The accuracy and rate of convergence are two important performance factors for initial ground alignment of a strapdown inertial navigation system (SINS). For navigation-grade SINS, gyro biases and accelerometer offsets can be modeled as constant values during the alignment period, and they can be calibrated through two-position ground alignment schemes. In many situations for SINS ground alignment, the azimuth of the vehicle remains nearly constant. This quasi-stationary alignment information can be used as an augmented measurement. In this paper, a piecewise combined Kalman filter utilizing relative azimuth constraint (RATP) is proposed to improve the alignment precision and to reduce the time consumption for error convergence. It is presented that a piecewise time-invariant linear system can be combined into a whole extended time-invariant linear system so that a piecewise combined Kalman filter can be designed for state estimation. A two-position ground alignment algorithm for SINS is designed based on the proposed piecewise combined Kalman filter. Numerical simulations and experimental results show its superiority to the conventional algorithms in terms of accuracy and the rate of convergence.
The rate of convergence of GMRES on a tridiagonal toeplitz linear system. II