Geometry-free Phase Combination Research Articles

Dual-frequency GPS Cycle Slip Detection and Repair Based on Dynamic Test

How to solve the multi-values and accurately detect the cycle slip of each frequency was particularly critical of dual-frequency GPS. This paper used the geometry-free phase combinations, proposed a dynamic test method to detect cycle slip outliers, which determined the cycle slip by constraining the value range of the cycle slip sequences of the dual-frequency GPS through the constantly updated its standard deviation. The dynamic test of cycle slip detection and repair method has been tested by using GPS data with sampling interval of 1s, 5s, 10 s and 15s. The method can not only solve the problem of multi-values, but also accurately detect the cycle slip values at various frequencies, whether the fixed cycle slip is added to the random position or the random cycle slip is added to the random position. Experiments with four different sampling intervals, the results showed that the proposed method of cycle slip detection and repair calculation success rate reaches 98.75%.

A Cycle Slip Detection and Repair Method Based on Inertial Aiding for BDS Triple-Frequency Signals

Cycle slip detection and repair is a prerequisite to obtain high-precision positioning based on a carrier phase. Traditional triple-frequency pseudorange and phase combination algorithm are highly sensitive to the pseudorange observation accuracy. To solve the problem, a cycle slip detection and repair algorithm based on inertial aiding for a BeiDou navigation satellite system (BDS) triple-frequency signal is proposed. To enhance the robustness, the INS-aided cycle slip detection model with double-differenced observations is derived. Then, the geometry-free phase combination is united to detect the insensitive cycle slip, and the optimal coefficient combination is selected. Furthermore, the L2-norm minimum principle is used to search and confirm the cycle slip repair value. To correct the INS error accumulated over time, the extended Kalman filter based on the BDS/INS tightly coupled system is established. The vehicular experiment is conducted to evaluate the performance of the proposed algorithm from a few aspects. The results indicate that the proposed algorithm can reliably detect and repair all cycle slips that occur in one cycle, including the small and insensitive cycle slips as well as the intensive and continuous cycle slips. Additionally, in signal-challenged environments, the cycle slips occurring 14 s after a satellite signal outage can be correctly detected and repaired.

Improving GNSS triple-frequency cycle slip repair using ACMRI algorithm

The processing of GNSS triple-frequency cycle slips is an important prerequisite for providing high-precision location services. Cycle slip detection is achieved by constructing a group of detection combinations, namely two geometry-free phase combinations and one pseudo-range phase combination of GNSS observations. However, cycle slip estimation would be strongly affected by ill-conditioned equations, which means that even a slight fluctuation in the observations will cause large biases to the final results. To deal with this problem, a new cycle slips estimation algorithm of adjusting coefficient matrix based on residual information (ACMRI algorithm) is proposed. In our algorithm, a parameter k is utilized to adjust the coefficient matrix of the normal equation to compensate for the deviation of the observations, so as to reduce the influence of the ill-conditioned normal equation. However, it is significantly challenging to search for the value of k. To solve this difficulty, we firstly developed a new way to obtain the search region of the parameters using the method of statistics–verification–optimization based on numerous experiments. Then, a new two-order search method, based on the principle of minimum least-square residual and rounding residual, is proposed. Once the cycle slips are determined, the two residuals are used as the reliability index of cycle slips repair. Two geometry-free phase combinations [1 1– 2], [1 –2 1] and one pseudo-range phase combination [1 4 –5] are selected for the experiments using BDS2, BDS3, GPS, and Galileo observations. Experimental results show the proposed algorithm improves the success rates of triple-frequency cycle slips repair from least-squares solution rates of 89.3% (Galileo), 14.5% (BDS2), and 48.1% (BDS3) to 100% for all systems, and reduces the RMS error of the residual between the float solutions of cycle slips and their true values more than 90% compared with the least-squares method. To further evaluate the feasibility of the algorithm, 60 groups of combinations are set for the four GNSS systems. Results indicate that the proposed algorithm can significantly improve the triple-frequency cycle slip estimation and the success rate of cycle slip repair for all combinations of all the four systems.

Real-Time Cycle Slip Detection and Repair Method for BDS-3 Five-Frequency Data

Theoretically, five-frequency observations can form combined observations with longer wavelength, smaller ionospheric delay and smaller noise, which may improve the performance of cycle slip detection and repair. Four geometry-free phase combinations and one geometry-free phase and pseudorange combination are formed to detect and repair the cycle slips in real time. Firstly, the high-quality geometry-free phase combinations of three, four and five frequencies are discussed, then the optimal five-frequency geometry-free phase combinations are selected to detect the cycle slips. Secondly, one geometry-free phase and pseudorange combination which is linearly independent with the above four phase combinations is added to ensure that all the cycle slips can be detected. Thirdly, a real-time cycle slip repair algorithm based on the LAMBDA search method is deduced. The five-frequency real-time cycle slip detection and repair method has been tested by using BDS-3 undifferenced data, even under the condition of active ionospheric and low sampling interval. The results showed that the proposed method is capable of detecting and repairing all the simulated cycle slips on the five carriers in real time.

Effect of selection of combined observations on cycle-slip repair success rate for BDS triple-frequency signals

Modern global navigation satellite systems introduce additional frequencies that benefit the performance of cycle-slip detection and repair. However, recent related studies have focused on the success rate (SR) of cycle-slip detection rather than that of repair. This study considered common combinations of triple-frequency observations and analyzed their advantages/disadvantages in detail. To detect and repair cycle slip, combinations of the two main forms of observation were constructed based on the classic least-squares ambiguity decorrelation adjustment (LAMBDA) method, with consideration of residual ionospheric variations. A large volume of simulation data was used to test the cycle-slip repair SR of different combinations of observations under different ionospheric conditions. Theoretical and experimental results showed that using different forms of two geometry-free (GF) phase or two extra-wide-lane (EWL) combinations to fix the cycle-slip solution using the LAMBDA method was irrelevant to the cycle-slip repair SR of the 1EWL & 2GF and 2EWL & 1GF phase combination forms, respectively. Under the same ionospheric conditions, the performance of 2EWL & 1GF phase combinations was significantly better than that of 1EWL & 2GF phase combinations in terms of cycle-slip repair SR. The difference was mainly reflected in the performance of cycle-slip detection. The larger the maximum threshold of ionospheric variation (MTIV) value of GF phase combination observations, which represents the ability to resist the insensitive cycle-slip group ±(1, 1, 1), the lower the cycle-slip repair SR for those combinations. Therefore, the optimal strategy would be to employ strong GF phase combinations with a large MTIV value to detect cycle slip, and to employ excellent GF phase combinations with a high SR to repair cycle slip.

Fast cycle slip determination for high-rate multi-GNSS RTK using modified geometry-free phase combination

Cycle slip determination plays an important role in continuous real-time kinematic (RTK) positioning. Since cycle slips should be processed at each epoch, a fast determination method is needed for high-speed RTK applications, such as autopilot and airborne positioning, in which case high-sampling-rate GNSS data (such as 50 HZ) are required to be processed in real time. The geometry-free (GF) phase combination is one of the most commonly used combinations to deal with the cycle slips. However, the GF phase combination cannot distinguish the frequency on which cycle slips occur. Therefore, other methods, such as the Hatch–Melbourne–Wubbena (HMW) combination, are usually adopted to determine the frequency and the size of the cycle slips. Since noisy code pseudorange measurements are introduced, it is difficult to identify the small cycle slips, especially when cycle slips occur in multiple satellites and multiple frequencies simultaneously. In this contribution, a modified geometry-free (MGF) phase-only linear combination is proposed to quickly determine cycle slips for high-sampling-rate multi-GNSS RTK. The MGF algorithm utilizes the decimal part of the time difference GF phase combination to determine cycle slips satellite by satellite. It can directly estimate the cycle slips on a specific frequency, rather than a combined cycle slip as in the GF combination. The MGF method is tested against airborne and other kinematic situations. The results show that the MGF method can quickly determine the small cycle slips on each frequency even when all carrier phases suffer from cycle slips simultaneously. Compared with the combined method of GF and HMW and using a 24-h 1-Hz GPS/BDS dataset, the MGF method is 144 times faster and reduces the number of incorrectly repaired cycle slips from 4005 to 141.

Accuracy Analysis of Ionospheric Prediction Models for Repairing Cycle Slips for BeiDou Triple-Frequency Observations

Both the code–phase combination and the Geometry-Free (GF) phase combination are widely employed to detect and repair cycle slips for BeiDou Navigation Satellite System (BDS) triple-frequency observations. However, the effect of residual ionospheric delay on Narrow-Lane (NL) or GF observations must be considered to avoid incorrect cycle–slip estimation. To improve the accuracy in repairing cycle slips, a corrective ionospheric delay value predicted from the previous ionosphere sequence is used to amend the NL or GF observations at the current epoch. The main purpose of the work reported here is to evaluate the efficacy of a three-step method proposed to detect and repair cycle slip using two extra-wide-lane code–phase and one GF phase combination observations. BDS triple-frequency data were processed in two stages: separate processing of geosynchronous Earth orbit satellites, and the division of inclined geosynchronous satellite orbit and medium Earth orbit satellites into two groups for processing at 30° elevation thresholds. Results revealed that using the prediction models to correct NL or GF observations could ensure a rounding success rate of cycle slip close to 100%, even under high ionospheric activity.

An Efficient Cycle-Slip Repair Model With High Success Rate for BDS Triple- Frequency Observations

An improved cycle-slip repair model is proposed for BDS triple-frequency undifferenced observations. Two extra-wide-lane code-phase combinations and one additional geometry-free (GF) carrier-phase combination are employed. To ensure the GF phase combination follows a normal distribution, the residual ionospheric variation of the GF phase combination is corrected in real-time using the previous observation sequence without cycle slip. The integer least squares principle, based on the least-squares ambiguity decorrelation adjustment, is used to solve the fixed value of cycle slip. The corresponding covariance matrix of floating cycle-slip estimations used for construction is updated in real time to improve the fixed efficiency of cycle slip. Moreover, for reliable repair of cycle slip for triple-frequency observations, the critical ratio value between the second-best and best cycle-slip candidates for different residual ionosphere accuracies and different repair success rates are given based on large amounts of simulated data. Lastly, a set of active ionosphere and low-sampling-rate real data was used for evaluation and analysis of the algorithm. Results showed the success rate of cycle-slip repair is 99.997%, even under active ionosphere conditions, with low satellite elevation and low sampling rate. Unfortunately, one cycle-slip group (1, 1, 1) of the C14 satellite was not detected successfully and repaired correctly because of insensitivity to the GF phase combination under bad observation conditions.

Real-time cycle slip correction for a single triple-frequency BDS receiver based on ionosphere-reduced virtual signals

Being an essential part of GNSS processing, cycle slip detection and repair has been intensively investigated. This paper develops an improved real-time cycle slip correction method based on three types of independent linear combinations of time-difference triple-frequency BDS observables. At first, one geometry-free pseudorange minus phase linear combination is selected as extra-wide lane (EWL) virtual signal and its cycle slips can be easily detected and repaired due to the long wavelength. Then, one geometry-free phase combination, treated as wide lane (WL) signal, is used to detect and repair cycle slips on WL combination based on fixed EWL ambiguity. Similarly, another one geometry-free phase combination is adopted to correct cycle slips on narrow lane (NL) signal. As a result of the short wavelength of NL combination, the residual ionospheric delay cannot be ignored and should be accurately estimated by the original observables. When the time-difference ambiguities of EWL, WL and NL signals are determined, the cycle slips on the original observables can be uniquely corrected by matrix operation. As the ionospheric delay plays a vital role in estimating ambiguities of combination signals, the second-order time-difference of ionospheric delay is used to detect the epoch with cycle slips and participate in estimating the time-difference ambiguity of NL signal. Considering that satellite elevation can be treated as quality factor of observables, we build a model to calculate the standard deviations of the selected combinations and 20° can be used as threshold value to correct cycle slips or not. The method has been tested on real 30 s triple-frequency BDS data with artificial cycle slips. Results show that the three-step method can detect and repair cycle slips correctly and effectively when the elevation is higher than 20°. While the elevation is lower than the threshold, the cycle slips should just be detected without repair to avoid miscalculation.

Real-time cycle-slip detection and repair for BeiDou triple-frequency undifferenced observations

A new method of real-time cycle-slip detection and repair for BeiDou navigation satellite system (BDS) triple-frequency undifferenced observations is proposed. The method, which is based on code–phase and geometry-free phase combinations, composes linearly independent combination observations to uniquely determine the cycle-slip of original frequency phase observations in two independent steps. First, two extra-wide lane (EWL) code–phase combinations are utilised to determine the EWL combination cycle-slips. The sum of the carrier phase combination coefficients is zero. Second, the geometry-free phase combination with a non-zero sum of combination coefficients composes linearly independent combination observations with two code–phase combinations. Ionospheric delay variance systematic deviation is corrected with several previous carrier-phase observations without cycle-slip, which seriously affect the accuracy of the geometry-free phase combination observations. The BDS triple-frequency carrier-phase and code observations of different satellite types at 30 s sampling interval, which involve increased active ionospheric conditions in 1 day, are utilised to test the method. Results show that the proposed method can efficiently detect and accurately repair any cycle-slip combinations in real-time for different satellite types under active ionospheric conditions. No erroneous and leakage judgments are observed in the test.

A new triple-frequency cycle slip detecting algorithm validated with BDS data

Triple-frequency global navigation satellite systems allow the introduction of additional linear observation combinations. We define two geometry-free phase combinations and one geometry-free pseud...