Wide-lane Observations Research Articles

Theoretical Analysis and Experimental Evaluation of Wide-Lane Combination for Single-Epoch Positioning with BeiDou-3 Observations

Multi-frequency signals can enable some wide-lane (WL) observations to achieve instantaneous ambiguity resolution (AR) in complex scenarios, but simply adding WL observations will also place additional pressure on real-time kinematic data transmission. With the official service of the third-generation Beidou Navigation Satellite System, which broadcasts five-frequency signals, this dilemma has become increasingly evident. It is significant to explore multi-frequency observation combination methods that take into account both positioning precision and data transmission burden. In this work, we use the least squares method to derive the theoretical precision of the single-epoch WL combination of 16 schemes with varying frequency numbers (three or more) under the ionosphere-fixed model and the ionosphere-float model. The baseline solutions of 4.3 km and 93.56 km confirm that the positioning results are broadly consistent with the theoretical derivations under both models. In the ionosphere-fixed mode, the five-frequency scheme (B1C, B1I, B3I, B2b, B2a) yields the best positioning performance, improving the 3-dimensional positioning error standard deviation, circle error probable (CEP), and spherical error probable at 75% probability by 7.8%, 11.5%, and 6.7%, respectively, compared with the optimal triple-frequency scheme (B1C, B3I, B2a). Under the ionosphere-float model, the quad-frequency scheme (B1C, B3I, B2b, B2a) provides the best positioning performance, with only the CEP at 75% improving by 1.3% over the triple-frequency scheme. Given that the optimal triple-frequency scheme has a lower data volume, this work recommends it as the preferred scheme.

Ambiguity Resolution for Long Baseline in a Network with BDS-3 Quad-Frequency Ionosphere-Weighted Model

For long baseline in a network, the traditional combined ionosphere-free (IF) + wide-lane (WL) strategy is commonly used, but the residual tropospheric delays and larger noise hamper the basic ambiguity resolution (AR). With the completion of the BeiDou global navigation satellite system (BDS-3) and the quad-frequency signals provided by BDS-3 satellites, we can construct more combinations that are conducive to ambiguity resolution. Compared with ionosphere-free linear combinations, we estimated ionospheric delay using three independent WL observations, and formed an ionosphere-weighted model using uncombined code and phase observations, which proved to be quite effective. Based on the real quad-frequency BDS-3 observations of two CORS (Continuously Operating Reference Stations) and two user stations, we processed eight days of data to study the formal and empirical ambiguity success rates and user positioning errors. The rounding success rate of WL ambiguity was significantly improved with ionospheric correction. The success rate of the basic ambiguity increased from 94.4 and 96.1% to 98.0% using the quad-frequency ionosphere-weighted (QFIW) model compared with the double-frequency ionosphere-free (DFIF) model and the triple-frequency geometry-based (TFGB) model. Furthermore, the user E/N/U positioning accuracy improved by 20.6/31.5/13.1% and 6.3/22.9/5.8%, respectively.

Tightly combined triple-frequency GPS and BDS for rapid wide-lane RTK positioning with consideration of carrier-phase differential inter-system bias

Multi-frequency signals have been accessible for most Global Navigation Satellite Systems . Existing studies have verified that using multi-frequency extra-wide-lane and wide-lane observations can realize decimeter, sub-decimeter and even centimeter rapid positioning. In this paper, a tightly combined wide-lane real-time kinematic positioning method using triple-frequency GPS and BDS is proposed. The differential inter-system bias is taken into consideration so that an inter-system differencing model is formed. Due to the influence of different frequencies between GPS and BDS, the double-difference wide-lane ambiguity between GPS and BDS reference satellites and the single-difference ambiguity of the BDS reference satellite are estimated jointly with the wide-lane differential inter-system bias. Thus, a full-rank model can be obtained without any external calibration. Using the stability of wide-lane differential inter-system bias in the estimation from epoch to epoch, redundant observations can be introduced, therefore the strength of the positioning model can be enhanced. Positioning performance under simulated obstructed environments is evaluated. The results show that the inter-system model can effectively improve the positioning compared with the conventional intra-system model for the severely obstructed situations.

A Tightly Coupled BDS/INS Integrated Positioning Algorithm Based on Triple-Frequency Single-Epoch Observations

Vehicular dynamic positioning based on tightly coupled (TC) Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integration in urban areas is due to either low accuracy of pseudorange or poor continuity of carrier phase, resulting in insufficient positioning performance. To enhance the stability while ensuring positioning accuracy, this paper proposed a tightly coupled Beidou Navigation Satellite System (BDS)/INS integration scheme by improving measurement modelling with triple-frequency observations: first, a stepwise single-epoch ambiguity resolution of extra-wide-lane (EWL)/wide-lane (WL) combined observations and then modelling the measurement equation with fixed WL observation instead of conventional pseudorange or carrier phase. Experiments were carried out for verification with data collected in real traffic by a measurement vehicle. The proposed method achieved single-epoch output with an RMS statistical accuracy of decimetre level of 0.152 m horizontally and 0.196 m vertically. The signal outage experiment verified that the proposed algorithm is restoring high-accuracy positioning output in single-epoch once the signal is recaptured. The proposed method obtained a positioning accuracy improvement of 43.6% horizontally and 6.2% vertically in signal outage sections compared to the conventional method. This avoids the multiepoch ambiguity searching to fix with conventional carrier-phase processing, thereby improving the positioning stability.

A new single-epoch method for resolving GNSS ambiguity with segmented search in short baseline

Correct ambiguity resolution (AR) is the key for high-precision positioning. In order to reliably resolve ambiguity, an improved single-epoch segmented ambiguity algorithm is proposed in this paper. First, the double-difference wide-lane ambiguities resolved by the Melbourne-Wubbena (MW) method are divided into two categories based on signal-to-noise ratio (SNR). One is the primary ambiguity group that can be resolved easily, and the other is the secondary ambiguity group that is difficult to resolve. Second, the primary ambiguity group is divided into different levels in a (4,1,1…1) pattern based on SNR, and the different levels’ ambiguities are resolved successively, and the method being that the integer ambiguity is selected from two candidate values built by rounding up and down. Third, the resolved primary ambiguity group is used as a constraint to solve the secondary ambiguity group. Finally, the wide-lane observation equation and the basic observation equation are combined to solve the ambiguity of the L1 carrier phase, and the resolved ambiguity can be obtained by directly rounding. The candidate values of the primary ambiguity group is limited to two cycles through this step, and the (4,1,1…1) pattern can reduce ambiguity search times. Since an appropriate selection enables the correct resolution of primary wide-lane ambiguities, the selection of the threshold for SNR is the key to group wide-lane ambiguity, and we use the data from Novatel receiver as an example to discuss how to confirm the SNR threshold in this paper. Static short baseline data and kinematic short baseline that were less than 20 km were collected to validate the proposed algorithm. These results were compared with the commercial software IE8.60. These experiments show that the successful rate reaches 100%, 99.78% and 99.42%, respectively, for the new single-epoch segmented ambiguity method in the three data sets, and the accuracy is similar to that of IE8.60 for the combined double difference.

GLONASS inter-frequency phase bias rate estimation by single-epoch or Kalman filter algorithm

GLONASS double-differenced (DD) ambiguity resolution is hindered by the inter-frequency bias (IFB) in GLONASS observation. We propose a new algorithm for IFB rate estimation to solve this problem. Although the wavelength of the widelane observation is several times that of the L1 observation, their IFB errors are similar in units of meters. Based on this property, the new algorithm can restrict the IFB effect on widelane observation within 0.5 cycles, which means the GLONASS widelane DD ambiguity can be accurately fixed. With the widelane integer ambiguity and phase observation, the IFB rate can be estimated using single-epoch measurements, called the single-epoch IFB rate estimation algorithm, or using the Kalman filter to process all data, called the Kalman filter-based IFB rate estimation algorithm. Due to insufficient accuracy of the IFB rate estimated from widelane observations, the IFB rate has to be further refined with L1 and L2 observations. A new reference satellite selection method is proposed to serve the IFB rate estimation. The experiment results show that the IFB rates on L1 and L2 bands are different, that an accurate IFB rate will help us to obtain more fixed solutions at places with serious occlusion, that the single-epoch IFB rate estimation algorithm can meet the requirements for real-time kinematic positioning with only 8% extra computational time, and that the Kalman filter-based IFB rate estimation algorithm is a satisfactory option for high-accuracy GLONASS positioning.

Single-Epoch Navigation Performance with Real BDS Triple-Frequency Pseudorange and EWL/WL Observations

Triple-frequency signals of China's BeiDou navigation satellite system (BDS) are now accessible in the Asia-Pacific region. It is well understood that the third frequency signal will improve the navigation performance. Some literatures have described several navigation methods by using triple-frequency signals, and evaluated the performance. However the experiments were mostly implemented on simulated or semi-simulated observations. In this paper we investigate the navigation performance using real BDS triple-frequency observations. Apart from the pseudorange observations, carrier observations are also used, since the extra-wide-lane and wide-lane ambiguities can be reliably resolved with a single epoch. Several single-epoch navigation methods using BDS triple-frequency observations are described and the corresponding navigation accuracy and reliability are assessed. Results show that P3 has the highest accuracy among the three pseudorange observations. For carriers, the wide-lane and extra-wide-lane observations can be used to obtain much higher navigation precision compared with pseudorange observations. Besides, the two ambiguity-fixed extra-wide-lane and wide-lane observations can also be combined to ionosphere-free form, which can still obtain sub-decimetre and decimetre navigation accuracy in horizontal and vertical directions respectively.

An improved approach to model regional ionosphere and accelerate convergence for precise point positioning

Given the severe effects of the ionosphere on global navigation satellite system (GNSS) signals, single-frequency (SF) precise point positioning (PPP) users can only achieve decimeter-level positioning results. Ionosphere-free combinations can eliminate the majority of ionospheric delay, but increase observation noise and slow down dual-frequency (DF) PPP convergence. In this paper, we develop a regional ionosphere modeling and rapid convergence approach to improve SF PPP (SFPPP) accuracy and accelerate DF PPP (DFPPP) convergence speed. Instead of area model, ionospheric delay is modeled for each satellite to be used as a priori correction. With the ionospheric, wide-lane uncalibrated phase delay (UPD) and residuals satellite DCBs product, the wide-lane observations for DF users change to be high-precision pseudorange observations. The validation of a continuously operating reference station (CORS) network was analyzed. The experimental results confirm that the approach considerably improves the accuracy of SFPPP. For DF users, convergence time is substantially reduced.

High-precision GPS-positioning using the phase observations of differential frequency

The results of developing a complex of new efficient algorithms and software for high-precision GPS-positioning of moving and stationary objects have been described using the phase observations of differential frequency (Wide Lane observations). Experimental investigations of the algorithms for the phase ambiguity resolution of Wide Lane observations and high-precision positioning were presented using the real measuring data during the performance of aerial photography on board the aircraft and stations of the permanent network in Ukraine. Peculiarities and opportunities of implementing the proposed procedures for processing of GPS observations were discussed. It was shown experimentally that the complete resolution of phase ambiguity and the subdecimeter accuracy of positioning can be achieved under the standard conditions of observations. Typical root-mean-square errors in determining the location of dynamic objects amount to 3–5 cm in terms of plane coordinates and 3–7 cm in terms of height at base distances of up to 150 km. For static determinations the root-mean-square errors do not exceed 2–4 cm for all coordinates at base distances of up to 170 km. The developed domestic algorithmic software package is a high-precision toolset for the processing of observations and can be recommended for different practical applications.