A Coarse Alignment Method Based on Vector Observation and Truncated Vectorized $\boldsymbol{\kappa}$-Matrix for Underwater Vehicle

This paper focuses on the coarse alignment problem for the strapdown inertial navigation system (SINS) applied to the underwater vehicle. The coarse alignment is one of the crucial technologies of underwater navigation and determines whether SINS can work normally. However, the traditional coarse alignment methods suffer from the complicated noises hidden in the inertial sensors’ outputs. To solve this problem, a new coarse alignment algorithm based on vector observation and truncated vectorized
$\boldsymbol{\kappa}$
-matrix is proposed in this paper. Different from previous methods based on the optimal quaternion, the proposed algorithm makes the matrix state-space formulae of the
$\boldsymbol{\kappa}$
-matrix vectorized, and truncates the resulting state vectors by implementing the linear dependence within the components of the
$\boldsymbol{\kappa}$
-matrix. On one hand, based on the vectorized and truncated
$\boldsymbol{\kappa}$
-matrix, a linear reduced model of
$\boldsymbol{\kappa}$
-matrix can be applied to the estimation process, and the measurement errors of inertial sensors can be easily restrained using the estimation algorithm. On the other hand, the proposed approach makes up for the drawbacks of the Optimal-REQUEST algorithm which has a conservative covariance matrix and scalar gain. The simulation test and practical experiment demonstrate that the proposed approach can reduce random noise effectively. Therefore, the performance of coarse alignment algorithm can be improved more enormously than the traditional algorithms.