Inertial-based navigation refers to the navigation methods or systems that have inertial information or sensors as the core part and integrate a spectrum of other kinds of sensors for enhanced performance. Through a series of papers, the authors attempt to explore information blending of inertial-based navigation by a polynomial optimization method. The basic idea is to model rigid motions as finite-order polynomials and then attacks the involved navigation problems by optimally solving their coefficients, taking into considerations the constraints posed by inertial sensors and others. In the current paper, a continuous-time attitude estimation approach is proposed, which transforms the attitude estimation into a constant parameter determination problem by the polynomial optimization. Specifically, the continuous attitude is first approximated by a Chebyshev polynomial, of which the unknown Chebyshev coefficients are determined by minimizing the weighted residuals of initial conditions, dynamics and measurements. We apply the derived estimator to the attitude estimation with the magnetic and inertial sensors. Simulation and field tests show that the estimator has much better stability and faster convergence than the traditional extended Kalman filter does, especially in the challenging large initial state error scenarios.

翻译：惯性导航是指以惯性信息或传感器为核心，并融合多种其他类型传感器以提升性能的导航方法或系统。通过一系列论文，作者尝试利用多项式优化方法探索惯性导航中的信息融合技术。基本思想是将刚体运动建模为有限阶多项式，进而通过优化求解多项式系数来处理相关导航问题，同时考虑惯性传感器等带来的约束。本文提出一种连续时间姿态估计方法，通过多项式优化将姿态估计转化为常参数确定问题。具体而言，首先用切比雪夫多项式逼近连续姿态，通过最小化初始条件、动力学和测量值的加权残差来确定未知的切比雪夫系数。我们将所推导的估计器应用于磁力与惯性传感器融合的姿态估计中。仿真与野外测试表明，该估计器相比传统扩展卡尔曼滤波器具有更好的稳定性和更快的收敛速度，尤其在初始状态误差较大的挑战性场景中表现突出。