A millisecond integer ambiguity search method based on the inter-satellite distance limit for coarse-time GPS positioning

A technique for finding a priori position with coarse-time assistance and partial measurements is proposed to improve time-free positioning algorithm. The positioning method can be described as follows. First, three satellites are selected by considering the balance of the geometric properties and search space in estimating the rough position with the altitude hypothesis. Additionally, the relationship between the maximum pseudorange difference and inter-satellite distance is analyzed and can be used to compress the search space. Second, the most reasonable position is chosen using the residual minimum root-sum-of-squares criterion. Finally, full pseudoranges are constructed and the user position can be estimated employing time-free positioning. Experimental results showed that, for sub-millisecond measurements, high success rates of 99.93, 99.75 and 99.58 % were achieved for time offsets of 1, 3 and 5 s, respectively, using the data file 'mars3650.14d.z' of the International GNSS Service, while the average number of search candidates was about 672. In addition, the success rate can still reach 100 % even if the time offset is hundreds of seconds with sub-20-ms measurements.