## 1 Introduction  
Conformal array antennas mounted on curved surfaces are commonly implemented in various areas, such as radar, sonar and wireless communication [1]. Particularly, integrated antennas are mounted on space-borne, airborne, missile and land vehicles. The conformal antennas could fulfill specific aerodynamics, space-saving, elimination of random-induced bore-sight error, provide a potential increase in available aperture and so on [2]. It can be seen that the conformal antenna has some promising applications. The excellent characteristics of the conformal array antenna have attracted many researchers in various fields. However, analysis of such an array is a great challenge because of the potential complexity of design as well as the possible material complexity [3]. Most research focuses on the design of antenna configuration [4; 5; 6], the transformation between the local coordinate and global coordinate [7; 8; 9; 10] and the pattern synthesis of conformal array antennas [11; 12; 13; 14; 15]. The traditional direction-of-arrival (DOA) estimation algorithms, for example, the multiple signal classification (MUSIC) and the estimation of signal parameters via rotational invariance techniques (ESPRIT) could not be used for conformal array antennas because of the varying curvature [16; 17]. Indeed, the \"shadow effect\" of the conformal array antenna is caused by the metallic shelter, leading to the condition that not all antennas could receive the signal. Therefore, the steering vector is not completed. As a result, the most commonly used DOA estimation algorithms are not suitable for conformal array antenna. Recently, DOA estimation algorithms for conformal array antennas, which have high resolution, are proposed [18; 19; 20; 21; 22]. The MUSIC algorithm and sub-array divided technique are employed, but the computational complexity of the spectrum peak searching is still too high [18; 19]. With the help of fourth-order cumulants and ESPRIT algorithm, a blind DOA estimation algorithm is proposed in [20], and the 2D DOA estimations are decoupled between the signal parameter and polarization. Based on the mathematical technique of geometric algebra, the 2D DOA and polarization parameter estimations are accomplished by iterative ESPRIT algorithm [21]. The joint frequency and 2D DOA estimations for cylindrical conformal array antenna are acquired using state-space and propagator method, and the interpolation technique is adopted for parameter pairing [22]. However, the mathematical model of steering vector is too complicated [20; 21; 22], and the elements with separation must be half of the wavelength [23]. Under the condition that the frequency of the incident signal is relatively higher, it causes the inter-element spacing to be rather close. The mutual coupling between the adjacent elements is serious [24]. In practice, due to the complexity of the DOA estimation algorithm for conformal arrays, the vast majority of the algorithms for ordinary arrays are not suitable. The ultra-wideband direction finding for conformal array antenna is still an extremely severe problem at present. The interferometer [25; 26; 27] direction-finding method is another kind of DOA estimation method which can be used for ultra-wideband direction finding [28; 29; 30; 31]. The algorithm in [28] does not need a grid search. Instead, the estimation result is a closed-form solution, which has a great advantage in real-time application. The interferometer has two small-diameter antennas and four movable planar mirrors, which are used to solve the phase-ambiguity problems [29]. The methods mentioned in [28; 29; 30; 31] assume that the antennas are coplanar. However, when conformal array antenna is mounted on aircraft, the antenna elements may not be arranged in the same plane. Thus the methods mentioned above will not work effectively.