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Error analysis of analytical coarse alignment formulations for stationary SINS

机译：固定式捷联惯导系统的解析粗对准公式的误差分析

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摘要

This paper presents a comprehensive error analysis of coarse alignment formulations for stationary strapdown inertial navigation systems (SINS). Analytical expressions for the residual normality, orthogonality, alignment, and Euler angle errors are systematically derived, allowing us to establish comparisons in terms of rapidity, accuracy, and autonomy requirements. For the purpose of the error analysis, geographic latitude and local gravity acceleration uncertainties are considered, in addition to the inertial sensor uncertainties. As the main contribution of this paper, an improved coarse alignment method is proposed, which is based on orthonormality constraints existing between the Euler angles and the attitude matrix. In contrast to the traditional methods, the proposed formulation does not imply normality and orthogonality errors, besides producing time-independent alignment and Euler angle errors. The latter is seen to be particularly interesting for situations wherein, due to time constraints, posterior fine alignment and orthonormalization procedures cannot be implemented. The superiority of the proposed formulation is validated through simulated and experimental tests, regardless of the SINS initial orientation. The accuracy degradation produced by each alignment formulation in the navigation stage is used as the performance index.
机译：本文介绍了固定捷联惯性导航系统（SINS）的粗对准公式的综合误差分析。系统地推导了残余法线，正交性，对齐和欧拉角误差的解析表达式，使我们能够在速度，准确性和自治性要求方面建立比较。为了进行误差分析，除了惯性传感器不确定性外，还考虑了地理纬度和局部重力加速度的不确定性。作为本文的主要贡献，提出了一种改进的粗对准方法，该方法基于欧拉角和姿态矩阵之间存在的正交约束。与传统方法相比，所提出的公式除了产生时间无关的对准和欧拉角误差外，也没有暗示正态性和正交性误差。对于由于时间限制而无法实现后部精细对齐和正交归一化程序的情况，后者显得尤为有趣。无论SINS的初始方向如何，通过模拟和实验测试都可以验证所提出配方的优越性。导航阶段中每个对齐方式公式产生的精度下降将用作性能指标。

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