In tracking applications, target dynamics is usually modeled in the Cartesian coordinates, while target measurements are got in the sensor coordinates, such as polar, spherical and direction cosine coordinates. Many well-known measurement-conversion techniques for polar and spherical measurements in mechanical rotating/scanning radars have been developed. However, they are not applicable to direction cosine measurements in electronic scanning radars, such as phased array radars. A new method directed to direction cosines measurements for target tracking with debiased consistent conversion (abb. CMKFDcos) is proposed. The converted measurements bias and covariance are explicitly derived. The consistency of converted measurements errors and the covariance is outlined. The simulation results validate that the converted measurements completely capture the true mean and covariance of the original measurements reported in direction cosines. The performance of CMKFDcos is superior to Extended Kalman filter (EKF) and Linear converted measurements KF (CMKFL) in accuracy and consistency for all practical situations. The proposed procedure can be employed in the cross-range errors being significantly large relative to the range errors with the efficiency and modest computational load.