In the field of maneuvering target tracking, the performance of Kalman filter and its improved algorithms depends on the accuracy of pre-designed process noise statistics. When the pre-designed process noise statistics do not match with the actual situation, it will be difficult to obtain a good filtering performance. But unbiased finite impulse response (UFIR) filter does not need the prior knowledge of process noise statistics. Furthermore, the iterative UFIR filter decreases the calculation of UFIR filter greatly. So this paper applies UFIR filter to the maneuvering target tracking. Then considering the generalized noise power gain (GNPG) of existing UFIR filer cannot change when linear models are fixed, an improved UFIR filer is proposed, which can dynamically adjust GNPG during filtering. The simulation results illustrates that the Kalman filter is optimal under linear minimum mean square error (LMMSE) criterion when process noise statistics is certain. But when process noise statistics is unknown, UFIR filter shows more robustness than Kalman filter and our improved UFIR filter has an even better filter performance.