Determining inter-system bias of GNSS signals with narrowly spaced frequencies for GNSS positioning

Abstract

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.

Multi-GNSS Relative Positioning with Fixed Inter-System Ambiguity

“…According to our experience, at least 3~4 satellites for each GNSS systems are needed, or else the b r may likely not be precise enough for improving the positioning accuracy. In addition, it is reported that the SD ambiguities could also be fixed by the particle filter method [20]. We therefore infer that the particle filter method could also be another alternative method to obtain the precise RUPD.…”

“…Different methods are developed to estimate the ISB precisely, such as fixing only intra-system DD ambiguities and adding a datum for each GNSS system [16], adding additional constraints [17] and a particle filter approach [19]. Meanwhile, Tian et al [20] developed a method for fixing inter-system ambiguities with narrowly spaced frequencies. However, in the above-mentioned methods, the frequency of the signals used for forming the inter-system ambiguity is required to be the same or to be narrowly spaced.…”

Tightly combined GPS + GLONASS positioning with consideration of inter-system code bias and GLONASS inter-frequency code bias

“…Considering the influence of GLONASS IFCBs, the general un-differenced GLONASS code observation models can be expressed as Equation (1) (Tian et al, 2018): where P is code observation, R refers to GLONASS, a refers to the receiver, q is the index of GLONASS satellites and stands for the number of GLONASS satellites. ρ is the distance between satellite and receiver, c represents the speed of light in a vacuum, t a and t * , s are the clock offsets for the receiver and satellite, respectively, I and T correspond to the ionosphere and troposphere biases, respectively, d R, q refers to the satellite hardware bias of GLONASS and is the same part of the code hardware bias for all GLONASS satellites.…”

Refinement of GLONASS Phase Inter-Frequency Biases and Their Applications on Single-Epoch Ambiguity Fixing

“…Therefore, IFB calibration affecting ambiguity fixing is important for positioning accuracy. For example, GLONASS data collected on DOY 180 of 2018 with a 30-s epoch interval were employed to solve the baseline MATG_MATZ with a length of 21·5 m. The pseudorange IFBs of the baseline were calibrated in advance using the look-up table method (Tian et al, 2018b) and the RATIO test with threshold of 3 was employed in the ambiguity fixing. The horizontal solutions with and without phase IFB calibration of IFB rate −24·6 mm/FN are plotted in Figure 7.…”