Geometric Algebra Based Kalman Filter Trajectory Prediction

To improve the safety and efficiency of aviation operation, a Kalman filtered trajectory prediction algorithm based on geometric algebra is proposed in this space. Firstly, the Kalman filter equations for trajectory prediction in geometric algebraic space are given by taking position, velocity and acceleration as state variables and position, velocity and acceleration in a typical trajectory as observations. Secondly, the matrix operation in the geometric algebraic space is simplified to the matrix operation by establishing a composite geometric algebraic space. Then, the versor operator in the conformal geometric algebraic space is introduced into the Kalman filter, and the steps of geometric algebra-based Kalman filter trajectory prediction are given to improve the prediction rate and accuracy. The experimental results show that the proposed trajectory prediction algorithm has the highest accuracy and the operation efficiency is improved by 27.66^% compared with the Kalman filter algorithm in Euclidean space and the DBSCAN clustering algorithm.