In this paper, the adaptive simplified spherical simplex unscented Kalman filter was proposed to calculate angular velocity in gyro-free strapdown inertial navigation system. Firstly, a general angular velocity calculation modeling method with time-varying process noise was proposed, which was not limited to a certain kind of accelerometer configuration. Then aiming at the issues of large amount of calculation of unscented Kalman filter and the time variation of the process noise, and based on the characteristics of additive noise and linear state equation, the adaptive simplified spherical simplex unscented Kalman filter was proposed to estimate the angular velocity. The sampling points were decreased in this method through adopting the spherical simplex sampling strategy and not augmenting the state, thus improving the calculation efficiency. Meanwhile, Sage–Husa suboptimal maximum a posteriori noise estimator was brought in to estimate the process noise in real time in order to settle the problem of filter divergence induced by the time variation. Lastly, the proposed algorithm was simulated and also contrasted with the integration method, the evolution method and the conventional adaptive UKF algorithm. The simulation results indicated that the adaptive simplified spherical simplex unscented Kalman filter algorithm has higher precision than the integration method and evolution method and has higher efficiency than the AUKF, which could effectively improve the calculation precision and meanwhile guarantee the calculation efficiency.

A novel inertial measurement unit scheme with five accelerometers and two gyros (5A2G) is proposed in this paper to achieve high precision measurement in high dynamic environment. The three channels are decoupled during the angular velocity calculation procedure to ensure the precision and efficiency. The yawing and pitching angular velocities are directly measured by gyros, while only the rolling angular velocity is inferred indirectly from the rolling angular information vector composed of rolling angular acceleration and quadratic component of rolling angular velocity. Based on the proposed scheme, the configuration ascertainment problem for acquiring the required installation parameters of accelerometers is transformed into a constraint optimization problem with the objective of minimizing the error of rolling angular information vector. A single channel rolling angular velocity calculation model is then established on the basis of the optimal configuration and the extended Kalman filter algorithm is utilized for state estimation. Simulations are implemented and results indicate that the optimal 5A2G scheme is feasible for high-speed rotating ammunition.