Attitude matrix is the foundation of strap down inertial navigation system (SINS). Equivalent rotation vector algorithm (ERVA) is now considered as the most effective method of computing the attitude matrix under the high-frequency dynamic environment. Most of the existing ERVA pay more attention to the method of optimizing the algorithmȁ9;s coefficients, which are aimed at the variant sample number and update frequency. Under the condition of the given sample number and update frequency, in order to more adequately make use of the rate gyroscopeȁ9;s output information, and more precisely compute the attitude matrix, a novel ERVA is presented, its key thought is to improve the precision of ERV by adding its higher order cross coupling items about the different angle increment during the period of the attitude update into the ERV update equation. Taking two-sample ERVA as the example, the derivation of the novel ERV update equation is given in detail, Simulation results of the novel ERVA demonstrates its validity of improving the ERV precision under the condition of the given sample number and update frequency.
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