Constant turn model for statically fused converted measurement Kalman filters

In this paper, the discrete temporal evolution equation of pseudo-states is derived for the constant turn (CT) motion with known turn rate. The pseudo-state vector consists of the converted Doppler (the product of target true range and range rate) and its first derivative. Based on the resulting linear state equation, the converted Doppler measurement Kalman filter (CDMKF) is formulated to extract information from the converted Doppler measurements. The pseudo-states from the CDMKF are fused statically with the outputs of the well known converted position measurement Kalman filter (CPMKF) by a static minimum mean squared error (MMSE) estimator designed for the proposed CT model, resulting in the statically fused converted measurement Kalman filter (SF-CMKF). The validity of the proposed CT model and its benefits to state estimation with Doppler as well as position measurements are demonstrated by assessing the performance of the CDMKF and SF-CMKF. Comparative results show the superior performance of the proposed technique especially in challenging scenarios with large position measurement errors.