access icon free Convergence analysis of non-linear filtering based on cubature Kalman filter

This study analyses the stability of cubature Kalman filter (CKF) for non-linear systems with linear measurement. The certain conditions to ensure that the estimation error of the CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Since adaptation law has a very important role in convergence, fuzzy logic is proposed to improve the versatility of the proposed adaptive noise covariance. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the modified CKF is compared to the CKF in two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF, while the MCKF is successfully able to estimate the states. In addition, the superiority of MCKF that uses fuzzy adaptation rules is shown.

Inspec keywords: error statistics; stability; fuzzy logic; nonlinear systems; nonlinear filters; adaptive estimation; adaptive Kalman filters; covariance analysis; state estimation; fuzzy set theory; convergence

Other keywords: nonlinear filtering; linear measurement; fuzzy adaptation rules; fuzzy logic; convergence analysis; adaptive process noise covariance; instability; nonlinear system; state estimation; estimation error; modified CKF; stability; MCKF; cubature Kalman filter

Subjects: Signal processing theory; Combinatorial mathematics; Other topics in statistics; Other topics in statistics; Filtering methods in signal processing; Combinatorial mathematics

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