAR) satellites flying in such a formation. Based on accuracy results obtained from differential GPS (DGPS) observations between the twin gravity recovery and climate experiment (GRACE) satellites, baseline uncertainties are derived for three interferometric scenarios of a dedicated SAR mission. For cross-track interferometry in a bistatic operational mode, a mean 2D baseline error (1σ) of 1.4 mm is derived, whereas baseline estimates necessary for a monostatic acquisition mode with a 50 km along-track separation reveal a 2D uncertainty of approximately 1.7 mm. Absolute orbit solutions based on reduced dynamic orbit determination techniques using GRACE GPS code and carrier-phase data allows a repeat-pass baseline estimation with an accuracy down to 4 cm (2D 1σ). To assess the accuracy with respect to quality requirements of high-resolution DEMs, topographic height errors are derived from the estimated baseline uncertainties. Taking the monostatic pursuit flight configuration as the worst case for baseline performance, the analysis reveals that the induced low-frequency modulation (height bias) fulfills the relative vertical accuracy requirement (σ<1 m linear point-to-point error) according to the digital terrain elevation data level 3 (DTED-3) specifications for most of the baseline constellations. The use of a GPS-based reduced dynamic orbit determination technique improves the baseline performance for repeat-pass interferometry. The problem of fulfilling the DTED-3 horizontal accuracy requirements is still an issue to be investigated. DGPS can be used as an operational navigation tool for high-precision baseline estimation if a geodetic-grade dual-frequency spaceborne GPS receiver is assumed to be the primary instrument onboard the SAR satellites. The possibility of using only single-frequency receivers, however, requires further research effort.

Reduced dynamic orbit determination using GPS code and carrier measurements

The three-dimensional nature of Global Positioning System (GPS) measurements provides a unique opportunity for accurately determining the position and velocity of satellites in low Earth orbit (LEO). For optimum results a reduced dynamic technique is commonly preferred, which combines the merits of kinematic positioning techniques with those of a fully dynamic trajectory modeling. As part of the present study two different approaches to reduced dynamic orbit determination are compared, both of which involve the estimation of empirical accelerations on top of a precise deterministic force model. In the batch least-squares estimator piece-wise constant accelerations are adjusted in consecutive sub-intervals that are sufficiently short compared to the orbital period. The extended Kalman filter/smoother approach, on the other hand, estimates the empirical accelerations using a first-order Gauss–Markov process noise model. Software implementations of both estimation methods have been used with GPS measurements of the GRACE mission to assess the individual merits of the different filtering schemes. Both approaches are shown to provide accurate and compatible results, which match an external reference solution to better than 5 cm when processing dual-frequency data and better than 10 cm when using single-frequency measurements. While the extended Kalman filter/smoother requires less computer resources in terms of memory and processing time, the batch least-squares estimator ensures a better smoothness of the resulting trajectory and was found to be more robust in case of data gaps.

Integrated adjustment of CHAMP, GRACE, and GPS data

Various types of observations, such as space-borne Global positioning system (GPS) code and phase data, accelerometer data, K-band range and range-rate data, and ground-based satellite laser ranging data of the CHAllenging Minisatellite Payload (CHAMP) and GRAvity Climate Experiment (GRACE) satellite missions, are used together with ground-based GPS code and phase data in a rigorous adjustment to eventually solve for the ephemerides of the CHAMP, GRACE, and GPS satellites, geocenter variations, and low-degree gravity field parameters. It turns out that this ‘integrated’ adjustment considerably improves the accuracy of the ephemerides for the high and low satellites, geocenter variations, and gravity field parameters, compared to the case when the adjustment is carried out stepwise or in individual satellite solutions.

GPS code and carrier multipath mitigation using a multiantenna system

Multipath is a major source of error in high precision Global Positioning System (GPS) static and kinematic differential positioning. Multipath accounts for most of the total error budget in carrier phase measurements in a spacecraft attitude determination system. It is a major concern in reference stations, such as in Local Area Augmentation Systems (LAAS), whereby corrections generated by a reference station, which are based on multipath corrupted measurements, can significantly influence the position accuracy of differential users. Code range, carrier phase, and signal-to-noise (SNR) measurements are all affected by multipath, and the effect is spatially correlated within a small area. In order to estimate and remove code and carrier phase multipath, a system comprising a cluster of five GPS receivers and antennas is used at a reference station location. The spatial correlation of the receiver data, and the known geometry among the antennas, are exploited to estimate multipath for each satellite in each antenna in the system. Generic receiver code and carrier tracking loop discriminator functions are analyzed, and relationships between receiver data, such as code range, carrier phase, and SNR measurements, are formulated and related to various multipath parameters. A Kalman filter is described which uses a combination of the available information from the antennas (receivers) in the multiantenna cluster to estimate various multipath parameters. From the multipath parameters, the code range and carrier phase multipath is estimated and compensated. The technique is first tested on simulated data in a controlled multipath environment. Results are then presented using field data and show a significant reduction in multipath error.

Synergy Between Global Positioning System Code, Carrier, and Signal-to-Noise Ratio Multipath Errors

Global positioning system code, carrier and signal-to-noise ratio (SNR) measurements are corrupted by multipath signals that can signiŽ cantly affect the quality of data used for static and kinematic positioning applications. A tool to simulate code, carrier, and SNR multipath errors in a user-deŽ ned, multiantenna and multire ector environment for multipath error analysis is developed and described. Various relationships between parameters such as the multipath amplitude, phase, and frequency with the satellite dynamics, antenna–re ector distance, antenna–re ector geometry, and signal frequency are derived. Multipath spatial and temporal correlation are analyzed using simulated and Ž eld data. The similarities and differences of code, carrier, and SNRmultipath error characteristics are also investigated.

Precision, Cross Correlation, and Time Correlation of GPS Phase and Code Observations

In high-precision Global Positioning System (GPS) relative positioning applications, the stochastic properties of the GPS observables play a crucial role. The misspecification of the a priori covariance matrix can lead ton non-optimal results and false decisions. In this article, the noise characteristics of seven commonly used GPS receivers are examined. The main areas of our study are the precision of the observations, the time correlation of the observations, and the correlation between the different observation types. In order to examine these characteristics, an experiment was carried out, which will be briefly discussed. As results, the autocorrelation functions, standard deviation, and correlation numbers will be given for the undifferenced observations of the seven receivers. The standard deviation of the phase observation is usually at the submillimeter level, and that of the code observations is some centimeters to decimeters. It will be also shown that none of the receivers are free from correlation between observation types and time correlation, especially the code observations, which suffer from time correlation. The results presented can help to refine stochastic models currently in use. © 2000 John Wiley & Sons, Inc.