基于高阶补偿模型的新圆锥算法

New coning algorithm based on high-order error compensation model

分析表明传统圆锥算法的误差由常值漂移误差和截断误差组成。通常截断误差大于漂移误差,是误差的主项应优先补偿。而传统圆锥算法一般通过增加单次更新周期内的子样数来提高算法精度,但子样数的增加只能减少漂移误差,对截断误差并没有改善作用。从Bortz的旋转矢量微分方程出发,在不增加采样数的前提下,通过高阶误差补偿模型,对圆锥运动产生的截断误差进行了有效的补偿,提高了算法精度。从理论上比较了该算法和传统3子样圆锥算法、4子样圆锥算法的误差,证明算法精度一般优于传统3子样圆锥算法和4子样圆锥算法。通过仿真证明了上述结论的正确性。虽然新算法增加了一定的计算量,但随着导航计算机性能的不断提高,实测的结果表明仍能满足实时性的要求。

The analysis indicates that the errors of traditional coning algorithms are composed by two parts：drift error and truncation error.Truncation error is often far larger than drift error,which means that the truncation error should be reduced firstly.The existing coning algorithms are usually by increasing the sample numbers to reduce the drift error,but the increment of the sample numbers has little positive effect on reducing truncation error.Based on the Bortz＇s rotation vector equation,a higher-order error compensation model was established without increasing the sampling numbers.From the compensation model,the truncation error was compensated effectively.The error of the new algorithm was compared with that of the traditional three and four-sample coning algorithm.The comparison results indicate that the new algorithm is superior to the traditional coning algorithms for the general case.Although the new algorithm has increased a little computational load,the test results show that the algorithm＇s real-time requirement is still satisfied thanks to the rapid development of computer speed.