No abstract

GLONASS could hardly reach the positioning performance of GPS, especially for fast and real-time precise positioning. One of the reasons is the phase inter-frequency bias (IFB) at the receiver end prevents its integer ambiguity resolution. A number of studies were carried out to achieve the integer ambiguity resolution for GLONASS. Based on some of the revealed IFB characteristics, for instance IFB is a linear function of the received carrier frequency and L1 and L2 have the same IFB in unit of length, most of recent methods recommend estimating the IFB rate together with ambiguities. However, since the two sets of parameters are highly correlated, as demonstrated in previous studies, observations over several hours up to 1 day are needed even with simultaneous GPS observations to obtain a reasonable solution. Obviously, these approaches cannot be applied for real-time positioning. Actually, it can be demonstrated that GLONASS ambiguity resolution should also be available even for a single epoch if the IFB rate is precisely known. In addition, the closer the IFB rate value is to its true value, the larger the fixing RATIO will be. Based on this fact, in this paper, a new approach is developed to estimate the IFB rate by means of particle filtering with the likelihood function derived from RATIO. This approach is evaluated with several sets of experimental data. For both static and kinematic cases, the results show that IFB rates could be estimated precisely just with GLONASS data of a few epochs depending on the baseline length. The time cost with a normal PC can be controlled around 1 s and can be further reduced. With the estimated IFB rate, integer ambiguity resolution is available B Yumiao Tian immediately and as a consequence, the positioning accuracy is improved significantly to the level of GPS fixed solution. Thus the new approach enables real-time precise applications of GLONASS.

In multi-GNSS integration, fixing inter-system double difference (DD) ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first then the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle-filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle-filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle-filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle-filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterwards, a two-dimensional particle-filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown.The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity fixed solutions have This is the Pre-Published Version.

Relative positioning using multi-GNSS (global navigation satellite systems) can improve accuracy, reliability, and availability compared to the use of a single constellation system. Intra-system double difference (DD) ambiguities (ISDDAs) refer to the DD ambiguities between satellites of a single constellation system, and can be fixed to an integer to derive the precise fixed solution. Inter-system ambiguities, which denote the DD ambiguities between different constellation systems, can also be fixed to integers on overlapping frequencies, once the inter-system bias (ISB) is removed. Compared with fixing ISDDAs, fixing both integer intra-and inter-system DD ambiguities (IIDDAs) means an increase of positioning precision through an integration of multiple GNSS constellations. Previously, researchers have studied IIDDA fixing with systems of the same frequencies, but not with systems of different frequencies. Integer IIDDAs can be determined from single difference (SD) ambiguities, even if the frequencies of multi-GNSS signals used in the positioning are different. In this study, we investigated IIDDA fixing for multi-GNSS signals of narrowly spaced frequencies. First, the inter-system DD models of multi-GNSS signals of different frequencies are introduced, and the strategy for compensating for ISB is presented. The ISB is decomposed into three parts: 1) a float approximate ISB number that can be considered equal to the ISB of code pseudorange observations, and thus can be estimated through single point positioning (SPP); 2) a number that is a multiple of the GNSS signal wavelength; and 3) a fractional ISB part, with a magnitude smaller than a single wavelength. Then, the relationship between intra-and inter-system DD ambiguity RATIO values and ISB was investigated by integrating Global Positioning System (GPS) L1 and GLONASS L1 signals. In our numerical analyses with short baselines, the ISB parameter and IIDDA were successfully fixed, even if the number of observed satellites in each system was small.