Pseudorange Error Research Articles

Adaptive multipath mitigation tracking system for GPS receiver

Multipath effects are the major source of error in GPS differential positioning. In this paper, an adaptive multipath mitigation tracking system is presented for GPS applications. It is comprised of four function blocks, those being (1) adaptive path estimator (APE), (2) multipath interference reproducer (MPIR), (3) Rake-based delay locked loop (RB-DLL), and (4) Rake-based phase locked loop (RB-PLL). Only the short delay condition with delay less than 1.5 PN chip is considered here, because GPS pseudorange error envelope decreases to zero for delay time greater than 1.5 PN chip. In order to estimate reflection profile in the correlation domain, the FFT-based circular correlation and block average method (BAM) are utilized to offer significant savings in computational complexity. The APE estimates the delayed profiles and coefficients of the reflection signals. By using the path parameters from APE, the corresponding multipath arms are activated to accomplish the multipath reproduction. These replica profiles are used for subtracting the reflection components from carrier and code discriminators before sending it into the Rake-based carrier/code tracking loops. Simulation results show that our proposed method provides a better performance in terms of multipath error envelope and carrier-phase error.

Study of a New Pseudo-Range Differential Method for the Correction of Ephemeris Error and Ionospheric Error

Pseudo-range differential is an important differential method, but the pseudo-range differential precision becomes decreased with the increase of distance between users and the reference stations. A new pseudo-range differential method is proposed, that is wide-area-weighted pseudo-range differential method. Six pseudo-range differential reference stations are built in China region, the user choose pseudo-range correction data of the reference stations near the user which use the weighted data as its pseudo-range correction, which can achieve high precision pseudo-range differential in wide area. Selection method of the right and reference station is researched, the method is verified by simulation test, the weighted data method of six, five, four and three reference stations for ephemeris and ionospheric error correction condition is analyzed, and simulation results show that: using the weighted pseudo-range observation error of the three stations nearest the users has the best correction effect among them, in the whole China region, which can achieve precision superior to 0.5m about pseudo-range differential.

GNSS accuracy enhancement based on pseudo range error estimation in an urban propagation environment

For new ITS applications, positioning solutions will require to be more accurate and available. The most common technique used today is composed of a GPS receiver, sometimes aided by other sensors. GPS, and GNSS in general, suffer from masking effects and propagation disturbances in urban areas that cause biases on pseudo range measurements. Mitigation solutions sometimes propose to detect and exclude outliers but in land transportation applications, such a decision reduces dramatically the service availability and thus, the interest of satellite-based solutions. In order to optimize the use the satellites received, we propose a new positioning algorithm based on signals only with pseudo range error modeling in association with an adapted filtering process. The model and the filter have been validated with simulation data performed along an urban bus line and have shown that both positioning error and availability can be improved. Along the trajectory tested, the mean accuracy has been reduced from 5.3m with a classical filter to 2.6m with our algorithm with 89% of the points more accurate than 5m instead of 64% before.

A novel LAAS pseudo-range error over-bound method based on improved pseudo-range error distribution model

The high level of safety demand of civil aviation requests local area augmentation system (LAAS) extremely high navigation integrity performance. A new LAAS pseudo-range error over-bound method is proposed in this paper to improve the integrity of LAAS. Firstly, a more practical pseudo-range error distribution model is established. Then, by calculating the relationship between the statistical uncertainty of the model parameter and the integrity risk, a new method is proposed to calculate the pseudo-range error over-bound model. This method can effectively reduce the inflation factor and the resulting conservativeness of the over-bound model. Comparative experiments show that the method proposed in this paper performs better and satisfies the requirements of real applications.

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.

LightSquared effects on estimated C/N 0, pseudoranges and positions

We present experimental results showing the impact of the proposed LightSquared (LS) Long-term Evolution (LTE) signals on both GPS and Galileo civil modulations in the L1/E1 band. The experiments were conducted in radiated mode in a large anechoic chamber. Three Galileo enabled receivers were chosen for the tests, and a state of the art GNSS signal generator was used to simulate both GPS and Galileo signals. The LTE signals were generated by an Agilent Programmable Signal Generator with a license to generate the signals according to the 3GPP LTE FDD standard. The interference impact was measured in terms of a Carrier-to-Noise power spectral density ratio (C/N 0) degradation, in accordance with the methodology which the LS/GPS Technical Working Group (TWG) established by mandate of the FCC. A model for determining the impact of the LS signal on the considered GNSS signals is provided and is validated against experimental data. It is shown that the Galileo E1 Open Service (OS) signal is marginally more susceptible to this form of interference than the GPS L1 C/A signal due to its greater proximity to the lower edge of the L1 band. The impact of LS interference was further analyzed in terms of pseudorange and position errors. Despite its relevance for most GNSS users, this aspect was not considered by the TWG. Measurement and position domain analysis along with the study of the LS impact on the Galileo OS signals are the major contributions. The analysis confirms the results obtained by the TWG and shows that the receiver front-end plays a major role in protecting GNSS signals against RF interference. While it appears that, for now, the LS network will not be deployed, the approach taken and the results obtained herein can be readily adapted for any future terrestrial mobile network that may take the place of LS.

ENHANCING KALMAN FILTERING–BASED TIGHTLY COUPLED NAVIGATION SOLUTION THROUGH REMEDIAL ESTIMATES FOR PSEUDORANGE MEASUREMENTS USING PARALLEL CASCADE IDENTIFICATION

Integrated global positioning system (GPS) solutions that utilize micro-electro-mechanical systems (MEMS)-based inertial sensors provide a more accurate navigation solution than stand-alone GPS in challenging scenarios. To keep the integrated solution less affected by sensor errors and to decrease the cost, a reduced inertial sensor system (RISS), which consists of only one gyroscope and two accelerometers, together with an odometer and integrated with GPS, is proposed. Tightly coupled integration is a better choice in demanding scenarios, as it can provide GPS aiding even when the number of visible satellites is three or less. However, inaccuracies of pseudoranges measured by the GPS receiver and used as aiding in the RISS/odometer/GPS integration solution will affect the overall positioning accuracy. This article explores the benefits of using parallel cascade identification (PCI), a nonlinear system identification technique that improves the overall navigation solution by modeling residual pseudorange correlated errors to be used by a Kalman filter (KF)–based tightly coupled RISS/odometer/GPS navigational solution. When less than four satellites are visible, the identified parallel cascade model for the still visible satellites is used to predict the residual pseudorange errors for these respective satellites, and the corrected pseudorange value is provided to KF. The performance of PCI for correcting the pseudoranges is examined and verified using road test trajectories and compared to a traditional tightly coupled RISS/odometer/GPS KF solution. The results demonstrate the advantages of this technique in correcting the pseudoranges and enhancing the positional solution.

Precise Orbit Determination Using Satellite Radar Ranging

Precise orbit determination can be achieved using only range measurements (no angle measurements) collected from several radars in a regional network. As uncompensated range biases are comparable to Global Positioning System pseudorange errors, 1 position and velocity errors smaller than 10 m and 1 cm=s are possible. Global Positioning System-level accuracies can be achieved rapidly during initial trilateration and maintained for the duration of the satellite pass (e.g., 1000 s) because initial velocity errors are small. Missile defense radars can benefit from trilateration because accurate orbit determination and excellent covariance fidelity can be achieved on a very short timeline. Covariance fidelity is improved with a recursive trilateration filter that characterizes the effects of range measurement biases on the estimation process. An important finding is that, for a multiple radar network, trilateration is more accurate than fused triangulation with uncalibrated angle biases.

Relative state estimation and observability for formation flying satellites in the presence of sensor noise

This paper presents an investigation of the relative state estimation and observability for two formation flying satellites using two different relative navigation sensor sets. The first set consists of a transmitter antenna on one satellite and a single receiver antenna on the other satellite to measure the inter-satellite range using a radiofrequency ranging signal. The second set uses three receiver antennas to measure multiple ranges, effectively providing angular information. In this paper, it is shown for the more complete sensor set that the estimation error in the relative state is a function of the pseudorange error, the inter-satellite distance, and the receiver antenna baselines. By varying these parameters, conditions are found for which the measurements obtained using the first sensor set result in relative state estimation and observability comparable to those obtained with the more complete sensor set. This offers potential reductions in cost and complexity for certain mission scenarios.

Estimation and exclusion of multipath range error for robust positioning

In integrated systems for accurate positioning, which consist of GNSS, INS, and other sensors, the GNSS positioning accuracy has a decisive influence on the performance of the entire system and thus is very important. However, GNSS usually exhibits poor positioning results in urban canyon environments due to pseudorange measurement errors caused by multipath creation, which leads to performance degradation of the entire positioning system. For this reason, in order to maintain the accuracy of an integrated positioning system, it is necessary to determine when the GNSS positioning is accurate and which satellites can have their pseudorange measured accurately without multipath errors. Thus, the objective of our work is to detect the multipath errors in the satellite signals and exclude these signals to improve the positioning accuracy of GNSS, especially in an urban canyon environment. One of the previous technologies for tackling this problem is RAIM, which checks the residual of the least square and identifies the suspicious satellites. However, it presumes a Gaussian measurement error that is more common in an open-sky environment than in the urban canyon environment. On the other hand, our proposed method can estimate the size of the pseudorange error directly from the information of altitude positioning error, which is available with an altitude map. This method can estimate even the size of non-Gaussian error due to multipath in the urban canyon environment. Then, the estimated pseudorange error is utilized to weight satellite signals and improve the positioning accuracy. The proposed method was tested with a low-cost GNSS receiver mounted on a test vehicle in a test drive in Nagoya, Japan, which is a typical urban canyon environment. The experimental result shows that the estimated pseudorange error is accurate enough to exclude erroneous satellites and improve the GNSS positioning accuracy.

Dirichlet Process Mixtures for Density Estimation in Dynamic Nonlinear Modeling: Application to GPS Positioning in Urban Canyons

In global positioning systems (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning, a good estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and nonlinearity and besides, it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a global navigation satellite system (GNSS)-based localization context where the GPS information may be inaccurate because of hard reception conditions.

Collaborative Vision-Integrated Pseudorange Error Removal: Team-Estimated Differential GNSS Corrections with no Stationary Reference Receiver

This paper presents an approach for generating Global Navigation Satellite System (GNSS) differential corrections by distributing GNSS and georeferenced vision measurements through a vehicle-to-vehicle (V2V) communications network. Conventionally, high-quality differential GNSS corrections are generated from a stationary reference receiver in close proximity to a set of mobile users. The proposed method, which is called Collaborative Vision Integrated Pseudorange Error Removal (C-VIPER), instead generates differential corrections using data from moving vehicles, thus eliminating the need for an infrastructure of stationary receivers. An important feature of the proposed algorithm is that individual differential corrections are computed for each satellite, so that corrections can be shared among users with different satellites in view. As demonstrated in simulation, measurement sharing significantly improves positioning accuracy in both the cross-track direction, where the quality of visual lane-boundary measurements is high, and the along-track direction, where the quality is low. Furthermore, because measurements are shared among many vehicles, the networked solution is robust to vision-sensor dropouts that may occur for individual vehicles.

INS/GPS for High-Dynamic UAV-Based Applications

The carrier-phase-derived delta pseudorange measurements are often used for velocity determination. However, it is a type of integrated measurements with errors strongly related to pseudorange errors at the start and end of the integration interval. Conventional methods circumvent these errors with approximations, which may lead to large velocity estimation errors in high-dynamic applications. In this paper, we employ the extra states to “remember” the pseudorange errors at the start point of the integration interval. Sequential processing is employed for reducing the processing load. Simulations are performed based on a field-collected UAV trajectory. Numerical results show that the correct handling of errors involved in the delta pseudorange measurements is critical for high-dynamic applications. Besides, sequential processing can update different types of measurements without degrading the system estimation accuracy, if certain conditions are met.

Non-Gaussian Error Modeling for GBAS Integrity Assessment

Four basic error sources exist for residual pseudo-range errors in a single frequency differential GPS system for ground based augmentation (GBAS): signal multipath, increased receiver noise (carrier-to-noise density ratios ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> )) due to interference, residual differential troposphere error, and the error induced by ionosphere gradients. Without restricting ourselves to classical Gaussian overbounding, we combine their probability density functions (pdfs) to a total pseudo-range error distribution. This distribution is propagated through the GBAS Hatch filter and then mapped into the position domain using a worst case (selected by maximum vertical dilution of precision (VDOP)) of a full 31 satellite constellation with the two most critical satellites failed observed at Braunschweig Airport, Germany. Our calculations yield a significant reduction amounting to 46% of the position domain error at the 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> integrity risk level when compared with the classical Gaussian overbounding approach.

Pseudolites/repeaters infrastructure autopositioning approach—mathematics and first simulation-based results

In the various infrastructure-based indoor positioning systems using Global Navigation Satellite System signals, i.e. pseudolites, repeaters, and repealites, there is the need for the terminal to know the positions of the various transmitters. Some techniques have been proposed for high accuracy pseudolite systems, but they require carrier phase measurements and a careful choice of some specific test locations. Other approaches consider that these data are simply available by any means: Of course, this can be achieved through manual distance measurements and the use of maps of the indoor environment. In this paper, we describe a new method that is based on a two-step approach. The first one consists in deploying the system. The second one is the calculation of the position of the transmitters through classic code measurements for a few specific chosen locations. Thus, the system can be deployed without any constraint and the locations of the transmitters calculated through a basic set of elementary measurements. The theoretical method is first described and the resulting accuracy of the position of the transmitters is then evaluated through theoretical calculations. In addition, electromagnetic simulations are carried out in order to estimate the pseudo-range errors of the proposed measurements: The accuracy of the determination of the position of the transmitters is then estimated (note that two receiver tracking loop implementations are considered). Thus, the accuracy of the proposed method is evaluated theoretically and through simulations.

GIOVE Satellites Pseudorange Error Assessment

Galileo is a global civil navigation satellite system developed in Europe as an alternative to the GPS controlled by the US Department of Defense and GLONASS controlled by Russian Space Forces. It is scheduled to be operative in 2013 and it will have 30 satellites orbiting on three inclined planes with respect to the equatorial plane at an altitude of about 24 000 km. The aim of this work is the study of the pseudorange error of the GIOVE satellites. To achieve this goal, the specifications defined in Giove A-B Navigation Signal in Space Interface Control Document (ICD) are used to develop a suitable software tool in MATLAB® environment. The tool is able to compute GIOVE A and GIOVE B position from the broadcast ephemerides, to calculate the pseudorange error and to process it. From the known receiver position and the computed satellite coordinates, the geometric range is obtained and compared with the pseudorange measurement, in order to obtain the pseudorange error.

가상기준점 기반 코드신호를 이용한 정밀 측위

스마트폰 사용자의 증가와 함께 다양한 응용분야에서 정밀한 3차원 위치정보가 요구되고 있다. 단일 주파수 민간용 코드 자료를 이용한 위치결정 정확도는 10m 내외이지만, 향후 스마트폰 응용프로그램은 서브미터 수준의 위치정확도를 안정적으로 확보할 필요가 있다. 따라서 일반적인 절대측위 대신 가상기준점을 기반으로 하는 상대측위 방식을 적용하였으며, 면보정계수를 이용하여 이중차분 오차를 보정하였다. 가상기준점은 로버 가까운 지점에 설정하고, 주 기준점 관측자료를 바탕으로 기하학적인 거리를 반영하였다. 이중차분으로 제거되지 않은 오차는 일반적으로 기선거리와 비례하므로, 로버 외부의 상시관측소 네트워크를 평면에 접합하여 면보정계수를 추정하였다. 이중차분 오차를 보정한 가상기준점과 로버의 24시간 C/A 코드 자료를 이용한 로버의 위치측정 결과 위도, 경도방향의 평균제곱근(RMS) 오차가 각각 37cm, 28cm 였으며, 높이 방향의 오차는 76cm 수준이었다. 또한 평면좌표의 성분별 오차는 전체의 약 90%에서 <TEX>${\pm}0.5m$</TEX> 이내의 결과를 보였으며, 특히 네트워크 기반의 오차모델링을 통해 평면좌표의 바이어스가 2-3cm 수준으로 크게 향상되었다. 따라서 가상기준점과 이중차분 오차모델링을 통해 단일 주파수코드 자료로부터 안정적인 서브미터 정확도의 위치결정이 가능하다. With the increase in the number of smartphone users, precise 3D positional information is required by various applications. The positioning accuracy using civilian single-frequency pseudoranges is at the level of 10 m or so, but most applications these days are asking for a sub-meter level Therefore, instead of an absolute positioning technique, the VRS-based differential approach is applied along with the correction of the double-differenced (DD) residual errors using FKP (Flachen-Korrektur-Parameter). The VRS (Virual Reference Station) is located close to the rover, and the measurements are generated by correcting the geometrical distance to those of the master reference station. Since the unmodeled errors are generally proportional to the length of the baselines, the correction parameters are estimated by fitting a plane to the DD pseudorange errors of the CORS network. The DD positioning accuracy using 24 hours of C/A code measurements provides the RMS errors of 37 cm, 28 cm for latitudinal and longitudinal direction, respectively, and 76 cm for height. The accuracy of the horizontal components is within <TEX>${\pm}0.5m$</TEX> for about 90% of total epochs, and in particular the biases are significantly decreased to the level of 2-3 cm due to the network-based error modeling. Consequently, it is possible to consistently achieve a sub-meter level accuracy from the single-frequency pseudoranges using the VRS and double-differenced error modeling.

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.

A stochastic sigma model for GLONASS satellite pseudorange

The GLONASS (Global Navigation Satellite System) is a satellite positioning system able to provide various numbers of air, marine, and any other type of users with all-weather three-dimensional positioning, velocity measuring, and timing anywhere in the world or near-earth space. As known, a GLONASS receiver performs passive measurements of pseudoranges and pseudorange rate of at least four GLONASS satellites as well as receives and processes navigation messages contained within navigation signals of the satellites. The navigation message supplies the satellites' position both in space and in time. Combined processing of the measurements and the navigation messages of the four (three) GLONASS satellites allows users to determine three (two) position coordinates, three (two) velocity vector constituents, and to refer user time scale to the national reference time UTC (SU). The purpose of this work was to define a stochastic model for pseudorange variances of GLONASS satellites able to provide its estimation. This evaluation is made for all satellites as a function of the elevation, independently of the user position, starting from real data. To achieve this goal, a suitable software tool MATLAB® is developed. The tool is able to create a GLONASS sky from the broadcast ephemeris, to compute the pseudorange error and to process it. The used data are extracted from observation and navigation RINEX files (containing both GPS and GLONASS measures). From the known receiver position and the computed satellite coordinates, the geometric range is obtained and compared with the pseudorange measurement, in order to achieve the pseudorange variance and build the model. In order to validate the sigma stationary stochastic model, the results are compared with further data obtained from different stations. The purpose of this work was the creation of an σ model particularly adapted in application as personal navigation device, characterized by the need of a real-time positioning and by a low computational power. The accuracy in real-time positioning can be improved, using a weighted least square (WLS) method for GNSS (GPS, GLONASS, and in the future GALILEO or other feasible systems) measurements. For GPS measurements, several suitable σ models for the WLS implementation are already in use; for GLONASS (or GLONASS-GPS together), the same is not available. So, there is need of studies about this topic.

A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver

This paper develops a new automated cycle slip detection and repair method that is based on only one single dual-frequency GPS receiver. This method jointly uses the ionospheric total electron contents (TEC) rate (TECR) and Melbourne–Wubbena wide lane (MWWL) linear combination to uniquely determine the cycle slip on both L1 and L2 frequencies. The cycle slips are inferred from the information of ionospheric physical TECR and MWWL ambiguity at the current epoch and that at the previous epoch. The principle of this method is that when there are cycle slips, the MWWL ambiguity will change and the ionospheric TECR will usually be significantly amplified, the part of artificial TECR (caused by cycle slips) being significantly larger than the normal physical TECR. The TECR is calculated based on the dual-frequency carrier phase measurements, and it is highly accurate. We calculate the ionospheric change information (including TECR and TEC acceleration) using the previous epochs (30 epochs in this study) and use the previous data to predict the TECR for the epoch needing cycle slip detection. If the discrepancy is larger than our defined threshold 0.15 TECU/s, cycle slips are regarded to exist at that epoch. The key rational of method is that during a short period (1.0 s in this study) the TECR of physical ionospheric phenomenon will not exceed the threshold. This new algorithm is tested with eight different datasets (including one spaceborne GPS dataset), and the results show that the method can detect and correctly repair almost any cycle slips even under very high level of ionospheric activities (with an average Kp index 7.6 on 31 March 2001). The only exception of a few detected but incorrectly repaired cycle slip is due to a sudden increased pseudorange error on a single satellite (PRN7) under very active ionosphere on 31 March 2001. This method requires dual-frequency carrier phase and pseudorange data from only one single GPS receiver. The other requirement is that the GPS data rate ideally is 1 Hz or higher in order to detect small cycle slips. It is suitable for many applications where one single receiver is used, e.g. real-time kinematic rover station and precise point positioning. An important feature of this method is that it performs cycle slip detection and repair on a satellite-by-satellite basis; thus, the cycle slip detection and repair for each satellite are completely independent and not affected by the data of other satellites.