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arXiv 2310.04886eess.SYcs.SY
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捷联惯性导航初值问题的闭式解

A Closed-form Solution for the Strapdown Inertial Navigation Initial Value Problem

James Goppert, Li-Yu Lin, Kartik Pant, Benjamin Perseghetti

AI总结:

针对捷联惯性导航初值问题,提出将其视为李群混合不变向量场的闭式解法,精度在测量值固定时精确,运算量仅为4阶龙格-库塔单步的1/12,具备推广价值。

摘要:

捷联惯性导航系统(SINS)在机器人技术与工程领域应用广泛,因为它们无需了解所搭载载体的动力学特性,仅通过机载运动学测量值就能估算刚体位姿。近期研究多聚焦于SINS估计误差的闭式演化(这对卡尔曼滤波至关重要),但运动学传播问题受到的关注较少。龙格-库塔积分法已被广泛用于求解该初值问题;然而我们的研究表明,利用SINS问题的特殊结构,并将其视为李群上的混合不变向量场,可得到闭式解。我们的闭式解在采样周期内陀螺仪和加速度计测量值固定的条件下是精确的,且与4阶龙格-库塔积分器的单步积分相比,所需浮点运算量减少11/12(即运算量仅为后者的1/12)。我们认为,这项工作的广泛适用性以及效率与精度的提升,值得在SINS中普遍采用该算法。

英文摘要:

Strapdown inertial navigation systems (SINS) are ubiquitious in robotics and engineering since they can estimate a rigid body pose using onboard kinematic measurements without knowledge of the dynamics of the vehicle to which they are attached. While recent work has focused on the closed-form evolution of the estimation error for SINS, which is critical for Kalman filtering, the propagation of the kinematics has received less attention. Runge-Kutta integration approaches have been widely used to solve the initial value problem; however, we show that leveraging the special structure of the SINS problem and viewing it as a mixed-invariant vector field on a Lie group, yields a closed form solution. Our closed form solution is exact given fixed gyroscope and accelerometer measurements over a sampling period, and it is utilizes 12 times less floating point operations compared to a single integration step of a 4th order Runge-Kutta integrator. We believe the wide applicability of this work and the efficiency and accuracy gains warrant general adoption of this algorithm for SINS.

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