Rotation modulation and self-calibration are the key techniques for error compensation of the strapdown inertial navigation system, which are generally implemented separately. The 16-sequence scheme is widely used for rotation modulation, while the 18-sequence scheme is used for self-calibration. To reduce the complexity of the practical operations, this paper proposes the combination of the rotation modulation scheme and the calibration path and six corresponding design principles of the scheme with both rotation modulation and self-calibration functions. A 48-sequence rotation scheme is designed, which unifies the scheme for self-calibration and rotation modulation. The simulation and experiment results prove that, compared with the 16-sequence rotation modulation scheme, the proposed 48-sequence scheme can reduce the mathematical platform misalignment angle errors and the sawtooth type velocity errors caused by the misalignments of the inertial measurement unit. Besides, its accuracy of self-calibration is better than that of the 18-sequence self-calibration scheme. The velocity errors and position errors can be reduced by about 0.1 m s−1 and 0.2 nm in 3 d.

In this paper, we focused on demonstrating the Liouville type theorem for the stationary magnetohydrodynamic equations. First, we improve the well-known L92(R3) result logarithmically. In addition, we are aimed to an asymptotic formula for an integral involving the total head pressure Q=12|u|2+|h|2+p and its derivative over domains enclosed by level surfaces of Q, which provides us with the additional sufficient condition for the triviality of solution for the magnetohydrodynamic equations.

The calibration accuracy of inertial measurement unit (IMU) is one of the important factors affecting the positioning accuracy of strapdown inertial navigation system (SINS). A 24-sequence calibration rotation scheme is proposed in this paper, which improves the observability and observability degree compared with the traditional 18-sequence scheme, and makes the calibration results more accurate. Simulation results show that the calibration results of 24-sequence scheme are closer to the actual value than those of 18-sequence scheme.

In this paper, we study evolution equation ∂tu = −Lαu + f and the corresponding Cauchy problem, where Lα represents the Laguerre operator Lα = 1 2 (− d 2 dx 2 + x 2 + 1 x 2 (α 2 − 1 4)), for every α ≥ − 1 2. We get explicit pointwise formulas for the classical solution and its derivatives by virtue of the parabolic heat-diffusion semigroup {e −τ (∂ t +Lα) } τ >0. In addition, we define the Poisson operator related to the fractional power (∂t + Lα) s and reveal weighted mixednorm estimates for revelent maximal operators.

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