The in-motion alignment of the strapdown inertial navigation system (SINS) is still a challenging problem due to the complex environmental changes that occur during carrier movement. This article proposes a novel initial alignment method by integrating the advantages of the Special Orthogonal Group of order 3 [SO(3)] representation and the optimal attitude estimation alignment idea. In this method, the SO(3) is used to represent the initial attitude matrix, and the optimal attitude estimation alignment model is established by analyzing the influence of the sensor error during the calculation process. Next, state-dependent extended Kalman filter is investigated by mapping the SO(3) equations to the Lie algebra space, and the Lagrange formula is used to separate the state-dependent errors in the Lie algebraic filtering equation. The simulation and experimental results indicate that the proposed initial alignment method can achieve better alignment accuracy and shorter alignment time than existing methods and can fulfill the in-motion alignment tasks for SINSs in various environments.
Aimed at the alignment problem of strapdown inertial navigation system (SINS) on the swing base, a novel coarse alignment method using special orthogonal group optimal estimation is proposed. There are two main contributions in this paper. First, based on the Lie group differential equation, the rotation matrix is updated directly by using error Lie algebra, which avoids the non-convexity of traditional methods and the need for non-collinear vector observation. Second is that a novel optimal estimation method is developed by using the exact error Lie algebra, which is calculated based on the physical definition of Lie algebra, as the innovation term to compensate the initial special orthogonal group in the estimation process. The asymptotic convergence of the proposed optimal estimation method is proved by Lyapunov's second law. The simulation and experimental results demonstrate that the proposed method exhibits better performance than existing methods in alignment accuracy and time, which can achieve the self-alignment of SINS on the swing base.
To address the initial self-alignment problem of strapdown inertial navigation system under marine mooring conditions, a rapid initial self-alignment method based on the constraint matrix Kalman filter (CMKF) is proposed in this paper. The novelties of this method are two-fold. First, based on the Lie group differential equation, a one-step direct self-alignment model without coarse alignment process is designed directly based on a special orthogonal group of rigid-body rotations. In addition, to improve the alignment accuracy, the sensor biases are augmented into the state matrix to be estimated and compensated during the alignment process. Second, because the state of the proposed model is a matrix containing a special orthogonal group, a CMKF is developed to ensure the estimated accuracy. And a Lagrange function is designed in the CMKF to maintain the orthogonality of the special orthogonal group during the filtering process. The simulation and experimental results demonstrate that the proposed method exhibits better performance than existing methods in alignment accuracy and time, which can achieve the self-alignment of SINS under marine mooring conditions.
In this paper, an in-motion initial alignment algorithm based on Lie group matrix kalman filter is proposed. According to the Lie group's properties and the attitude optimization-based initial alignment idea, the attitude matrix is decomposed into three continuous special orthogonal matrices to separate the rotation information and motion information under the in-motion conditions. A linear system model is established based on the differential equation of Lie group, which can replace the traditional quaternion model and avoid the non-uniqueness of unit quaternion representation. Then the Lie Group Matrix Kalman Filter is proposed for estimating the initial inertial matrix directly. And the Simplified Lie Group Matrix Kalman Filter with special process noise is proposed in some specific situations. From the simulation, the alignment accuracy and stability of the two algorithms satisfies the SINS navigation requirements. These two methods have good application prospects for the in-motion initial alignment of SINS.
In order to solve the coarse alignment problem of the strapdown inertial navigation system on a rocking base, a fast coarse alignment method using the Special Orthogonal Group optimization has been proposed in this paper. In this method, based on the alignment idea of tracing gravitational apparent motion in inertial frame, the model of coarse alignment on a rocking base has been established using the Special Orthogonal Group directly. A new attitude error function has been proposed on the basis of the cosines between the measurement vector and predictive vector to describe the error between the estimated attitude and the true one. In order to directly reflect the change in the attitude error in the new innovation term and enable the attitude error to converge to zero as fast as possible, the gradient of the new attitude error function has been selected as the new innovation term to compensate for the attitude in the estimation process. Finally, the stability of the proposed optimization estimation method has been proved by employing the Lyapunov stability theory. Simulation and experiment results show that the method presented in this paper exhibits good performance in terms of alignment accuracy and time and can be applied to coarse alignment under a rocking base under different environments.
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