With the advantage that antenna pattern and scanning features can be described conveniently in phased array radar, direction cosine coordinates (COS) is widely used. Unfortunately, measurements reported in the COS are non-linear relative to the target states described in the Cartesian coordinates. In addition, it has been proved by the theory and practice that the tracker can perform better by making full use of the Doppler measurement. This study mainly focuses on dealing with the position and Doppler measurement in the COS. Firstly, a pseudo measurement constructed by the product of range measurement and Doppler measurement is utilized to reduce the high non-linearity between the target state and the Doppler measurement. Then, via taking the fourth-order terms of a Taylor series expansion, the consistent estimation of converted measurements errors is obtained based on current measurements. Finally, in order to process the converted position measurements and pseudo measurement sequentially, Cholesky decomposition is exploited to decorrelate the converted position and pseudo measurement errors. Simulation results illustrate that the filter presents a higher estimation accuracy of target states, whether the target is moving or static. Furthermore, compared with unscented Kalman filter, the calculation load of the proposed filter is reduced significantly.