Accuracy analysis of three deterministic sampling nonlinear filtering algorithms

Abstract

To study the estimation accuracy of nonlinear Kalman filter in transfer alignment system, the Taylor expansion of multivariable function is utilized to analyze the estimation accuracy of the three typical deterministic sampling nonlinear Kalman filters, such as high-degree cubature Kalman filter (HCKF), cubature Kalman filter (CKF) and unscented Kalman filter (UKF). The Taylor expansion analyses demonstrate that CKF and UKF produce truncation error since the fourth degree term, while HCKF can capture fifth degree term of Taylor series expansion. The three nonlinear filtering algorithms are applied to carrier-aircraft transfer alignment system under large misalignment angle. The simulation results show that CKF and UKF have the same accuracy, and HCKF has higher estimation accuracy than the other two, which is consistent with the theoretical analysis results.