Title: Multi-antenna and Geometry Based Differential GNSS Positioning

Assume four satellites are visible and four antennas are distributed in a plane with a rectangular shape. First the positions of satellites and antennas are given, and the true differenced phase integer ambiguity N_1n⁽ⁱ⁾ is calculated. The positioning error is around 15 meters if the antenna uses the pseudoranges measured based on the time arrivals to find its position. Hence, we let each dimension of the antenna position vary in the range of [x₀-10, x₀+10], [y₀-10, y₀+10], [z₀-10, z₀+10], respectively, where (x₀, y₀, z₀) are the true coordinates of the antenna. We try to find another possible  N_1n⁽ⁱ⁾ group which is identical to the true one when the antenna positions change within the positioning error range and meanwhile maintain the formed geometry unchanged.

Considering lane-level positioning accuracy, the antenna position changes with step of 1 meter in each dimension (it is not required that the position changes in three dimensions simultaneously). The simulation results show that no other group of  N_1n⁽ⁱ⁾ is identical to the true one on satisfying the given conditions. The MATLAB codes are available here (please change the suffix ".pdf" to ".m" before running):

check_delta_N_uniqueness_pub.pdf

Note that, the searching process for  N_1n⁽ⁱ⁾ is time consuming. To reduce the running time, the antenna position changing range can be bounded to [-5, +5] in each dimension.

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