A discrete filter is examined for the joint estimation of the coordinates, velocity, and angular rate W of a target performing a steady turn, based on indirect (polar/spherical) radar measurements. When W is included in the augmented state vector, the increment conversion matrix becomes a nonlinear function of W itself; consequently, linearization – as employed in previously studied versions of the extended Kalman filter for indirect measurements – requires recalculating the Jacobian matrix at each step and introduces an additional methodological error. An unscented transformation of the augmented state vector is proposed to eliminate the need for linearizing the motion and measurement models. Monte Carlo statistical simulations (N_run = 545) were conducted to compare the proposed algorithm with its linearized counterpart across eight standard surveillance radar types (2D and 3D) and five target turn rates. The results demonstrate that the proposed algorithm yields a root-mean-square error for the W estimate that is, on average, 4.3 times lower (median 4.0; range 1.4–14.0 across all observation conditions) than that of the linearized extended Kalman filter, while offering a more modest improvement (averaging 1.2 times) in the root-mean-square error of the position estimate.

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