Wide Lane Research Articles

An Improved BeiDou-2 Satellite-Induced Code Bias Estimation Method.

Different from GPS, GLONASS, GALILEO and BeiDou-3, it is confirmed that the code multipath bias (CMB), which originate from the satellite end and can be over 1 m, are commonly found in the code observations of BeiDou-2 (BDS) IGSO and MEO satellites. In order to mitigate their adverse effects on absolute precise applications which use the code measurements, we propose in this paper an improved correction model to estimate the CMB. Different from the traditional model which considering the correction values are orbit-type dependent (estimating two sets of values for IGSO and MEO, respectively) and modeling the CMB as a piecewise linear function with a elevation node separation of 10°, we estimate the corrections for each BDS IGSO + MEO satellite on one hand, and a denser elevation node separation of 5° is used to model the CMB variations on the other hand. Currently, the institutions such as IGS-MGEX operate over 120 stations which providing the daily BDS observations. These large amounts of data provide adequate support to refine the CMB estimation satellite by satellite in our improved model. One month BDS observations from MGEX are used for assessing the performance of the improved CMB model by means of precise point positioning (PPP). Experimental results show that for the satellites on the same orbit type, obvious differences can be found in the CMB at the same node and frequency. Results show that the new correction model can improve the wide-lane (WL) ambiguity usage rate for WL fractional cycle bias estimation, shorten the WL and narrow-lane (NL) time to first fix (TTFF) in PPP ambiguity resolution (AR) as well as improve the PPP positioning accuracy. With our improved correction model, the usage of WL ambiguity is increased from 94.1% to 96.0%, the WL and NL TTFF of PPP AR is shorten from 10.6 to 9.3 min, 67.9 to 63.3 min, respectively, compared with the traditional correction model. In addition, both the traditional and improved CMB model have a better performance in these aspects compared with the model which does not account for the CMB correction.

BDS code bias periodical mitigation by low-pass filtering and its applications in precise positioning

The code-phase divergences, which are minimal for GPS, GLONASS, and Galileo satellites, are commonly found in BeiDou Navigation Satellite System (BDS) Geostationary Orbit (GEO), Inclined GeoSynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. Several precise positioning applications which use code observations are severely affected by these code biases. We present an analysis of code bias based on multipath (MP) combination observations. To mitigate the effect of BDS code bias on precise positioning, we proposed a periodical correction method using a low-pass filter for BDS GEO, IGSO and MEO satellites. The auto-correlation of MP series over long periods is analyzed to obtain the periods of the dominant repeating components for three types of BDS satellites. The periods of the dominant daily repeating components are close to 86,160 s for BDS GEO and IGSO satellites while 603,120 s for MEO satellites. The zero phase-shift low-pass filter was used to extract the low-frequency components of MP series and then low-frequency components are applied to mitigate the code bias periodically. The developed correction methods can make a more remarkable improvement for the accuracy of MP series, compared to the current elevation-dependent correction models. Data sets collected at 50 Global Navigation Satellite System (GNSS) ground stations including 15 of the International GNSS Monitoring and Assessment System (iGMAS) and 35 of the Multi-GNSS Experiment (MGEX) stations are employed for this study. To analyze the influence of code bias on precise positioning and validate the effectiveness of the correction methods, some applications such as single point positioning (SPP), wide-lane (WL) ambiguity analysis and Uncalibrated Phase Delays (UPDs) estimation are conducted. After applying the proposal correction method to the code observations, SPP solutions outperform the uncorrected ones in term of positioning accuracy. The positioning accuracy decreased by 0.28 and 0.1 m in the north and east components and the improvements are more significant for the U components decreased by 0.42 m. In addition, the systematic variations of Melbourne-Wübbena (MW) combination are greatly removed and the convergence time of the MW series are decreased. Moreover, significant improvement is also achieved in terms of the usage rate and residuals of UPDs estimation.

Adaptive Kalman filter based on variance component estimation for the prediction of ionospheric delay in aiding the cycle slip repair of GNSS triple-frequency signals

In order to incorporate the time smoothness of ionospheric delay to aid the cycle slip detection, an adaptive Kalman filter is developed based on variance component estimation. The correlations between measurements at neighboring epochs are fully considered in developing a filtering algorithm for colored measurement noise. Within this filtering framework, epoch-differenced ionospheric delays are predicted. Using this prediction, the potential cycle slips are repaired for triple-frequency signals of global navigation satellite systems. Cycle slips are repaired in a stepwise manner; i.e., for two extra wide lane combinations firstly and then for the third frequency. In the estimation for the third frequency, a stochastic model is followed in which the correlations between the ionospheric delay prediction errors and the errors in the epoch-differenced phase measurements are considered. The implementing details of the proposed method are tabulated. A real BeiDou Navigation Satellite System data set is used to check the performance of the proposed method. Most cycle slips, no matter trivial or nontrivial, can be estimated in float values with satisfactorily high accuracy and their integer values can hence be correctly obtained by simple rounding. To be more specific, all manually introduced nontrivial cycle slips are correctly repaired.

GPS receiver phase biases estimable in PPP-RTK networks: dynamic characterization and impact analysis

The integer ambiguity resolution enabled precise point positioning (PPP-RTK) has been proven advantageous in a wide range of applications. The realization of PPP-RTK concerns the isolation of satellite phase biases (SPBs) and other corrections from a network of Global Positioning System (GPS) reference receivers. This is generally based on Kalman filter in order to achieve real-time capability, in which proper modeling of the dynamics of various types of unknowns remains crucial. This paper seeks to gain insight into how to reasonably deal with the dynamic behavior of the estimable receiver phase biases (RPBs). Using dual-frequency GPS data collected at six colocated receivers over days 50–120 of 2015, we analyze the 30-s epoch-by-epoch estimates of L1 and wide-lane (WL) RPBs for each receiver pair. The dynamics observed in these estimates are a combined effect of three factors, namely the random measurement noise, the multipath and the ambient temperature. The first factor can be overcome by turning to a real-time filter and the second by considering the use of a sidereal filtering. The third factor has an effect only on the WL, and this effect appears to be linear. After accounting for these three factors, the low-pass-filtered, sidereal-filtered, epoch-by-epoch estimates of L1 RPBs follow a random walk process, whereas those of WL RPBs are constant over time. Properly modeling the dynamics of RPBs is vital, as it ensures the best convergence of the Kalman-filtered, between-satellite single-differenced SPB estimates to their correct values and, in turn, shortens the time-to-first-fix at user side.

Visual Correlates of Fitness to Drive in Adults With Multiple Sclerosis.

The impact of visual and visual-cognitive impairments on fitness to drive in persons with multiple sclerosis (PwMS) are not well studied. We quantified visual correlates of fitness to drive in 30 PwMS. PwMS completed visual ability and visual attention assessments, and a standardized on-road assessment, and were compared with 145 older volunteer drivers. PwMS (vs. older volunteer drivers) made more total ( W = 12,139, p = .03) and critical driving errors (predictive of crashes) in adjustment to stimuli ( W = 11,352, p < .0001), vehicle positioning ( W = 11,449, p < .0001), and wide lane turns ( W = 9,932, p < .0001). PwMS who failed (vs. passed) made more total ( W = 325, p = .04), adjustment to stimuli ( W = 321.5, p = .02), and gap acceptance errors ( W = 333, p = .03). For PwMS, adjustment to stimuli errors moderately correlated with visual acuity (ρ = .50, p = .006), and gap acceptance errors moderately correlated with visual processing speed (ρ = .40, p = .03). Visual-cognitive impairments may be indicative of critical driving errors and help identify PwMS at-risk for fitness to drive.

A modified geometry- and ionospheric-free combination for static three-carrier ambiguity resolution

The reliability of the classical geometry- and ionospheric-free (GIF) three-carrier ambiguity resolution (TCAR) degrades when applied to long baselines of hundreds of kilometers. To overcome this deficiency, we propose two new models, which are used sequentially to resolve wide-lane (WL) and narrow-lane (NL) ambiguities and form a stepwise ambiguity resolution (AR) strategy. In the first model, after a successful extra-wide-lane AR, the pseudorange and phase observations are combined to estimate WL ambiguities, in which the residual ionospheric delays and geometry effects are eliminated. In the second model, using the resolved ambiguities from the first step, the two WL ambiguities are combined to remove ionospheric and geometry effects. The unknown coefficients in the two models are determined in such that they minimize the formal errors in the ambiguity estimates to optimize the ambiguity estimation. Using experimental BeiDou triple-frequency observations, we evaluate our method and identify three advantages. First, the two models use double-differenced phase observations that are not differences across frequency. Second, the two models are entirely free from ionospheric delay and geometry effects. Third, the unknown estimates in the two models satisfy the minimum noise condition, which makes the formal errors in the float NL ambiguity estimates much lower than those obtained with common GIF TCAR methods, thereby directly and significantly increasing the success rate of AR compared to the cascaded integer resolution method and two other GIF combinations.

Wide-area Kinematic Positioning with BeiDou Triple-frequency Signals

Article free to read on jounal website. A key challenge of wide-area kinematic positioning using the BeiDou system is to reduce the effects of the elevation-dependent hardware biases in code signals. Based on three geometry-free/ionosphere-free combinations, the elevation-dependent code biases are modeled for all BeiDou satellites. Results from the data sets for 5 baselines of 533 to 2545 km demonstrate that the wide-lane (WL) integer-fixing success rates of 95% to 99% can be achieved within 50 independent epochs. Under the condition of HDOP less than 2, the overall RMS statistics of ionospheric-free WL single-epoch solutions achieve 24 to 50 cm in the horizontal direction. Smoothing processing over the moving window of 40 epochs reduces the RMS values by a factor of about 2. Considering the distance-independent nature, the above results show the potential for achieving reliable and high-precision positioning with sparsely distributed ground stations regionally or globally.

Method and assessment of BDS triple-frequency ambiguity resolution for long-baseline network RTK

Fast and reliable ambiguity resolution (AR) over long baselines is one of the major challenges for large-scale GNSS network real-time kinematic (RTK) positioning. In the dual-frequency case, wide-lane (WL) ambiguities are usually fixed firstly, followed by the procedure of determination of the narrow-lane (NL) ambiguity integers based on the ionosphere-free model. For long-baseline network RTK, there are still some problems faced, for instance the WL AR still needs to take over tens of epochs due to the influence of pseudorange noises and multipath effects; the NL AR model is weak since more parameters are introduced, thus much time is needed to guarantee the precision of float ambiguity solutions. Along with the deployment of modernized GPS, BDS and other GNSS, the triple-frequency AR with real data gradually becomes feasible. Many literatures have proven the third signal will make AR faster and more reliable. In this paper based on the characteristics of network RTK, a modified ionosphere-free model was proposed to improve EWL/WL AR performance for long baselines, followed by the comparison with several commonly-used EWL/WL AR models. The NL AR performance with triple-frequency and dual-frequency observations was also tested. In NL AR, a partial AR strategy is adopted to weaken the negative influence of new-rising or low-elevation satellites. Experiments were conducted using real BDS triple-frequency data on 74km and 241km baselines. Results show that the modified ionosphere-free model can balance the ambiguity precision and ambiguity bias better for the EWL/WL AR. The NL AR with triple-frequency observations also performs significantly better than that in dual-frequency mode, with 29.9% and 32.9% improvement in time-to-first-fix (TTFF) for the 74km and 241km baselines respectively.

Rapid ambiguity resolution over medium-to-long baselines based on GPS/BDS multi-frequency observables

Medium-long baseline RTK positioning generally needs a long initial time to find an accurate position due to non-negligible atmospheric delay residual. In order to shorten the initial or re-convergence time, a rapid phase ambiguity resolution method is employed based on GPS/BDS multi-frequency observables in this paper. This method is realized by two steps. First, double-differenced un-combined observables (i.e., L1/L2 and B1/B2/B3 observables) are used to obtain a float solution with atmospheric delay estimated as random walk parameter by using Kalman filter. This model enables an easy and consistent implementation for different systems and different frequency observables and can readily be extended to use more satellite navigation systems (e.g., Galileo, QZSS). Additional prior constraints for atmospheric information can be quickly added as well, because atmospheric delay is parameterized. Second, in order to fix ambiguity rapidly and reliably, ambiguities are divided into three types (extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL)) according to their wavelengths and are to be fixed sequentially by using the LAMBDA method. Several baselines ranging from 61km to 232km collected by Trimble and Panda receivers are used to validate the method. The results illustrate that it only takes approximately 1, 2 and 6 epochs (30s intervals) to fix EWL, WL and NL ambiguities, respectively. More epochs’ observables are needed to fix WL and NL ambiguity around local time 14:00 than other time mainly due to more active ionosphere activity. As for the re-convergence time, the simulated results show that 90% of epochs can be fixed within 2 epochs by using prior atmospheric delay information obtained from previously 5min. Finally, as for positioning accuracy, meter, decimeter and centimeter level positioning results are obtained according to different ambiguity resolution performances, i.e., EWL, WL and NL fixed solutions.

Improved ambiguity resolution for URTK with dynamic atmosphere constraints

Raw observation processing method with prior knowledge of ionospheric delay could strengthen the ambiguity resolution (AR), but it does not make full use of the relatively longer wavelength of wide-lane (WL) observation. Furthermore, the accuracy of calculated atmospheric delays from the regional augmentation information has quite different in quality, while the atmospheric constraint used in the current methods is usually set to an empirical value. A proper constraint, which matches the accuracy of calculated atmospheric delays, can most effectively compensate the residual systematic biases caused by large inter-station distances. Therefore, the standard deviation of the residual atmospheric parameters should be fine-tuned. This paper presents an atmosphere-constrained AR method for undifferenced network RTK (URTK) rover, whose ambiguities are sequentially fixed according to their wavelengths. Furthermore, this research systematically analyzes the residual atmospheric error and finds that it mainly varies along the positional relationship between the rover and the chosen reference stations. More importantly, its ionospheric part of certain location will also be cyclically influenced every day. Therefore, the standard deviation of residual ionospheric error can be modeled by a daily repeated cosine or other functions with the help of data one day before, and applied by rovers as pseudo-observation. With the data collected at 29 stations from a continuously operating reference station network in Guangdong Province (GDCORS) in China, the efficiency of the proposed approach is confirmed by improving the success and error rates of AR for 10-20 % compared to that of the WL-L1-IF one, as well as making much better positioning accuracy.

Mitigating BeiDou Satellite-Induced Code Bias: Taking into Account the Stochastic Model of Corrections

The BeiDou satellite-induced code biases have been confirmed to be orbit type-, frequency-, and elevation-dependent. Such code-phase divergences (code bias variations) severely affect absolute precise applications which use code measurements. To reduce their adverse effects, an improved correction model is proposed in this paper. Different from the model proposed by Wanninger and Beer (2015), more datasets (a time span of almost two years) were used to produce the correction values. More importantly, the stochastic information, i.e., the precision indexes, were given together with correction values in the improved model. However, only correction values were given while the precision indexes were completely missing in the traditional model. With the improved correction model, users may have a better understanding of their corrections, especially the uncertainty of corrections. Thus, it is helpful for refining the stochastic model of code observations. Validation tests in precise point positioning (PPP) reveal that a proper stochastic model is critical. The actual precision of the corrected code observations can be reflected in a more objective manner if the stochastic model of the corrections is taken into account. As a consequence, PPP solutions with the improved model outperforms the traditional one in terms of positioning accuracy, as well as convergence speed. In addition, the Melbourne-Wübbena (MW) combination which serves for ambiguity fixing were verified as well. The uncorrected MW values show strong systematic variations with an amplitude of half a wide-lane cycle, which prevents precise ambiguity determination and successful ambiguity resolution. After application of the code bias correction models, the systematic variations can be greatly removed, and the resulting wide lane ambiguities are more likely to be fixed. Moreover, the code residuals show more reasonable distributions after code bias corrections with either the traditional or the improved model.

Improved Method to Detect and Repair Cycle Slip for GNSS Medium–Long Baseline in Real-Time Marine Surveys

ABSTRACTDistance-related errors complicate the resolution of real-time ambiguity in medium–long baseline marine surveys. Therefore, detection and recovery of cycle slips in real time is required to ensure high accuracy of global navigation satellite system positioning and navigation in marine surveys. To resolve this, an improved method was presented, where linear combinations of the triple-differenced (TD) between carriers L1 and L2 were formed for a wide lane and free ionosphere. To overcome severe ill-conditioned problems of the normal equation, the Tikhonov regularization method was used. The construction of a regularized matrix by combining a priori information of known coordinates of reference stations, followed by the determination of the corresponding regularized parameter are suggested. A float solution was calculated for the TD ambiguity. The search cycle slip (TD integer ambiguity) was obtained using the least-squares ambiguity decorrelation adjustment (LAMBDA) method. Using our method, cycle slips of several reference station baselines with lengths of a few hundred to one thousand kilometers were detected in real time. The results were consistent with professional software, with a success rate of 100%.

BDS ambiguity resolution with the modified TCAR method for medium-long baseline

As the BeiDou Navigation Satellite System (BDS) attained initial regional operational status at the end of October 2012, real BDS data are available to investigate triple-frequency ambiguity resolution (AR) performance. In this contribution, analysis of the classical TCAR models and limiting factors is given. It is concluded that the residual double-differencing (DD) ionospheric delay is the key limitation to the medium and long range narrow-lane (NL) ambiguity resolution in step 3 of the classical TCAR method. To improve this algorithm, the third step of the classical TCAR method is modified accordingly. The modified TCAR comprises three major steps. Step 1 and step 2 are the same as the classical TCAR, which is the geometry-free determination of the extra-wide-lane (EWL) and wide-lane (WL) ambiguities. Then we can derive the DD first-order ionospheric delay estimated from the ambiguity-fixed EWL. As the noise term of the estimated DD ionospheric delay is very large, the smooth method is employed to correct the estimated DD ionospheric delay. In step 3, the smooth DD ionospheric delay is used to completely correct the single-epoch DD float NL ambiguity resolution. It is also noted that there exist cycle-slips which influence the process of the ionosphere-smooth method. This is followed by a procedure to repair the cycle-slip. As a result, the modified-TCAR method shows a much better performance than the classical TCAR method over medium and long baseline.

An Improved Geometry-free Three Carrier Ambiguity Resolution Method for the BeiDou Navigation Satellite System

BeiDou satellites transmit triple-frequency signals, which bring substantial benefits to carrier phase Ambiguity Resolution (AR). The traditional geometry-free model Three-Carrier Ambiguity Resolution (TCAR) method looks for a suitable combination of carrier phase and code-range observables by searching and comparing in the integer range, which limits the AR success probability. By analysing the error characteristics of the BeiDou triple-frequency observables, we introduce a new procedure to select the optimal combination of carrier phase and code observables to resolve the resolution of Extra-Wide-Lane (EWL) and Wide-Lane (WL) ambiguity. We also investigate a geometry-free and ionosphere-eliminated method for AR of the Medium-Lane (ML) and Narrow-Lane (NL) observables. In order to evaluate the performance of the improved TCAR method, real BeiDou triple-frequency observation data for different baseline cases were collected and processed epoch-by-epoch. The results show that the improved geometry-free TCAR method increases the single epoch AR success probability by up to 90% for short baseline and 80% for long baseline. The A perfect (100%) AR success probability can also be effortlessly achieved by averaging the float ambiguities over just tens of epochs.

Instantaneous Real-Time Kinematic Decimeter-Level Positioning with BeiDou Triple-Frequency Signals over Medium Baselines.

Many applications, such as marine navigation, land vehicles location, etc., require real time precise positioning under medium or long baseline conditions. In this contribution, we develop a model of real-time kinematic decimeter-level positioning with BeiDou Navigation Satellite System (BDS) triple-frequency signals over medium distances. The ambiguities of two extra-wide-lane (EWL) combinations are fixed first, and then a wide lane (WL) combination is reformed based on the two EWL combinations for positioning. Theoretical analysis and empirical analysis is given of the ambiguity fixing rate and the positioning accuracy of the presented method. The results indicate that the ambiguity fixing rate can be up to more than 98% when using BDS medium baseline observations, which is much higher than that of dual-frequency Hatch-Melbourne-Wübbena (HMW) method. As for positioning accuracy, decimeter level accuracy can be achieved with this method, which is comparable to that of carrier-smoothed code differential positioning method. Signal interruption simulation experiment indicates that the proposed method can realize fast high-precision positioning whereas the carrier-smoothed code differential positioning method needs several hundreds of seconds for obtaining high precision results. We can conclude that a relatively high accuracy and high fixing rate can be achieved for triple-frequency WL method with single-epoch observations, displaying significant advantage comparing to traditional carrier-smoothed code differential positioning method.

BeiDou phase bias estimation and its application in precise point positioning with triple-frequency observable

At present, the BeiDou system (BDS) enables the practical application of triple-frequency observable in the Asia-Pacific region, of many possible benefits from the additional signal; this study focuses on exploiting the contribution of zero difference (ZD) ambiguity resolution (AR) to the precise point positioning (PPP). A general modeling strategy for multi-frequency PPP AR is presented, in which, the least squares ambiguity decorrelation adjustment (LAMBDA) method is employed in ambiguity fixing based on the full variance-covariance ambiguity matrix generated from the raw data processing model. Because of the reliable fixing of BDS L1 ambiguity faces more difficulty, the LAMBDA method with partial ambiguity fixing is proposed to enable the independent and instantaneous resolution of extra wide-lane (EWL) and wide-lane (WL). This mechanism of sequential ambiguity fixing is demonstrated for resolving ZD satellite phase bias and performing triple-frequency PPP AR with two reference station networks with a typical baseline of up to 400 and 800 km, respectively. Tests show that about $$90\,\%$$ of the EWL and WL phase bias of BDS has a consistency of better than 0.1 cycle, and this value decreases to $$<$$ 80 % for L1 phase bias for Experiment I, while all the solutions of Experiment II have a similar RMS of about 0.12 cycles. In addition, the repeatability of the daily mean phase bias agree to 0.093 cycles and 0.095 cycles for EWL and WL on average, which is much smaller than 0.20 cycles of L1. To assess the improvement of fixed PPP brought by applying the third frequency signal as well as the above phase bias, various ambiguity fixing strategy are considered in the numerical demonstration. It is shown that the impact of the additional signal is almost negligible when only float solution involved. It is also shown that by fixing EWL and WL together, as opposed to the single ambiguity fixing, will leads to an improvement in PPP accuracy by about $$20.6\,\%$$ on average. Attributed to the efficient resolution of EWL $$+$$ WL within about 2 min in Experiment I, the 0.5 m level positioning can be achieved in 10 min for both horizontal and vertical, compared to 50 min for horizontal and 30 min for vertical by the NONE/EWL/WL fixed solution. While, for Experiment II, the improvement in the convergence can only be seen for the horizontal as the TTFF takes about 40 min for EWL and WL to be resolved.

Ionospheric effects in uncalibrated phase delay estimation and ambiguity-fixed PPP based on raw observable model

Zero-difference (ZD) ambiguity resolution (AR) reveals the potential to further improve the performance of precise point positioning (PPP). Traditionally, PPP AR is achieved by Melbourne–Wubbena and ionosphere-free combinations in which the ionosphere effect are removed. To exploit the ionosphere characteristics, PPP AR with L1 and L2 raw observable has also been developed recently. In this study, we apply this new approach in uncalibrated phase delay (UPD) generation and ZD AR and compare it with the traditional model. The raw observable processing strategy treats each ionosphere delay as an unknown parameter. In this manner, both a priori ionosphere correction model and its spatio-temporal correlation can be employed as constraints to improve the ambiguity resolution. However, theoretical analysis indicates that for the wide-lane (WL) UPD retrieved from L1/L2 ambiguities to benefit from this raw observable approach, high precision ionosphere correction of better than 0.7 total electron content unit (TECU) is essential. This conclusion is then confirmed with over 1 year data collected at about 360 stations. Firstly, both global and regional ionosphere model were generated and evaluated, the results of which demonstrated that, for large-scale ionosphere modeling, only an accuracy of 3.9 TECU can be achieved on average for the vertical delays, and this accuracy can be improved to about 0.64 TECU when dense network is involved. Based on these ionosphere products, WL/narrow-lane (NL) UPDs are then extracted with the raw observable model. The NL ambiguity reveals a better stability and consistency compared to traditional approach. Nonetheless, the WL ambiguity can be hardly improved even constrained with the high spatio-temporal resolution ionospheric corrections. By applying both these approaches in PPP-RTK, it is interesting to find that the traditional model is more efficient in AR as evidenced by the shorter time to first fix, while the three-dimensional positioning accuracy of the RAW model outperforms the combination model by about \(7.9\,\%\). This reveals that, with the current ionosphere models, there is actually no optimal strategy for the dual-frequency ZD ambiguity resolution, and the combination approach and raw approach each has merits and demerits.

Three-carrier ambiguity resolution using the modified TCAR method

Multi-frequency technique is expected to be widely adopted with the new generations of global navigation satellite system, which is anticipated to benefit ambiguity resolution (AR). Three-carrier AR (TCAR) is a classical AR method based on triple-frequency observations, which is efficient for AR of short baseline. However, this method ignores the residual ionospheric delay, which degrades the reliability in active ionosphere situations and reduces the success of AR for medium and long baselines. We investigate the classical TCAR method and identify the major deficiency that hampers its application, especially to medium and long baselines. To improve this algorithm, the second and third steps of the classical TCAR are modified accordingly. In step 2, the ambiguity-resolved extra-wide-lane (EWL) combination and three pseudorange observations are employed to eliminate or reduce the residual ionospheric delay, in addition to the geometry term. In step 3, besides the EWL combination and pseudoranges, the ambiguity-resolved wide-lane (WL) combination is used to completely eliminate the ionosphere and geometry terms. The combination coefficients of these pseudoranges and combinations are optimized to minimize the noise of the ambiguity estimates. In order to assess the performances, real triple-frequency observations of BeiDou navigation system of baselines with different lengths are processed by the two methods. Results show that, the classical TCAR method is very sensitive to ionospheric delay and limited to short baseline application, while the modified TCAR method is free from ionospheric delay and can be applied to AR of median and long baselines. For WL AR, the modified TCAR method shows a comparable performance with the classical TCAR method, and a better performance can be expected when the baseline becomes longer, e.g., from 100s to 1,000s kilometers. For narrow-lane AR, the modified TCAR method performs much better than the classical TCAR method for median and long baselines.

Real-time detection and repair of cycle slips in triple-frequency GNSS measurements

Cycle slip detection and repair are prerequisites to the use of the global navigation satellite system (GNSS) carrier phases for precise positioning. Modern GNSS techniques introduce triple- or multi-frequency signals that are beneficial for cycle slip detection and repair. We present a new real-time cycle slip detection and repair method based on the independent linear combinations of undifferenced triple-frequency GNSS observations. The proposed method forms three types of linear combinations based on the original observations. These combinations are called extra-wide lane (EWL), wide lane (WL), and narrow lane (NL). Cycle slips on the combinations are determined sequentially in three cascaded steps. The first step employs the geometry-free and ionosphere-free Hatch–Melbourne–Wübbena combination to determine and repair the EWL cycle slips. The second step subtracts the cycle-slip-repaired EWL combination from the WL combination to eliminate the geometry part of the WL combination. This subtraction results in a new function that contains the WL ambiguity and residual ionospheric delay. This function is differenced at two consecutive epochs to determine the WL cycle slips. The residual ionospheric delay difference is ignored because of its small magnitude relative to WL wavelength. The third step determines the NL cycle slips in the same manner as in the second step. The difference is that the cycle-slip-repaired EWL combination is replaced with the more accurate cycle-slip-repaired WL combination. Moreover, the residual ionospheric delay difference is compensated by the ionospheric delay rate derived from the original carrier phase observations. When the EWL, WL, and NL cycle slips are determined, cycle slips on the original carrier phase observations can be uniquely identified. The proposed approach has been tested on 30-s triple-frequency BeiDou navigation satellite system data under different levels of ionospheric variations, and on 30-s triple-frequency global positioning system and quasi-zenith satellite system data. Results indicate that the approach can effectively detect and correct cycle slips even for one cycle under low sampling rate or active ionospheric conditions on each frequency in real time.

The carrier-multipath observable: a new carrier-phase multipath mitigation technique

Modeling and mitigating carrier-phase multipath errors continue to be a significant challenge for high-accuracy positioning using global navigation satellite systems. The multipath error is dependent on the operational environment and therefore cannot be mitigated by differencing techniques. The effect of multipath is accentuated when observables based on linear combinations of measurements from two or more frequencies are formulated. We develop a new carrier-phase multipath error observable that isolates the inter-frequency carrier-phase multipath error for linear combinations of observables, such as wide-lane (WL). Real-time kinematic positioning results from varying baseline lengths show that a significant reduction in between 14 and 47 % in the time to initial ambiguity resolution are achieved by correcting the WL observable using the new carrier-phase multipath error observable.