Reply to “Comments on ‘L-Shape Two-Dimensional Arrival Angle Estimation With Propagator Method’”

It is correct that one can estimate the elevation angles by using [1, Eq. (25)], because the direction cosine relative to the z-axis v̂k only contains the information of the elevation angle ̂k . However, the elevation angle estimate ̂k and (̂2;x)kk in [1, Eq. (32)] are not one-to-one related to the direction cosines v̂k and ŵk (k = 1; 2; . . . ; K), respectively. Thus, the expression of [1, Eq. (32)] is incorrect. At the same time, it is worth mentioning that the so-called two L-shape algorithm in [1] has the similar problem in pair matching. To remove this problem, coupling information must be employed. We can resort to the “rotational perturbation” method proposed by A. J. van der Veen et al. (see [2] and [3] for more details) to pair the respective members of two sets of estimates. The same numerical example as Fig. 1 is conducted to evaluate the pairing performance, and the results are presented in Fig. 2. We observe that no failure occurs after applying the rotational perturbation method. REFERENCES