Shuguo Pan

Improving Ambiguity Resolution for Medium Baselines Using Combined GPS and BDS Dual/Triple-Frequency Observations

The regional constellation of the BeiDou navigation satellite system (BDS) has been providing continuous positioning, navigation and timing services since 27 December 2012, covering China and the surrounding area. Real-time kinematic (RTK) positioning with combined BDS and GPS observations is feasible. Besides, all satellites of BDS can transmit triple-frequency signals. Using the advantages of multi-pseudorange and carrier observations from multi-systems and multi-frequencies is expected to be of much benefit for ambiguity resolution (AR). We propose an integrated AR strategy for medium baselines by using the combined GPS and BDS dual/triple-frequency observations. In the method, firstly the extra-wide-lane (EWL) ambiguities of triple-frequency system, i.e., BDS, are determined first. Then the dual-frequency WL ambiguities of BDS and GPS were resolved with the geometry-based model by using the BDS ambiguity-fixed EWL observations. After that, basic (i.e., L1/L2 or B1/B2) ambiguities of BDS and GPS are estimated together with the so-called ionosphere-constrained model, where the ambiguity-fixed WL observations are added to enhance the model strength. During both of the WL and basic AR, a partial ambiguity fixing (PAF) strategy is adopted to weaken the negative influence of new-rising or low-elevation satellites. Experiments were conducted and presented, in which the GPS/BDS dual/triple-frequency data were collected in Nanjing and Zhengzhou of China, with the baseline distance varying from about 28.6 to 51.9 km. The results indicate that, compared to the single triple-frequency BDS system, the combined system can significantly enhance the AR model strength, and thus improve AR performance for medium baselines with a 75.7% reduction of initialization time on average. Besides, more accurate and stable positioning results can also be derived by using the combined GPS/BDS system.

A method of GPS/BDS/GLONASS combined RTK positioning for middle-long baseline with partial ambiguity resolution

As Chinas BeiDou Navigation Satellite System (BDS) has become operational in the Asia-Pacific region, it is important to demonstrate the capabilities that a combination of GPS, BDS and GLONASS to high-precision positioning. Multi-constellation combination increases the available satellites and thus improves the positioning reliability. However at the same time, it will bring some challenges to the high-dimension ambiguity resolution (AR). In this contribution, a GPS/BDS/GLONASS combined real time kinematic (RTK) positioning method for middle-long baseline is proposed. In order to reduce the influence of troposphere and ionosphere delays on AR, a two-step AR strategy is adopted, where wide-lane and ionosphere-free observation model are used respectively. In the integer ambiguity search process, a partial ambiguity resolution (PAR) method is proposed to improve the AR performance. In the PAR method, satellite cutoff elevation, satellite number, AR success rate and ratio are used together to determine the ambiguity subset, which can be fixed reliably. A set of baselines ranging from about 30 to 60 km, which all contain GPS/BDS/GLONASS observations, are used to test RTK positioning performance. Experiment results demonstrate that GPS/BDS/GLONASS combined RTK positioning with partial ambiguity resolution can get much improved performance for middle-long baseline both in positioning speed and accuracy, as within about 20 s and 5 cm, respectively.

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

An inter-system differencing model between two Global Navigation Satellite Systems (GNSS) enables only one reference satellite for all observations. If the associated differential inter-system biases (DISBs) are priori known, double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can also be fixed to integers. This can provide more redundancies for the observation model, and thus will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning. However, for Global Positioning System (GPS) and the regional BeiDou Navigation Satellite System (BDS-2), there are no overlapping frequencies. Tight combination of GPS and BDS needs to process not only the DISBs but also the single-difference ambiguity of the reference satellite, which is caused by the influence of different frequencies. In this paper, we propose a tightly combined dual-frequency GPS and BDS RTK positioning model for medium baselines with real-time estimation of DISBs. The stability of the pseudorange and phase DISBs is analyzed firstly using several baselines with the same or different receiver types. The dual-frequency ionosphere-free model with parameterization of GPS-BDS DISBs is proposed, where the single-difference ambiguity is estimated jointly with the phase DISB parameter from epoch to epoch. The performance of combined GPS and BDS RTK positioning for medium baselines is evaluated with simulated obstructed environments. Experimental results show that with the inter-system differencing model, the accuracy and reliability of RTK positioning can be effectively improved, especially for the obstructed environments with a small number of satellites available.

Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris

Satellite orbit error and clock bias are the keys to precise point positioning (PPP). The traditional PPP algorithm requires precise satellite products based on worldwide permanent reference stations. Such an algorithm requires considerable work and hardly achieves real-time performance. However, real-time positioning service will be the dominant mode in the future. IGS is providing such an operational service (RTS) and there are also commercial systems like Trimble RTX in operation. On the basis of the regional Continuous Operational Reference System (CORS), a real-time PPP algorithm is proposed to apply the coupling estimation of clock bias and orbit error. The projection of orbit error onto the satellite-receiver range has the same effects on positioning accuracy with clock bias. Therefore, in satellite clock estimation, part of the orbit error can be absorbed by the clock bias and the effects of residual orbit error on positioning accuracy can be weakened by the evenly distributed satellite geometry. In consideration of the simple structure of pseudorange equations and the high precision of carrier-phase equations, the clock bias estimation method coupled with orbit error is also improved. Rovers obtain PPP results by receiving broadcast ephemeris and real-time satellite clock bias coupled with orbit error. By applying the proposed algorithm, the precise orbit products provided by GNSS analysis centers are rendered no longer necessary. On the basis of previous theoretical analysis, a real-time PPP system was developed. Some experiments were then designed to verify this algorithm. Experimental results show that the newly proposed approach performs better than the traditional PPP based on International GNSS Service (IGS) real-time products. The positioning accuracies of the rovers inside and outside the network are improved by 38.8% and 36.1%, respectively. The PPP convergence speeds are improved by up to 61.4% and 65.9%. The new approach can change the traditional PPP mode because of its advantages of independence, high positioning precision, and real-time performance. It could be an alternative solution for regional positioning service before global PPP service comes into operation.

A new approach for optimising GNSS positioning performance in harsh observation environments

Maintaining good positioning performance has always been a challenging task for Global Navigation Satellite Systems (GNSS) applications in partially obstructed environments. A method that can optimise positioning performance in harsh environments is proposed. Using a carrier double-difference (DD) model, the influence of the satellite-pair geometry on the correlation among different equations has been researched. This addresses the critical relationship between DD equations and its ill-posedness. From analysing the collected multi-constellation observations, a strong correlation between the condition number and the positioning standard deviation is detected as the correlation coefficient is larger than 0·92. Based on this finding, a new method for determining the reference satellites by using the minimum condition number rather than the maximum elevation is proposed. This reduces the ill-posedness of the co-factor matrix, which improves the single-epoch positioning solution with a fixed DD ambiguity. Finally, evaluation trials are carried out by masking some satellites to simulate common satellite obstruction scenarios including azimuth shielding, elevation shielding and strip shielding. Results indicate the proposed approach improves the positioning stability with multi-constellation satellites notably in harsh environments.

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

Triple-frequency signals of Chinas 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.

Analysis of ill posedness in double differential ambiguity resolution of BDS

Abstract The ill posedness in a variance–covariance matrix will directly determine the convergence speed and accuracy of integer ambiguities. Unlike GPS or GLONASS, BDS (BeiDou Navigation Satellite System) consists of not only MEO satellites but also GEO and IGSO satellites, both of which are high orbit satellites. The angular velocities of the GEO and IGSO satellites are much smaller compared with MEO satellites. The changes of the geometric structure between satellites and stations of the high orbit satellites GEO/IGSO in BDS are not obvious during short observational spans due to their relatively small angular velocity. This results in stronger correlation of equations between adjacent epochs while calculating ambiguities, leading to serious ill posedness. In this paper the ill posedness of double differential (DD) ambiguity resolution (AR) of the current BDS was analysed. On this basis, some different combinations of GEO, IGSO and MEO satellites of BDS were used in the AR experiments to reveal the characteristics of ill posedness. Moreover, AR experiments of GPS, GLONASS and BDS/GPS/GLONASS fusion were also carried out for comparison with BDS. These experiments indicate that the AR of the current BDS is a more serious ill posed problem, and therefore takes much more time for AR fixing than GPS or GLONASS. The fusion with GPS or GLONASS, however, will solve the ill posed problem effectively and improve the AR much more, achieving fixes even instantaneously.

The Analysis of Ill Posedness in GNSS High-Precision Differential Positioning

GNSS high-precision differential positioning generally requires the high-precision float solution and the reasonable covariance matrix for ambiguity integers in short observational time spans. But station-star geometric changes little in short observational time spans, which causes the design matrix to be ill-conditioned seriously during adjustment calculation and leads to the solving of parameters is unstable. With the development of Compass Navigation Satellite System, the GNSS high-precision positioning is now entering the multi-system combined ages. GPS, GLONASS and Compass have different orbits and operating features so that there is some difference from each other in adjustment calculation. The paper combining with the analysis theory on ill-conditioned system, analyses the ill posedness of GPS, GLONASS and Compass comparatively through a method called spectrum analysis of eigenvalue. The paper reveals the characteristics of the ill condition in several different positioning forms. The conclusion that the faster the satellites runs, the weaker the ill posedness of the parameters solving system will be is presented.

Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases

Double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can be fixed to integers if the associated differential inter-system biases (DISBs) are well known. In this case, only one common pivot satellite is sufficient for inter-system ambiguity resolution. This will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning especially when only a few satellites are observed. However, for GPS and current operational BDS-2, there are no overlapping frequencies. Due to the influence of different frequencies, the inter-system DD ambiguities still cannot be fixed to integers even if the DISBs are precisely known. In this contribution, we present an inter-system differencing model for combined GPS and BDS single-frequency RTK positioning through real-time estimation of DISBs. The stability of GPS L1 and BDS B1 DISBs is analyzed with different receiver types. Along with parameterization and using the short-term stability of DISBs, the DD ambiguities between GPS and BDS pivot satellites and the between-receiver single-difference ambiguity of the GPS pivot satellite can be estimable jointly with the differential phase DISB term from epoch to epoch. Then the inter-system differencing model can benefit from the near time-constant DISB parameters and thus has better multi-epoch positioning performance than the classical intra-system differencing model. The combined GPS and BDS single-frequency RTK positioning performance is evaluated with various simulated satellite visibilities. It will be shown that compared with the classical intra-system differencing model, the proposed model can effectively improve the positioning accuracy and reliability, especially for severely obstructed situations with only a few satellites observed.

Ambiguity resolution with double troposphere parameter restriction for long range reference stations in NRTK System

The correct ambiguity resolution between reference stations is the key to calculate the high precision Network Real-Time Kinematic (NRTK) differential information. For long range reference stations (≧50 km), the double difference troposphere model residuals should be considered as the parameters being solved, but this will aggravate the ill conditioning of ambiguity resolution (AR) model between reference stations; as a result, the ambiguity fixing becomes more difficult for the case of long range station ambiguity resolution. In the paper, a new method with double troposphere parameters restriction is put forward for ambiguity resolution of long range reference stations. The proposed method applies GPT2 model, which is called the state of the art empirical troposphere model, to form a high precision troposphere a priori estimation to provide high accuracy double difference troposphere delay estimation. Based on the principles of TIKHONOV regularisation, a regularisation criterion for the double difference restriction model is then built. The difference between the troposphere estimation and the truth value is used as a restriction parameter to improve the estimation of the unknown parameters and optimisation of the ambiguity search range. Trials verify the significant reduction in the ill conditioning of the parametric resolution functions when the double troposphere restriction model is applied. The success rate of ambiguity resolution within 60 s is above 98% for baselines over 80 km, which is an immense improvement from conventional methods.