Inertial-Based Navigation by Polynomial Optimization: Inertial-Magnetic Attitude Estimation

Inertial-based navigation refers to the navigation methods or systems that have inertial information or sensors as the core part and integrated 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 the polynomial optimization method. The basic idea is to model rigid motions as finite-order polynomials and then attack the involved navigation problems by optimally solving their coefficients, considering the constraints posed by inertial sensors and others. This article proposes a continuous-time attitude estimation approach, which transforms attitude estimation into a constant parameter determination problem by polynomial optimization. Specifically, the continuous attitude is first approximated by the 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 that of the traditional extended Kalman filter, especially in challenging large initial state error scenarios.