The performance of an inertial navigation system (INS) operated on a moving base greatly depends on the accuracy of rapid transfer alignment (RTA). However, in practice, the coexistence of large initial attitude errors and uncertain observation noise statistics poses a great challenge for the estimation accuracy of misalignment angles. This study aims to develop a novel robust nonlinear filter, namely the stochastic integration H
filter (SIH
F) for improving both the accuracy and robustness of RTA. In this new nonlinear H
filter, the stochastic spherical-radial integration rule is incorporated with the framework of the derivative-free H
filter for the first time, and the resulting SIH
F simultaneously attenuates the negative effect in estimations caused by significant nonlinearity and large uncertainty. Comparisons between the SIH
F and previously well-known methodologies are carried out by means of numerical simulation and a van test. The results demonstrate that the newly-proposed method outperforms the cubature H
filter. Moreover, the SIH
F inherits the benefit of the traditional stochastic integration filter, but with more robustness in the presence of uncertainty.
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