$\chi^{2}$ Test Based Cubature Kalman Filter Algorithm and its Application in SINS Alignment

Addressing the issue of abnormal measurements influencing the accuracy of navigation state filtering during the in-motion alignment process, a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\chi^{2}$</tex> test based Cubature Kalman Filter (CTCKF) algorithm is proposed. This algorithm aims to enhance system robustness without increasing computational load. By leveraging the state estimates obtained from both the time prediction and measurement update steps in the cubature Kalman filtering process, and assuming that the difference between these two estimates follows a Gaussian distribution, a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\chi^{2}$</tex> test function is established to examine the measurement information. Through the implementation of a constructed fuzzy membership function, the measurement noise in the filtering process is adaptively amplified, thereby mitigating the impact of abnormal measurements on state estimation. Simulation experiments with unmanned aerial vehicles demonstrate that the proposed the CTCKF algorithm enhances system robustness without imposing additional computational burden.