In this study, the error distribution of a highly nonlinear triangulation positioning system in a typical short-range vehicle-to-vehicle environment is analyzed. To investigate the influence of the measured signal-direction error on the measured position of a target vehicle, a small circle in the measuring-parameter space corresponding to the standard deviation of measured signal directions is mapped to the position space. The analytical results reveal that a small circle in the signal-direction space is mapped to a thin, long, and slender ‘oval’ in the position space depending on the coordinates of the target vehicle due to the specific geometric characteristics of the triangulation positioning system. The positioning system is very sensitive to the error in the longitudinal direction. That is, in the far region any small inaccurate measured signal direction may lead to a very large positioning error. In addition to the random error, the influence of the systematic error incurred by multipath scattering, imperfect calibration of hardware, and misalignment of signal-direction sensors is also investigated. The results of this work successfully explain our previous measurements and would also help deeply understand the influence of the inaccurate measured signal direction on triangulation positioning in noisy environments. Based on this study, further improvement of positioning accuracy by a deliberate design of statistical position-extracting algorithm is expected.
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