Cycle Slips Research Articles

GNSS multi-frequency receiver single-satellite measurement validation method

A method is presented for real-time validation of GNSS measurements of a single receiver, where data from each satellite are independently processed. A geometry-free observation model is used with a reparameterized form of the unknowns to overcome rank deficiency of the model. The ionosphere error and non-constant biases such as multipath are assumed changing relatively smoothly as a function of time. Data validation and detection of errors are based on statistical testing of the observation residuals using the detection---identification---adaptation approach. The method is applicable to any GNSS with any number of frequencies. The performance of validation method was evaluated using multi-frequency data from three GNSS (GPS, GLONASS, and Galileo) that span 3 days in a test site at Curtin University, Australia. Performance of the method in detection and identification of outliers in code observations, and detection of cycle slips in phase data were examined. Results show that the success rate vary according to precision of observations and their number as well as size of the errors. The method capability is demonstrated when processing four IOV Galileo satellites in a single-point-positioning mode and in another test by comparing its performance with Bernese software in detection of cycle slips in precise point-positioning processing using GPS data.

Pilot-symbols-aided cycle slip mitigation for DP-16QAM optical communication systems

A pilot-symbols-aided phase unwrapping (PAPU), which utilizes the time-division multiplexed pilot symbols that are transmitted with data, is proposed to do cycle slip detection and correction with the carrier phase estimation (CPE). Numerical simulations for 10 Gbaud dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) systems show that the block averaging quadrature phase-shift keying (QPSK) partitioning with PAPU greatly eliminates the performance degradation caused by cycle slips, maintains a low CS probability with less influence of filter length, and achieves a bit-error-rate (BER) performance below soft-decision forward error correction (FEC) limit 2 × 10⁻² at 15 dB optical signal-to-noise ratio with only 1.56% overhead and 6 MHz combined laser linewidth.

Cycle Slip Detection and Correction Through Classification of Modulation Code Failures

In high-density recording systems, synchronization might be lost due to increased noise and/or inaccurate sampling/filtering. In such, long bursts of errors occur due to bits either erased from or inserted into the bit stream. At low signal-to-noise ratios, such bit slips (also known as cycle slips) lead to excessive post-error correction code (post-ECC) failures. In order to reduce the rate of the post-ECC failures, cycle slips should be detected and corrected. In the past, the majority of the research was concentrated on iterative joint timing recovery and error decoding methodologies. In this study, we propose to detect and correct cycle slips using a decoding failure analysis of maximum transition run (MTR) codeword sequences in conjunction with a general-purpose classification algorithm. First, noncyclic properties of constrained coding are identified by realizing that MTR codewords render invalid more often if bit shifts happen. Later, we present a method to use such invalid codewords to help detect and correct cycle slips. Finally, some numerical results are presented to show the effectiveness of the proposed detection/correction scheme using MTR codes and the support vector machines. It is demonstrated that such a combination has the potential for BER and post-ECC failure rate performance improvements by eliminating cycle slips for the generalized partial response channels.

A novel two-stage phase noise estimation algorithm for coherent optical OFDM systems

In coherent optical orthogonal frequency-division-multiplexing (CO-OFDM) receivers, the phase noise caused by the instabilities of the local oscillator is a potentially serious problem. In order to deal with the common phase error (CPE) caused by the phase noise in actual CO-OFDM receiver, a novel two-stage Least Mean Square (LMS) phase noise adaptive estimation algorithm is proposed. In the proposed estimation algorithm, an initial coarse estimation of the optical carrier phase to exploit the knowledge of pilot symbols is followed by a fine LMS adaptive estimation. The main advantage of the proposed method is that the phase-ambiguity problem is avoided after a cycle slip and the Bit Error Rate (BER) performance is improved. Furthermore, the phase noise effect induced by the transmitter laser and receiver Local Oscillator (LO) is analyzed. A simple CO-OFDM transmission system with QPSK to apply the proposed adaptive estimation algorithm is simulated, the simulation analysis shows that the proposed adaptive estimation algorithm has a more excellent performance.

Predicting atmospheric delays for rapid ambiguity resolution in precise point positioning

Integer ambiguity resolution in precise point positioning (PPP) can shorten the initialization and re-initialization time, and ambiguity-fixed PPP solutions are also more reliable and accurate than ambiguity-float PPP solutions. However, signal interruptions are unavoidable in practical applications, particularly while operating in urban areas. Such signal interruptions can cause discontinuity of carrier phase arc, which introduces new integer ambiguities. Usually it will take approximately 15min of continuous tracking to a reasonable number of satellites to fix new integer ambiguities. In many applications, it is impractical for a PPP user to wait for such a long time for the re-initialization. In this paper, a method for rapid ambiguity fixing in PPP is developed to avoid such a long re-initialization time. Firstly, the atmospheric delays were estimated epoch by epoch from ambiguity-fixed PPP solutions before the data gap or cycle slip occurs. A random walk procedure is then applied to predict the atmospheric delays accurately over a short time span. The predicted atmospheric delays then can be used to correct the observations which suffer from signal interruptions. Finally, the new ambiguities can be fixed with a distinct WL-LX-L3 (here LX denotes either of L1, L2) cascade ambiguity resolution strategy. Comprehensive experiments have demonstrated that the proposed method and strategy can fix zero-difference integer ambiguities successfully with only a single-epoch observation immediately after a short data gap. This technique works even when all satellites are interrupted at the same time. The duration of data gap bridged by this technique could be possibly extended if a more precise atmospheric delay prediction is found or on-the-fly (OTF) technology is applied. Based on the proposed method, real-time PPP with integer ambiguity fixing becomes more feasible in practice.

On Decision Aided Carrier Phase and Frequency Offset Estimation in Coherent Optical Receivers

We investigate carrier estimation (CE) for coherent optical receivers where the received signal is impaired by additive white Gaussian noise, laser phase noise, and frequency offset. Best practical 4-, 8-, and 16-point constellations are identified. A generalized differential encoding rule for signal constellations is presented. Performance of our complex-weighted decision-aided maximum-likelihood (CW-DA-ML) phase noise and frequency offset estimator is analyzed at low signal-to-noise ratio (SNR) and the optimal filter lengths are found. CW-DA-ML CE is put in perspective with respect to two fundamental estimators in the literature: (i) differential frequency estimator followed by block <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th power phase estimator (DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE), and (ii) fast Fourier transform based frequency estimator followed by block <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th power phase estimator (FFTbE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE), in terms of laser linewidth tolerance, frequency estimation range and speed, SNR threshold, and cycle slip probability. CW-DA-ML CE is 2.5 and 10.5 times faster than DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE in 4 phase-shift keying and 16 quadrature amplitude modulation signals, respectively, at a 1-dB system penalty for a bit-error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Our CE has lower cycle slip probability and transmission overhead than DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th and FFTbE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE. Hence, our CE is shown to be favourable in pilot-assisted (PA) systems. A PA CW-DA-ML CE is introduced and shown to be robust against time-varying frequency offset with minimal training overhead. Analog-to-digital convertor quantization error on our CE performance is also addressed.

On the improvements of the single point positioning accuracy with Locata technology

This work focuses on the performances of Locata technology in single point positioning using different firmware versions (v2.0 and v4.2). The main difference is that the Locata transmitters with firmware v2.0 are single frequency, whereas in the v4.2, they are dual frequency. The performance of the different firmware versions has been measured in different environments including an urban canyon-like environment and a more open environment on the roof of the Nottingham Geospatial Building. The results obtained with firmware v4.2 show that with more available signals, cycle slips can be more easily detected, together with the improvement of the detection of multipath fading on the received signal. As a result, the noise level on the carrier phase measurements recorded with firmware v4.2 is equal on average to a third of the level of noise on the measurements recorded with firmware v2.0. In addition, with either firmware, the accuracy of the position is at the sub-centimeter level on the East and North coordinates. The Up coordinate accuracy is generally less accurate and more sensitive to the geometry of the network in our experiments. We then show the importance of the geometry of the Locata network on the accuracy of Locata positioning system through the demonstration of the relationship between the dilution of precision value and the confidence ellipse. We also demonstrate that the model of the noise on the Locata coordinates is a white Gaussian noise with the help of the autocorrelation function. To some extent, this technique can help to detect whether the Wi-Fi technology is interfering with the Locata technology and degrades the positioning accuracy.

Transmission performance improvement in digital coherent system by suppressing cycle slip using statistical analysis algorithm

Cycle slip adversely affects transmission performance in digital coherent systems. Proposed is an algorithm using statistical analysis for suppressing cycle slip in a digital coherent system. The cycle slip suppression effect, transmission performance, and nonlinear tolerance of the proposed algorithm were numerically investigated. The proposed algorithm enables cycle-slip-free wavelength division multiplex transmission under the presence of nonlinear optical effect and improves transmission performance.

PERFORMANCE ANALYSIS OF DOPPLER AIDED GPS/QZSS PRECISE POSITIONING FOR LAND VEHICLES

ABSTRACT For ITS (Intelligent Transport Systems), especially for land vehicles, precise position is the prime information. GNSS is the most popular navigation system. Generally, ITS demands lane distinguishable positioning accuracy. However urban area is most environments of land vehicles and the signal blocks of satellite with low elevation angle, multipath error and etc. make unreliable positioning results. Especially, lack of number of visible satellites (fewer than 4 satellites) cannot provide positioning results. QZSS (Quasi-Zenith Satellite System) which operated by Japan has high interoperability. In addition, its elevation angle is very high in long time in Korea. It means QZSS signal can be received in urban area and it can be great advantage for land vehicles. The most positioning errors are occurred by multipath, cycle slip, and etc. For example, multipath error is unexpected momentary error. In order to reduce position error, smoothing technique in position domain is needed. In this paper, precise positioning for land vehicles was evaluated. First, by using QZSS, probability of navigation solution was enhanced. Second, the reliability is improved by smoothing positioning result using Doppler measurement. The analysis was performed by trajectory analysis using precise map data.

Bayesian methods for outliers detection in GNSS time series

This article is concerned with the problem of detecting outliers in GNSS time series based on Bayesian statistical theory. Firstly, a new model is proposed to simultaneously detect different types of outliers based on the conception of introducing different types of classification variables corresponding to the different types of outliers; the problem of outlier detection is converted into the computation of the corresponding posterior probabilities, and the algorithm for computing the posterior probabilities based on standard Gibbs sampler is designed. Secondly, we analyze the reasons of masking and swamping about detecting patches of additive outliers intensively; an unmasking Bayesian method for detecting additive outlier patches is proposed based on an adaptive Gibbs sampler. Thirdly, the correctness of the theories and methods proposed above is illustrated by simulated data and then by analyzing real GNSS observations, such as cycle slips detection in carrier phase data. Examples illustrate that the Bayesian methods for outliers detection in GNSS time series proposed by this paper are not only capable of detecting isolated outliers but also capable of detecting additive outlier patches. Furthermore, it can be successfully used to process cycle slips in phase data, which solves the problem of small cycle slips.

Cycle slips detection algorithm for low cost single frequency GPS RTK positioning

Conventionally, cycle slips are detected by combining phase observations or phase/code observations. However, this is unsuitable for single frequency receivers in real time kinematic (RTK) positioning. Therefore, this study introduces an algorithm based on outlier detection concept to the detection and repair of cycle slip during GPS RTK positioning. The efficacy of the algorithm was verified on a low cost single frequency GPS receiver. To investigate the ability of the algorithm to detect error within a single cycle, minimum detectable bias (MDB) of less than one cycle was used as the index of success. Experiments verified the availability of the algorithm up to 96·12% (10° mask angle). The algorithm was able to accurately detect the time when cycle slips occur and precisely estimate their size in various simulated scenarios. Finally, tests were performed based on real data, and the results confirm that the proposed algorithm is applicable for single frequency RTK positioning.

Correlation of scintillation occurrence with interplanetary magnetic field reversals and impact on Global Navigation Satellite System receiver tracking performance

Ionospheric scintillation is characterized by rapid fluctuations in the amplitude and phase of transionospheric radio signals as they pass through small scale ionospheric plasma density irregularities. Over the auroral regions, the occurrence of scintillation is associated with large‐scale plasma structures and is mainly enhanced during geomagnetic storms. Scintillation can cause cycle slips and degrade the positioning accuracy in Global Navigation Satellite System (GNSS) receivers. This paper investigates the correlation between the southward reversals of the interplanetary magnetic field (IMF) Bz and the occurrence of scintillation, along with the consequential impact on the tracking performance of a GNSS receiver located at a high‐latitude station, Bronnoysund (geographic latitude 65°N) in Norway. The analysis revealed that the occurrence of scintillation at this station is largely controlled by the IMF conditions. The receiver tracking performance under strong scintillations is evaluated by the receiver PLL (phase‐locked loop) tracking jitter variance. The dependence of the PLL jitter variance on phase scintillation can be best represented by a quadratic fit.

Ambiguity-Free Method for Fast and Precise GNSS Differential Positioning

AbstractMethods based on integer ambiguity determination, such as the least-squares ambiguity decorrelation adjustment (LAMBDA) method, are currently used for precise global navigation satellite system (GNSS) differential positioning. In the present paper, the author proposes an ambiguity-free method based on a dedicated mixed (stochastic/deterministic) optimization algorithm that, unlike the LAMBDA method, is capable of providing reliable and accurate results using few observation epochs (e.g., 1-cm accuracy with just two epochs), having the additional advantages of insensitivity to cycle slips and impossibility of wrong ambiguity fixation. In addition, it is demonstrated that the application of the linear (deterministic) part of this algorithm yields the correct baseline results much more easily and quickly than methods requiring integer ambiguity determination, provided the initial approximate coordinates are accurate to a few centimeters. However, the use of ambiguity-free methods requires that the in...

Cycle Slips Detection and Correction of GPS Based on Carrier Phase Differences and Polynomial Fitting

Cycle Slips Detection and Correction of GPS Based on Carrier Phase Differences and Polynomial Fitting

Improved precise point positioning in the presence of ionospheric scintillation

Ionospheric disturbances can be detrimental to accuracy and reliability of GNSS positioning. We focus on how ionospheric scintillation induces significant degradation to Precise Point Positioning (PPP) and how to improve the performance of PPP during ionospheric scintillation periods. We briefly describe these problems and give the physical explanation of highly correlated phenomenon of degraded PPP estimates and occurrence of ionospheric scintillation. Three possible reasons can contribute to significant accuracy degradation in the presence of ionospheric scintillation: (a) unexpected loss of lock of tracked satellites which greatly reduces the available observations and considerably weakens the geometry, (b) abnormal blunders which are not properly mitigated by positioning programs, and (c) failure of cycle slip detection algorithms due to the high rate of total electronic content. The latter two reasons are confirmed as the major causes of sudden accuracy degradation by means of a comparative analysis. To reduce their adverse effect on positioning, an improved approach based on a robust iterative Kalman filter is adopted to enhance the PPP performance. Before the data enter the filter, the differential code biases are used for GNSS data quality checking. Any satellite whose C1---P1 and P1---P2 biases exceed 10 and 30 m, respectively, will be rejected. Both the Melbourne---Wubbena and geometry-free combination are used for cycle slip detection. But the thresholds are set more flexibly when ionospheric conditions become unusual. With these steps, most of the outliers and cycle slips can be effectively detected, and a first PPP estimation can be carried out. Furthermore, an iterative PPP estimator is utilized to mitigate the remaining gross errors and cycle slips which will be reflected in the posterior residuals. Further validation tests based on extensive experiments confirm our physical explanation and the new approach. The results show that the improved approach effectively avoids a large number of ambiguity resets which would otherwise be necessary. It reduces the number of re-parameterized phase ambiguities by approximately half, without scarifying the accuracy and reliability of the PPP solution.

Real-time clock jump compensation for precise point positioning

Over the past decades, a number of methods have been proposed to handle cycle slips in the carrier phase measurements, but few researches have investigated receiver clock jumps, which may produce undesirable effects on GPS data processing. Such events are generally ignored in double-differenced positioning. For undifferenced processing, such as precise point positioning (PPP) techniques, it is unwise to neglect the impact of clock jumps. Failure to properly detect and account for receiver clock jumps may sometimes cause unexpected behavior of the GPS software and large errors in the resulting PPP solution. This is particularly troublesome when there are irregular (types 2 or 3) millisecond clock jumps represented in RINEX observation files. In this study, we first provide an intuitive description of the receiver clock jump phenomenon, and a comprehensive classification of clock jumps is presented according to its influence on three fundamental quantities (time tag, pseudorange, and carrier phase) of RINEX observation files. To follow the RINEX convention, the observable consistency is analyzed for various types of clock jump; and a simple but robust real-time clock jump compensation (RTCJC) method is proposed for reconstructing a consistent set of observables. Numerous validation tests with various GPS data show that the method is applicable to millisecond clock jumps. Without RTCJC, clock jumps are prone to cause failure of gross error and cycle slip detection algorithms and so result in repeated re-initialization or even non-convergent solutions, which lead to gross errors in the PPP solution. When RTCJC is applied, all clock jumps present in the GPS data can be effectively identified and repaired accurately, and the problem of re-initialization in PPP will no longer be triggered by receiver clock jumps, which results in significant improvement of PPP accuracy and reliability.

Cycle Slip Detection and Correction Methods with Time-Differenced Model for Single Frequency GNSS Applications

Cycle Slip Detection and Correction Methods with Time-Differenced Model for Single Frequency GNSS Applications

Mitigating the impact of ionospheric cycle slips in GNSS observations

Processing of data from global navigation satellite systems (GNSS), such as GPS, GLONASS and Galileo, can be considerably impeded by disturbances in the ionosphere. Cycle-slip detection and correction thus becomes a crucial component of robust software. Still, dealing with ionospheric cycle slips is not trivial due to scintillation effects in both the phase and the amplitude of the signals. In this contribution, a geometry-based approach with rigorous handling of the ionosphere is presented. A detailed analysis of the cycle-slip correction process is also tackled by examining its dependence on phase and code noise, non-dispersive effects and, of course, the ionosphere. The importance of stochastic modeling in validating the integer cycle-slip candidates is emphasized and illustrated through simulations. By examining the relationship between ionospheric bias and ionospheric constraint, it is shown that there is a limit in the magnitude of ionospheric delay variation that can be handled by the cycle-slip correction process. Those concepts are applied to GNSS data collected by stations in northern Canada, and show that enhanced cycle-slip detection can lead to decimeter-level improvements in the accuracy of kinematic PPP solutions with a 30-s sampling interval. Cycle-slip correction associated with ionospheric delay variations exceeding 50 cm is also demonstrated, although there are risks with such a procedure and these are pointed out.

Research of Double-Differenced Carrier Phase Cycle Slip Detection Based on Wavelet Analysis

It is easier to develop the cycle slip phenomena during the carrier phase observation in GPS. In order to improve the reliability and accuracy of the system measurement, we need to diagnose and find out the position of the cycle slip, and then fix it before the data pretreatment stage which is ahead of the adjustment. Using the double-differenced carrier phase observables can eliminate the correlative error term and improve the accuracy of the measurement. Therefore, the essay studies the method of the double-differenced carrier phase cycle slip detection based on the wavelet analysis, and finally test the measured data. The experimental results showed that the detection of cycle slip is very sensitive when we select the suitable wavelet base.

지능형 교통시스템에 적합한 위성항법 기반의 정밀측위 구조 설계

In this paper, a structure of precise positioning based on satellite navigation system is proposed. The proposed system is consisted with three parts, range domain filter, navigation filter and position domain filter. The range domain filter generates carrier phase-smoothed-Doppler and Doppler-smoothed-code measurements. And the navigation filter calculates position and velocity using double-differenced code/carrier phase/Doppler measurements. Finally, position domain filter smooth position error, and it means enhancement of positioning performance. The proposed positioning method is evaluated by trajectory analysis using precise map date. As a result, the position error occurred by multipath or cycle slip was reduced and the calculated trajectory was in true lane.