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Objectives: In order to make full use of the observed value information of each frequency, an undifferenced and uncombined integer ambiguity resolution method between BeiDou satellite navigation system (BDS) long-range reference stations is proposed. Methods: First, the error observation equation is established directly by using the observations of different frequencies, and the relative zenith tropospheric wet delay error and ionospheric delay error are estimated by random walk strategy to increase the constraint between epochs. Second,a linear calculation method of undifferenced integer ambiguity real-time is used to obtain the undifferenced integer ambiguity of all satellites in the current epoch of the reference network. It solves the problem that ambiguity needs to be inherited or re-superimposed on normal equations in the reference star transformation. Because the information of each frequency observation is fully utilized, the influence of linear combination amplification noise on integer ambiguity fixing is avoided, and the ambiguity fixing success rate of uncombined method is much higher than that of ionosphere-free combination method. Results and Conclusions: The results show that the average fixed speed of ambiguity of each reference station is 20 epochs (sampling interval 1 s). The integer ambiguity resolution of the carrier phase of the reference station can be realized quickly. [ABSTRACT FROM AUTHOR]

The uncertainty of distance‐related error of global navigation satellite system is gradually increasing with the increase of distance between the reference stations and the rover station. Therefore, the dual ‐sys‐ tems of global positioning system (GPS) and BeiDou satellite navigation system (BDS) network real ‐ time kinematic (RTK) method was presented to meet the demand of high‐precision long range positioning RTK. Firstly, the wide‐lane ambiguities were fixed by the multi‐frequency observation data of GPS and BDS be‐ tween long‐range reference stations. The satellite clock errors can be eliminated by the double‐difference so‐ lution model, simultaneously the atmospheric error and satellite orbit errors can be weakened. Then the double ‐ difference carrier phase integer ambiguities can be fixed by the resolution model including atmo‐ spheric error and carrier phase ambiguity. The method of classification error corrections between long‐range reference stations network was used. The observation errors were classified, according to the characteris‐ tics of observation errors between long‐range reference station network. The ionosphere errors and non‐dis‐ persive errors of the rover station were calculated by using the reference stations’error correction and regional error interpolation. The atmospheric errors and satellite orbit errors of the rover station can be weakened by the method of interpolation. Then the errors of GPS/BDS carrier phase observation of the rover station were removed by the calculation errors. The carrier phase integer ambiguities of the rover station can be fixed by the method of resolution integer ambiguity with multi ‐frequency carrier phase, and the position of the rover station was obtained by the fixed ambiguities. The algorithm validation was carried out by the data on long ‐ range reference station network. Three long ‐ range reference stations and one rover station were used to test in Central China. The positioning accuracy of centimeter can be obtained by the algorithm of du‐ al ‐ systems of GPS and BDS network RTK. At the same time, single system can also get the centimeter level of position and the GPS is better than BDS. The method of dual ‐systems of GPS and BDS network RTK can guarantee the positioning accuracy of the rover station. The results of experiment indicate that the GPS/BDS long ‐ range network RTK can be realized and the centimeter level positioning accuracy can be achieved by this algorithm. [ABSTRACT FROM AUTHOR]

In most GPS (Global Positioning System) receivers, the pseudo-range measurement error is bigger than the wavelength of WL (Wide Lane) carrier phase measurement. It will probably cause one cycle WL integer ambiguity resolution error in case the DD (Double Differenced) WL integer ambiguity is rounded by DD pseudo-range measurement according to the WL integer bootstrapping model. In this view of, we propose a modified WL bootstrapping ambiguity resolution algorithm. The proposed algorithm mainly aims at detecting and repairing one cycle WL integer ambiguity error. The WL integer ambiguity error detector is designed according to the characteristic that the integer ambiguity is an integer. The designed detector is compared with the theoretical threshold calculated by the Carrier Noise Ratio (CNR) to judge whether the WL integer ambiguity is wrong. There are only 3 degrees of freedom in all the ambiguities, therefore we fix the wrong ambiguities by the right ambiguities. We analyze the feasibility of the proposed algorithm in Gaussian noise environment. The results show all the carrier phase measurement in normal CNR environment can judge whether the WL integer ambiguity has one cycle error. The maximum carrier phase error is calculated in case we consider the multipath and other carrier phase measurement error. The probability of one cycle WL integer ambiguity error is analyzed with pseudo-range measurement error in different orders of magnitude. Field tests were carried out by using GPS short baseline data. The proposed algorithm increases the success rate of the WL integer bootstrapping ambiguity resolution algorithm from less than 1/3 to nearly 100%. [ABSTRACT FROM AUTHOR]

Tightly-coupled GNSS/INS integration has been shown to provide better performance than loosely-coupled approach in GNSS degraded environments. However， it is difficult to achieve reliable ambiguity resolution (AR) when the number of satellites is below four. In this case, ambiguity search in the ambiguity domain is not possible，which means other AR method should be considered. Also, it is likely to wrongly fix the ambiguities，which will lead to biased state estimate or even filter divergence. In this paper，a tightly-coupled RTK/INS algorithm based on centralized Kalman Filter (KF) is implemented， in which ambiguity parameters are augmented into the state vector. Ambiguity-fixed or -float carrier phase observables can be used to update the filter even if the number of satellites is less than four，and this improves the accuracy of the integrated system in complex environments. A field vehicular test was conducted to evaluate the performance of the tightly-coupled algorithm in terms of the position drift error during GNSS signal outages and ambiguity recovery time after outages. Test results indicate that by utilizing tactical-grade inertial measurement units (IMUs)，the horizontal position drift error is about 0.3m during 30-second partial outage and the average time for reliable ambiguity recovery is 1 to 2 seconds when the number of satellites in view is three. Besides, the performance of float solution is only slightly worse than the fixed solution for shout-time (e.g. 60 seconds) partial outages, but both of them are much better than the case of full GNSS outages. [ABSTRACT FROM AUTHOR]

A single-epoch ambiguity resolution algorithm without a search process is proposed. Four basic satellites are selected, whose integer ambiguities are estimated by using the INS position, then (1,-1) and (-3,4) ambiguity combinations are formed. The ionospheric error of the (-3,4) combination is polynomially fitted. After systematic influences such as the ionospheric error are compensated, the ambiguity combination can be fixed by simple rounding. The ambiguities of each frequency can be determined by the combination and returned to resolve the receiver position. Based on the receiver position, the ambiguities of all other satellites can be calculated directly and fixed by rounding. The algorithm was validated by field test GNSS/INS data. [ABSTRACT FROM AUTHOR]

The ambiguity resolution is one of the primary problems in GNSS carrier phase measurement. To acquire carrier phase integer ambiguity rapidly and accurately, we often take advantage of integer least-squares (ILS) estimation criterion to resolve ambiguity. Due to ILS problem can be regarded as closest vector problem (CLP) in lattice theory, therefore, lattice reduction could help to accelerate ambiguity enumeration process, shorten the search time, and further to improve the computation efficiency of ambiguity resolution. Among many of lattice reduction algorithms, Lenstra-Lenstra-Lovász (LLL) is a most popular and widely used reduction algorithm in many fields. It includes two reduction conditions, size reduction and basis vector swapping. However, size reduction is aimed at all matrix elements and basis vector swapping is only limited to two adjacent vectors, that will result in the unnecessary elements size reduction and excessive basis vector swapping times. Hence, both of them are not conducive to improving the ambiguity reduction efficiency, especially for high-dimensional ambiguity resolution. To overcome this problem, we adopt the greedy algorithm and partial column vector reduction to reduce the number of basis swapping and size reduction, in this contribution the computing complexity of LLL reduction algorithm is reduced, where LLL reduction algorithm has a long time-consuming under high-dimensional conditions. Simulations and real data validations have clearly shown that the modified LLL reduction algorithm can significantly improve the computational efficiency. Therefore our modified LLL algorithm has a certain useful value for fast resolution under high-dimensional case. [ABSTRACT FROM AUTHOR]

Receiver initial phase biases are significant in integer ambiguity resolution. Based on a study of Beidou receiver Initial phase bias, we derived calculation formulas of single-difference-between-receivers (SDBR) inter-frequency receiver initial phase biases. The analysis results using zero-baseline data indicate that the SDBR inter-frequency receiver initial phase biases do not vary with the satellite elevation angles, which suggests that the biases have a short-time stability. When the receiver is just beginning to track satellites, a certain time is needed for the SDBR inter-frequency receiver initial phase biases to be stabilized. The SDBR inter-frequency receiver initial phase biases are changed after the receiver restarts to track satellites, indicating that the biases do not have a long-time stability. The SDBR inter-frequency receiver initial phase biases on the same combination of two frequencies are nearly identical for different satellites. [ABSTRACT FROM AUTHOR]