Abstract
This paper presents a PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) for L1 and L2 in GPS measurements. The method determines and ambiguities based on the ambiguity functions: and . These ambiguity functions have been described in detail in this work. The developed method of ambiguity initialization and reinitialization in relative positioning can use Global Positioning System (GPS) measurements from only two satellites and one measurement epoch. To resolve and ambiguities, a variance-covariance (VC) matrix of the float solution is not needed. The size of the search area in the PREFMAR method depends on code and phase accuracy as well as on the GNSS signal frequencies. Therefore, the search area is specific for every double or triple Global Navigation Satellite Systems (GNSS) data frequency. However, this part of the research only presents the ambiguity search area for L1 and L2 of GPS measurements. Additionally, a numerical example has been analyzed in detail with the use of the PREFMAR method and a float solution (, ). Finally, the elaborated algorithms were successfully tested on real L1 and L2 GPS measurements for instantaneous ambiguity reinitialization. The PREFMAR method allows instantaneous ambiguity reinitialization if all satellites lose contact with a GNSS antenna, for short and long baselines. Therefore, the PREFMAR has a great potential for precise real-time kinematic GNSS navigation.
Highlights
Attempts to determine the total ambiguities in phase measurements in Global Positioning System (GPS) observations date back to the late 1970s—i.e., GPS satellites were first placed in Earth orbits in 1978 [1,2]
The first research paper to appear on GPS measurement and determination of ambiguities in phase measurements for GPS observations was published by Counselman and Gourevitch [3]
A detailed description of mathematical functions used in the PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) approach was investigated earlier for the use of L1-L5 or E1-E5a GPS/GALILEO data [19], but each double combination of Global Navigation Satellite Systems (GNSS) frequencies must be carefully analyzed to find specific properties for fast and precise ambiguity initialization and reinitialization
Summary
Attempts to determine the total ambiguities in phase measurements in GPS observations date back to the late 1970s—i.e., GPS satellites were first placed in Earth orbits in 1978 [1,2]. Based on numerical tests performed by Hatch, a single-epoch solution was possible under the following conditions: (1) dual frequency data are available, (2) distances are limited to a few tens and the ionospheric refraction effect is not too severe, (3) seven or more total satellites are available for processing with good geometry This was revolutionary research that shows that a precise kinematic surveying or precise navigation is possible when L1 and L2 GPS measurements are available. A detailed description of mathematical functions used in the PREFMAR approach was investigated earlier for the use of L1-L5 or E1-E5a GPS/GALILEO data [19], but each double combination of GNSS frequencies must be carefully analyzed to find specific properties for fast and precise ambiguity initialization and reinitialization.
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