导航中单位矢量的二次旋转乘法观测模型

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。

Twice-rotation Multiplicative Measurement Model for Observed Unit Vectors in the Navigation

The implementation of autonomous navigation using line-of-sight measurements is receiving considerable attention in research. In this paper, a twice-rotation multiplicative measurement model for observed unit vectors is introduced which attempts to deal with the non-norm of the additive measurement model and the impractical error distribution of the multiplicative measurement model. The error is modeled as twice rigid rotations of the true direction about axes orthogonal to it. Though the ultimate form of the model is identical to that of the multiplicative measurement model, the rotation angle obeys the Rayleigh random distribution. The statistical characteristics of the estimation error are obtained and the speciality of couple vectors is developed, followed by geometrical explanation. Results of numerical tests show that the twice-rotation multiplicative measurement model well makes up for the error caused by the linearized additive measurement model, consequently more accurate. Potential areas to apply the model are hereby given.