For the conventional truncated unscented Kalman filtering (TUKF) algorithm requires the measurement to be a bijective function, a novel improved truncated unscented Kalman filtering is proposed. In the proposed algorithm, we linearize the bijective measurements function based on the statistical linear regression (SLR) in order to obtain the only inverse function of the measurement function. It is a modified algorithm which extends the range of practical application of the filtering problems. Finally, the experiments show that the performance of the proposed algorithm is better than the unscented Kalman filter (UKF) and the quadrature Kalman filter (QKF). This approach can efficiently deal with this problem that measurement functions are not bijective.