Single-frequency Data Research Articles

GB decomposition method based on standard particle swarm algorithm

Groom-Bailey decomposition method is the most widely used method of tensor decomposition of magnetotelluric impedance, which is referred to as GB decomposition. The essence of the GB decomposition method is to solve the nonlinear over-determined equations derived from the GB decomposition definition. Traditional GB decomposition methods often use linear optimization methods to solve the equations, which have low calculation accuracy and slow speed. In this regard, this article introduces the standard particle swarm optimization algorithm into the GB decomposition method for the first time. The standard particle swarm algorithm is used to solve the equations. The global optimization method is used to implement the magnetotelluric GB decomposition method, and the synthesized single-point single-frequency data is used. The 3D / 2D model forward data is used to perform decomposition experiments. The experimental results show that the standard electromagnetic particle decomposition method based on the standard particle swarm algorithm is effective.

On negative induced polarization in frequency domain measurements

SUMMARY Induced polarization (IP) has been widely used to non-invasively characterize electrical conduction and polarization in the subsurface resulting from an applied electric field. Earth materials exhibit a lossy capacitance defined by a negative intrinsic phase in frequency-domain IP (FDIP) or a positive intrinsic chargeability in time-domain IP (TDIP). However, error-free positive apparent phase or negative apparent chargeability (i.e. negative IP effects) can occur in IP measurements over heterogeneous media. While negative IP effects in TDIP data sets have been discussed, no studies have addressed this topic in detail for FDIP measurements. We describe theory and numerical modelling to explain the origin of negative IP effects in FDIP measurements. A positive apparent phase may occur when a relatively high polarizability feature falls into negative sensitivity zones of complex resistivity measurements. The polarity of the apparent phase is determined by the distribution of subsurface intrinsic phase and resistivity, with the resistivity impacting the apparent phase polarity via its control on the sensitivity distribution. A physical explanation for the occurrence of positive apparent phase data is provided by an electric circuit model representing a four-electrode measurement. We also show that the apparent phase polarity will be frequency dependent when resistivity changes significantly with frequency (i.e. in the presence of significant IP effects). Consequently, negative IP effects manifest themselves in the shape of apparent phase spectra recorded with multifrequency (spectral IP) data sets. Our results imply that positive apparent phase measurements should be anticipated and should be retained during inversion and interpretation of single frequency and spectral IP data sets.

Epoch-by-epoch phase difference method to evaluate GNSS single-frequency phase data quality

The quality of Global Navigation Satellite SystemsGlobal Navigation Satellite Systems Global Navigation Satellite Systems (Global Navigation Satellite Systems Global Navigation Satellite Systems Global Navigation Satellite Systems GNSS) data is one important factor for precise navigation and positioning by using GNSS technique. We proposed a new method to monitor GNSS single-frequency phase data quality by using high-rate epoch-by-epoch phase difference (EEPD). We analyzed the influence of ephemeris, carrier frequency (L1, L2 and L3) and latitude (high latitude, middle latitude and low latitude) on the phase data quality evaluation. It is concluded that the use of broadcast and final orbit has little effect on the phase data quality evaluation with EEPD. The broadcast ephemeris can be used while analyzing GNSS single-frequency data quality in real time. The results obtained by using L1, L2 and L3 observations are almost the same and the GNSS phase quality evaluation can be analyzed by using single-frequency data. The latitudes of stations have a great influence on the quality evaluation of phase data using EEPD. At the same time, Bernese software is used to analyze the feasibility and reliability of EEPD. The results obtained with EEPD are compared with those obtained by Bernese. The results by different methods show good consistency, which shows that EEPD can be reliably used to evaluate the GNSS data quality.  &nbsp

Impact of poroelastic effects on the inversion of fracture properties from amplitude variation with offset and azimuth data in horizontal transversely isotropic media

The identification and characterization of fractures is an important objective in many areas of earth and environmental sciences. Amplitude variation with offset and azimuth (AVOAz) analysis of seismic reflection data is a key method for achieving these tasks. Theoretical and experimental studies have shown that the presence of pore fluids together with the strong mechanical contrast between the fractures and their embedding background give rise to wave-induced fluid flow (WIFF) effects. This implies that the effective stiffness tensor of a fluid-saturated fractured rock defining its seismic response becomes viscoelastic and frequency-dependent. In spite of this, AVOAz analysis typically relies on end-member-type elastic stiffness models that either assume a relaxed (i.e., equilibrated) or unrelaxed (i.e., unequilibrated) state of the wave-induced fluid pressure in the rock. In general, however, neither the appropriateness of the chosen model nor the associated errors in the inversion process are known. To investigate this topic, we have considered a poroelastic medium containing parallel vertical fractures and generate synthetic seismic AVOAz data using the classic Rüger approximations for PP-wave reflection coefficients in horizontally transversely isotropic media. A Markov chain Monte Carlo method is used to perform a Bayesian inversion of the synthetic seismic AVOAz data. We quantify the influence of WIFF effects on the AVOAz inversion results when elastic relaxed and unrelaxed models are used as forward solvers of inversion schemes to estimate the fracture volume fraction, the elastic moduli, and the porosity of the background rock, as well as the overall weakness of the medium due to the presence of fractures. Our results indicate that, when dealing with single-frequency data, relaxed elastic models provide biased but overall better inversion results than unrelaxed ones, for which some fracture parameters cannot be resolved. Improved inversion performance is achieved when using frequency-dependent data, which illustrates the importance of accounting for poroelastic effects.

Investigation of Tightly Combined Single-Frequency and Single-Epoch Precise Positioning Using Multi-GNSS Data

The loose combination (LC) and the tight combination (TC) are two different models in the combined processing of four global navigation satellite systems (GNSSs). The former is easy to implement but may be unusable with few satellites, while the latter should cope with the inter-system bias (ISB) and is applicable for few tracked satellites. Furthermore, in both models, the inter-frequency bias (IFB) in the GLObal NAvigation Satellite System (GLONASS) system should also be removed. In this study, we aimed to investigate the performance difference of ambiguity resolution and position estimation between these two models simultaneously using the single-frequency data of all four systems (GPS + GLONASS + Galileo + BeiDou Navigation Satellite System (BDS)) in three different environments, i.e., in an open area, with surrounding high buildings, and under a block of high buildings. For this purpose, we first provide the definition of ISB and IFB from the perspective of the hardware delays, and then propose practical algorithms to estimate the IFB rate and ISB. Thereafter, a comprehensive performance comparison was made between the TC and LC models. Experiments were conducted to simulate the above three observation environments: the typical situation and situations suffering from signal obstruction with high elevation angles and limited azimuths, respectively. The results show that in a typical situation, the TC and LC models achieve a similar performance. However, when the satellite signals are severely obstructed and few satellites are tracked, the float solution and ambiguity fixing rates in the LC model are dramatically decreased, while in the TC model, there are only minor declines and the difference in the ambiguity fixing rates can be as large as 30%. The correctly fixed ambiguity rates in the TC model also had an improvement of around 10%. Once the ambiguity was fixed, both models achieved a similar positioning accuracy.

A New Fuzzy-Cluster-Based Cycle-Slip Detection Method for GPS Single-Frequency Observation

The development of low-cost, small, modular receivers and their application in diverse scenarios with complex data quality has increased the requirements of single-frequency carrier-phase data preprocessing in real time. Different methods have been developed, but successful detection is not always ensured. The issue is crucial for high-precision positioning with Global Positioning System (GPS). Aiming at a high detection rate and low false-alarm rate, we propose a new cycle-slip detection method based on fuzzy-cluster. It consists of two steps. The first is identification of the epoch when cycle slips appear using Chi-square test based on time-differenced observations. The second is identification of the satellite which suffers from cycle slips using the fuzzy-cluster algorithm. To verify the performance of the proposed method, we compared it to a current robust method using real single-frequency data with simulated cycle slips. Results indicate that the proposed method outperforms the robust estimation method, with a higher correct-detection rate and lower undetection rate. As the number of satellites simulated with cycle slips increases, the correct-detection rate rapidly decreases from 100% to below 50% with the robust estimation method. While the correct-detection rate using the proposed method is always more than 60%, even if the number of satellites simulated with cycle slips reaches five. In addition, the proposed method always has a lower undetection rate than the robust estimation method. Simulation showed that when the number of satellites with cycle slips exceeds three, the undetection rate increases to more than 30%, reaching ~70% for the robust estimation method and less than 30% for the proposed method.

Combined use of single-frequency data and global ionosphere maps to estimate BDS and Galileo satellite differential code biases

Differential code biases (DCBs) are the most significant systematic errors in global navigation satellite system (GNSS) ionospheric total electronic content (TEC) monitoring and other code-related applications. Currently, the rapidly developing GNSS benefits from the Chinese BeiDou (BDS) and European Galileo systems that continuously offer position, navigation and timing services. In this way, the determination of satellite DCBs (SDCBs), which generally relies on GNSS data collected from dual- or multi-frequency geodetic-grade receivers, is of great importance, especially for the BDS and Galileo systems. However, the use of these geodetic-grade receivers implies a substantial increase in hardware costs. In this paper, we propose a single-frequency (SF) method for the determination of the BDS (C2I–C7I) and Galileo (C1X–C5X) satellite DCBs with the combined use of global ionospheric maps (GIMs) and low-cost SF multi-GNSS receivers, thereby greatly reducing the hardware costs. The mean precision of the satellite DCBs estimated from multi-GNSS data of a standalone SF receiver is approximately 0.35 ns for Galileo and 0.51 ns for BDS, when taking the DCB products published by the Deutsches zentrum für Luft-und Raumfahrt (DLR) as ground truth.

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.

Does economic growth cause military expenditure to go up? Using MF-VAR model

Former time-series analyses on the influence of causal relationship between economic growth and military spending may encounter the potential accumulation and neglected variable deviates from accumulating high frequency data generally employed to evaluate business cycles, e.g., monthly macroeconomic and quarterly gross domestic product per capita data, into low frequency data, e.g., yearly military spending data. The mixed frequency vector auto-regressive (MF-VAR) model for solving such temporal aggregation problem in this study, is firstly applied to assess the causal link between economic growth and military spending from the first quarter (Q1) of 1975 to the fourth quarter (Q4) of 2017 in Taiwan. These results via the prediction error variance shows that the MF-VAR model reaches higher explanatory power than the traditional VAR model belonging to single frequency data. Although not only counter-cyclicality but also pro-cyclicality of military spending on economic growth shock in Taiwan is found for the feedback hypothesis via the mixed frequency Granger causality tests, a varying correlation between military spending and economic growth results from the impulse-response analyses via the MF-VAR model. The above-mentioned findings significantly meet the arguable results with respect to former time-series analyses on the business-cycle effect on military spending.

The Second-Order Derivative of GPS Carrier Phase as a Promising Means for Ionospheric Scintillation Research

The carrier phase observable is the most preferable means for observation of ionospheric scintillation events. As the ionospheric scintillations show different features at different GNSS frequencies the single-frequency data should be used for complex analysis and data interpretation. The second-order derivative of the GPS signal carrier phase is suggested as a promising means to detect small-scale ionospheric disturbances. The high-rate L1 phase data with no additional processing are used for this purpose. Modeling and experimental results proved the hypothesis. It was revealed the strict dependence of sensitivity of the second-order derivative parameter on GPS receiver hardware features and carrier phase sampling rate.

Health progress and economic growth in the United States: the mixed frequency VAR analyses

Previous time series analyses on the effect of business cycles on population health suffered from potential aggregation and omitted variable biases stemming from the aggregation of the high frequency data commonly used to measure business cycles (such as quarterly GDP per capita or monthly unemployment rate) into low frequency data (such as annual GDP per capita or unemployment rate). In order to deal with this temporal aggregation issue, this study applies the Mixed Frequency Vector Auto-regressive (MF-VAR) model to investigate the causal relationship between health progress and economic growth during the period of 1948:Q1–2016:Q4 in the US for the first time. Our results based on the forecast error variance decomposition suggest that the MF-VAR model achieves higher explanatory power than the conventional VAR model with single frequency data. Despite a bi-directional causation between health progress and economic growth being identified using the mixed frequency Granger causality tests, the impulse-response analyses under the MF-VAR model found a changing correlation between health progress and economic growth across the four quarters within each 1-year time period. These findings effectively reconcile the controversial results from previous time series analyses on the effect of business cycles on population health.

Spectral Decomposition and a Waveform Cluster to Characterize Strongly Heterogeneous Paleokarst Reservoirs in the Tarim Basin, China

The main components of the Ordovician carbonate reservoirs in the Tahe Oilfield are paleokarst fracture-cavity paleo-channel systems formed by karstification. Detailed characterization of these paleokarst reservoirs is challenging because of heterogeneities in characteristics and strong vertical and lateral non-uniformities. Traditional seismic analysis methods are not able to solve the identification problem of such strongly heterogeneous reservoirs. Recent developments in seismic interpretation have heightened the need to describe the fracture-cavity structure of a paleo-channel with more accuracy. We propose a new prediction model for fracture-cavity carbonate reservoirs based on spectral decomposition and a waveform cluster. By the Matching Pursuit decomposition algorithm, the single-frequency data volumes are obtained. The specific frequency data volume that is the most sensitive to the reservoir is chosen based on seismic synthesis traces of well-logging data and geological interpretability. The waveform cluster is then applied to delineate the complex paleokarst systems, particularly the fracture-caves in the runoff zone. This method was applied to the area around Well T615 in the Tahe oilfield, and a paleokarst fracture-cavity system with strong heterogeneity in the runoff zone was delineated and characterized. The findings of this research provide insights for predicting other similar karst systems, such as karstic groundwater and karst hydrogeological systems.

Multifrequency Polarimetric SAR Image Despeckling by Iterative Nonlocal Means Based on a Space-Frequency Information Joint Covariance Matrix

This paper presents an iterative nonlocal means (NLM) filtering method under the Bayesian framework to deal with the issue of multifrequency fully polarimetric synthetic aperture radar (PolSAR) image despeckling. Differing from most of the PolSAR filters designed for single-frequency data, the proposed NLM method is developed based on a space-frequency information joint covariance matrix, which can not only utilize multifrequency polarimetric information but also exploit the correlation between any two pixels in an image patch. Furthermore, with the aim of accelerating the filtering procedure and better retaining image details, an effective preselection step is employed. The filtering results obtained with both a simulated dataset and real multifrequency PolSAR datasets acquired by the AIRSAR system confirm the good performance of the proposed method in both reducing speckle and retaining details, when compared with some of the state-of-the-art despeckling algorithms.

A Multispectral Bayesian Classification Method for Increased Acoustic Discrimination of Seabed Sediments Using Multi-Frequency Multibeam Backscatter Data

Multi-frequency backscatter data collected from multibeam echosounders (MBESs) is increasingly becoming available. The ability to collect data at multiple frequencies at the same time is expected to allow for better discrimination between seabed sediments. We propose an extension of the Bayesian method for seabed classification to multi-frequency backscatter. By combining the information retrieved at single frequencies we produce a multispectral acoustic classification map, which allows us to distinguish more seabed environments. In this study we use three triple-frequency (100, 200, and 400 kHz) backscatter datasets acquired with an R2Sonic 2026 in the Bedford Basin, Canada in 2016 and 2017 and in the Patricia Bay, Canada in 2016. The results are threefold: (1) combining 100 and 400 kHz, in general, reveals the most additional information about the seabed; (2) the use of multiple frequencies allows for a better acoustic discrimination of seabed sediments than single-frequency data; and (3) the optimal frequency selection for acoustic sediment classification depends on the local seabed. However, a quantification of the benefit using multiple frequencies cannot clearly be determined based on the existing ground-truth data. Still, a qualitative comparison and a geological interpretation indicate an improved discrimination between different seabed environments using multi-frequency backscatter.

Optimized Wishart Network for an Efficient Classification of Multifrequency PolSAR Data

High-resolution wide-area images are required in the diverse field of research ranging from urban planning and disaster prediction to agriculture and geology. Sometimes the image is taken under harsh weather conditions or at night time. Current optical remote sensing technology does not have the capability to acquire images in such conditions. Synthetic aperture radar (SAR) uses microwave signal which has a long-range propagation characteristic that allows us to capture images in difficult weather conditions. In addition to this, some polarimetric SAR (PolSAR) systems are also capable of capturing images using multifrequency bands simultaneously resulting into a multitude of information in comparison to the optical images. In this letter, we propose a single-hidden layer optimized Wishart network (OWN) and extended OWN for classification of the single-frequency and multifrequancy PolSAR data, respectively. Performance evaluation is conducted on a single-frequency as well as multifrequency SAR data obtained by Airborne Synthetic Aperture Radar. We observed that for combining multiple band information, proposed single-hidden layer network outperforms deep learning-based architecture involving multiple hidden layers.

Rough surface reconstruction from phaseless single frequency data at grazing angles

We develop a method for the reconstruction of a perfectly reflecting rough surface from phaseless measurements of a field arising from single frequency scattering at grazing angles. Formulations are given for both Dirichlet and Neumann boundary conditions, and numerical experiments are presented in which close agreement is found with the exact solution. The approach is a marching method based on the parabolic integral equation, which recovers the surface progressively in range, and is iterated a small number of times to produce the final result. It is found that the approach is robust with respect to spatially localized perturbations and to measurement noise.

Multifrequency and Full-Polarimetric SAR Assessment for Estimating Above Ground Biomass and Leaf Area Index in the Amazon Várzea Wetlands

The aim of this study is to evaluate the potential of multifrequency and Full-polarimetric Synthetic Aperture Radar (SAR) data for retrieving both Above Ground Biomass (AGB) and Leaf Area Index (LAI) in the Amazon floodplain forest environment. Two specific questions were proposed: (a) Does multifrequency SAR data perform more efficiently than single-frequency data in estimating LAI and AGB of várzea forests?; and (b) Are quad-pol SAR data more efficient than single- and dual-pol SAR data in estimating LAI and AGB of várzea forest? To answer these questions, data from different sources (TerraSAR-X Multi Look Ground Range Detected (MGD), Radarsat-2 Standard Qual-Pol, advanced land observing satellite (ALOS)/ phased-arrayed L-band SAR (PALSAR-1). Fine-beam dual (FDB) and quad Polarimetric mode) were combined in 10 different scenarios to model both LAI and AGB. A R-platform routine was implemented to automatize the selection of the best regression models. Results indicated that ALOS/PALSAR variables provided the best estimates for both LAI and AGB. Single-frequency L-band data was more efficient than multifrequency SAR. PALSAR-FDB HV-dB provided the best LAI estimates during low-water season. The best AGB estimates at high-water season were obtained by PALSAR-1 quad-polarimetric data. The top three features for estimating AGB were proportion of volumetric scattering and both the first and second dominant phase difference between trihedral and dihedral scattering, extracted from Van Zyl and Touzi decomposition, respectively. The models selected for both AGB and LAI were parsimonious. The Root Mean Squared Error (RMSEcv), relative overall RMSEcv (%) and R2 value for LAI were 0.61%, 0.55% and 13%, respectively, and for AGB, they were 74.6 t·ha−1, 0.88% and 46%, respectively. These results indicate that L-band (ALOS/PALSAR-1) has a high potential to provide quantitative and spatial information about structural forest attributes in floodplain forest environments. This potential may be extended not only with PALSAR-2 data but also to forthcoming missions (e.g., NISAR, Global Ecosystems Dynamics Investigation Lidar (GEDI), BIOMASS, Tandem-L) for promoting wall-to-wall AGB mapping with a high level of accuracy in dense tropical forest regions worldwide.

Three-Dimensional Holographic Imaging Using Single Frequency Microwave Data

Three-dimensional (3D) microwave and millimeter wave imaging techniques based on the holographic principles have been successfully employed in several applications such as security screening, body shape measurement for the apparel industry, underground imaging, and wall imaging. The previously proposed 3D holographic imaging techniques require the acquisition of wideband data over rectangular or cylindrical apertures. Requirement for wideband data imposes limitations on the hardware (in particular at very high or very low frequencies). It may also lead to errors in the produced images if the media is dispersive (e.g., in biomedical imaging) and not modeled properly in the image reconstruction process. To address these limitations, here, we propose a technique to perform 3D imaging with single frequency data. Instead of collecting data at multiple frequencies, we acquire the backscattered fields with an array of resonant antennas. We demonstrate the possibility of 3D imaging with the proposed setup and perform a comprehensive study of the capabilities and limitations of the technique via simulations. To perform a realistic study, the simulation data is contaminated by noise.

Vessel fusion tracking with a dual-frequency high-frequency surface wave radar and calibrated by an automatic identification system

High-frequency surface wave radar (HFSWR) and automatic identification system (AIS) are the two most important sensors used for vessel tracking. The HFSWR can be applied to tracking all vessels in a detection area, while the AIS is usually used to verify the information of cooperative vessels. Because of interference from sea clutter, employing single-frequency HFSWR for vessel tracking may obscure vessels located in the blind zones of Bragg peaks. Analyzing changes in the detection frequencies constitutes an effective method for addressing this deficiency. A solution consisting of vessel fusion tracking is proposed using dual-frequency HFSWR data calibrated by the AIS. Since different systematic biases exist between HFSWR frequency measurements and AIS measurements, AIS information is used to estimate and correct the HFSWR systematic biases at each frequency. First, AIS point measurements for cooperative vessels are associated with the HFSWR measurements using a JVC assignment algorithm. From the association results of the cooperative vessels, the systematic biases in the dualfrequency HFSWR data are estimated and corrected. Then, based on the corrected dual-frequency HFSWR data, the vessels are tracked using a dual-frequency fusion joint probabilistic data association (JPDA)-unscented Kalman filter (UKF) algorithm. Experimental results using real-life detection data show that the proposed method is efficient at tracking vessels in real time and can improve the tracking capability and accuracy compared with tracking processes involving single-frequency data.

A new approach for cycle slip detection and fix using single GPS receiver\u2019s single satellite dual frequency data containing arbitrarily large pseudorange errors

This paper presents a new cycle slip detection and repair method using Total Electron Content Rate (TECR) information derived from individual satellite dual-frequency data of a single Global Positioning System (GPS) receiver while pseudorange measurements are subject to arbitrarily large range errors. Sudden Increase of Pseudorange Error (SIPE), similar to cycle slips in nature, is quite common in various data acquisition scenarios. The basic principle of this method is to take advantage of the fact that the ionospheric TECR does not exceed certain threshold, which is set as 0.35 TECU/s in this study. Analytic expressions to evaluate the effect of SIPE on cycle slip detections have been developed. The search spaces for cycle slip candidate pairs are defined, given a predefined (sufficiently large) SIPE value. Two cycle slip validation rules are proposed to validate the cycle slip candidates. Over 99.9% of candidates can be rejected with the application of two validation rules. The theoretically maximal number of remaining cycle slip candidate pairs (NRCP) can be exactly calculated based on the magnitude of SIPE, TECR threshold, and the data sampling interval. After applying validation rules, the correct cycle slip pairs can be identified using a modified low-order polynomial fitting method. This method is tested on 13 high rate (1-Hz) dual-frequency datasets recorded by both ground-based static and satellite-borne high dynamic GPS receivers under various levels of ionospheric activities. Simulated cycle slips in 12 different possible cases and varying SIPE magnitudes are introduced into the data sets. In each test scheme, averagely 600–750 pairs of cycle slips are simulated. The SIPE magnitudes are set to vary from 50.0 m to 1000.0 m. Test results show that all the cycle slips in all the test schemes and all the datasets have been successfully detected and fixed even with a maximum SIPE of 1000.0 m in pseudoranges. A distinct advantage of this method is that it works in real-time with individual satellite’s data from a single dual-frequency receiver, even if the carrier phases have virtually any size of cycle slips and the pseudoranges have virtually arbitrarily large errors.