Linear fitting Kalman filter

Dynamic estimation in signal processing and target tracking often involves non-linear models. These non-linear models are usually linearised through the first-order Taylor approximation in estimation process. However, the error generated by the first-order Taylor approximation is not negligible when the non-linearity of a model is high or the input error is large. This study proposes a new linearisation method through minimising the error between a non-linear function and its linear approximation. A weighted least squares (WLS) algorithm is developed to estimate a linear fitting (LF) function based on the sigma points of the random variable in non-linear transformation. A linear fitting Kalman filter (LKF) is developed based on this principle. The accuracy of the LF transform is analysed using the Kullback-Leibler (KL) distance. The results show that the LF transform has less KL distance to the true distribution compared with the first-order Taylor approximation. To evaluate the estimation performance, simulations are conducted and the results are compared with those of extended Kalman filter (EKF) and unscented Kalman filter (UKF). The results demonstrate that the LKF provides better accuracy than the EKF, and has similar accuracy to the UKF with lower computational cost.