This study proposes a new linear state estimation filter for radar target tracking. Unlike the conventional converted measurement technique, target motion and radar measurements are modeled in mixed Cartesian coordinate systems. Considering the coordinate transformation relationship between radar measurements and state variables, radar target tracking is described as a state estimation problem for a linear measurement model. This model is useful in practice because it guarantees the whiteness of the measurement noise sequence and the unbiasedness of the target state estimator. Based on this observation, the design of a tracking filter is described as a stochastic minimization problem of an indefinite quadratic form linked to a linear time-varying system whose measurement matrix includes the random coordinate transform uncertainty. The resulting solution almost surely converges to the true state, even when an uncertain coordinate transform matrix is used. Computer simulations show that the proposed filter performs better and more consistently than the existing methods regarding target tracking performance.