The two-sample numerical updating algorithm of strapdown inertial navigation systems (SINS) for hypersonic vehicles has a relatively large navigation error. To solve this problem, this paper proposes an error-free SINS numerical updating algorithm in the launch-centered Earth-fixed (LCEF) frame. First, the gyroscopes and accelerometers in SINS output angular increment and velocity increment respectively, while the proposed algorithm takes angular velocity and specific force as input, so the methods of angular increment fitting angular velocity and velocity increment fitting specific force are proposed. Then, according to the SINS differential equation in the LCEF frame, the error-free SINS numerical updating algorithm in the LCEF frame is designed by adopting the Taylor series expansion method. The derivation process of the algorithm shows that the proposed algorithm can achieve precise compensation for the non-exchangeable errors of attitude, velocity, and position, and selecting the LCEF frame as the navigation frame has greater advantages than the local-level frame. Finally, two-sample and error-free numerical updating algorithms are simulated and compared by taking the hypersonic boost-gliding vehicle as the object. Under the influence of a pure SINS algorithm, the velocity error of the two-sample algorithm with a simulation duration of 1100 s is in the order of 10⁻² m/s, and the position error is in the order of 10 m. In contrast, the velocity error of the proposed algorithm is in the order of 10⁻⁷ m/s, and its position error is in the order of 10⁻⁴ m.

高超声速飞行器捷联惯导系统（SINS）二样本数值更新算法存在较大的导航误差。为了解决这个问题，本文提出了一种在以发射为中心的地球固定（LCEF）框架下的无误差 SINS 数值更新算法。首先，SINS中的陀螺仪和加速度计分别输出角增量和速度增量，而本文算法以角速度和比力为输入，因此提出了角增量拟合角速度和速度增量拟合比力的方法。然后，根据LCEF框架下的SINS微分方程，采用泰勒级数展开的方法，设计了LCEF框架下的无差错SINS数值更新算法。算法推导过程表明，所提算法能够实现对姿态、速度、位置等不可交换误差的精确补偿，选择LCEF坐标系作为导航坐标系比局部坐标系具有更大的优势。最后，以高超声速助推滑翔飞行器为对象，对双样本无误差数值更新算法进行了仿真比较。在纯 SINS 算法的影响下，仿真持续时间为 1100 s 的双样本算法的速度误差为 10 量级 以高超声速助推滑翔飞行器为对象，对双样本无误差数值更新算法进行了仿真比较。在纯 SINS 算法的影响下，仿真持续时间为 1100 s 的双样本算法的速度误差为 10 量级 以高超声速助推滑翔飞行器为对象，对双样本无误差数值更新算法进行了仿真比较。在纯 SINS 算法的影响下，仿真持续时间为 1100 s 的双样本算法的速度误差为 10 量级⁻² m/s，位置误差在10 m量级。相比之下，所提出算法的速度误差约为 10 ^-7 m/s，其位置误差约为 10 ^-4 m。