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视线矢量观测是实现自主导航的重要方式。本文针对单位矢量的加法观测模型中观测矢量非单位化问题和乘法观测模型中测量噪声与实际情况不符的问题,提出二次旋转乘法观测模型。通过真实矢量在正交方向上进行的两次刚体旋转,获得了与现有乘法观测模型形式相同、但旋转角服从瑞利分布的正确观测方程。推导了测量误差的统计特性和双矢量观测的性质,并从空间几何角度给予了解释。数值仿真结果表明,二次旋转乘法观测模型弥补了由加法观测模型线性化所引起的问题,具有更精确的误差形式,由此给出了模型的潜在应用范围。
Line of sight vector observation is an important way to achieve autonomous navigation. In this paper, we propose a quadratic rotation multiplication observational model to solve the problem of non-unitized observation vector in multiplicative observational model of unit vector and the discrepancy between measured noise and actual situation in multiplicative observational model. Through the two rigid rotations of real vectors in orthogonal directions, the correct observation equations with the same form as the existing multiplicative observational models but with the rotation angles following the Rayleigh distribution are obtained. The statistical properties of measurement errors and the properties of bi-vector observations are deduced and explained from the perspective of spatial geometry. Numerical simulation results show that the quadratic rotation multiplication observation model makes up for the problems caused by the linearization of the addition observation model, and has a more accurate error form, thus the potential application range of the model is given.