Optimized Least Square DOA Estimation Algorithm Based on Phase Interferometer Array

Aiming at the complex process of phase interferometer ambiguity resolution and the strict requirement of baseline comparison, an optimized least square ambiguity resolution algorithm for multi-baseline phase interferometer is proposed. This algorithm is a backward-forward derivation method. First, phase matrix is generated by off-line calculation. Then verify the uniqueness condition of correctly ambiguity resolution, and the angle of arrival (AOA) is solved by criterion function. The algorithm uses the mean square operation instead of the time-consuming cosine function calculation. The algorithm can be applied to the complex array of interferometers and makes the test of the uniqueness condition simpler. Simulation experiments are carried out under the condition of one-dimensional linear array. The result show that the algorithm is effective and has high anti-noise performance. Introduction Phase interferometer is widely used in the measurement and control of direction of arrival (DOA) in passive location, and it is of great significance in DOA Location and tracking [1]. The phase interferometer has the advantages of high direction-finding accuracy, passive direction finding, simple internal structure and observation frequency bandwidth [2]. With the improvement of single satellite information processing ability, phase interferometer is widely used in passive location. The phase detection range of phase interferometer is (-π, π). When the length between two baselines exceeds half wavelength (λ/2), phase ambiguity will occur. Therefore, for single baseline phase interferometer, there is a contradiction between direction finding accuracy and maximum non ambiguity angle [3,4]. In reference [5], the long-short baseline method limits the length of the short baseline. In order to meet the requirement of wide-band direction finding of phase interferometer and ensure the realization of system physics, a method based on virtual baseline is proposed in reference [6,7]. The construction of virtual baseline is obtained by subtracting adjacent entity noise-added baseline, so the virtual baseline will increase the disturbance of noise. Moreover, the virtual baseline will limit the placement of two long baselines adjacent to the short baseline. The reference [8] puts forward multi-pare unwrap ambiguity algorithm. The baseline is required to be mutual prime. The phase ambiguity can be obtained by two-dimensional integer search, but each group is required to contain the correct ambiguity number. The reference [9] puts forward stagger-baseline algorithm and require the baselines satisfied stagger qualification. The ambiguity number of each baseline can be obtained by multi-dimensional integer search. In reference [10], the cosine function is used to eliminate the resolution of the ambiguity number. The operation of the algorithm is mainly concentrated in the calculation of multiple cosine functions. In reference [11], a high-precision AOA algorithm is introduced, and the maximum allowable phase error is analyzed. In the case of multi-baseline, the phase value of the longest baseline needs to be obtained through the above processes more times. In reference [12], direction finding with uniform circular array (UCA), searching for ambiguity number with look-up table, and then calculating DOA with ambiguity number. In this paper, an optimized least square DOA estimation algorithm is proposed. The algorithm is based on the fact that the phase difference corresponding to each incoming wave angle is constant in the case of noiseless. A matrix can be built offline to store the phase difference at each angle, and a criterion function can be built to solve the DOA. This algorithm has three advantages compared with above methods. First, it avoids the process of solving the ambiguity number, does not need multi-dimensional integer search, and has a small amount of calculation. Second, the algorithm generates the phase matrix, which makes the test of uniqueness condition simpler. Third, the algorithm is not only applicable to linear array, and it is suitable for plane array, such as L array and UCA. DOA Estimation Algorithm Based on Least Square Criterion One Dimensional Linear Phase Interferometer Array Suppose that there is a phase interferometer array with N+1 elements distributed on a one-dimensional straight line, the baseline 0 A is defined as the reference baseline of phase 0, and the distance between 1 ~ N A A is 1 2 , , , N D D D , as shown in Fig. 1. The radiation source is in the far-field position relative to the interferometer, the wavelength is  , the angle of the incoming wave is  , and the phase difference between the baseline 1 ~ N A A and 0 A is: 2 sin( ), 1,2, , n n N D n       (1) The actually received phase difference n  differs from n  by a number of 2π: 2 , [ ) , n n n n M           (2) where n M is the phase ambiguity number between n A and 0 A . Figure 1. One-dimensional N+1 baseline phase interferometer. In the case of noise, the observed phase n  is the modulus of 2π after the phase noise n v is superimposed on n  : m ) ( ) od(2 n n n v      (3) Obviously, in the noiseless case, under a certain angle 0  , the value of 2 1, , , N    are determined. According to this characteristic, we can store all the phase values in the interval [ ] ,    to generate a phase matrix. Then we can use the optimized least square criterion to solve the DOA. Design of Phase Matrix The construction of phase matrix is a very important step in DOA estimation. The matrix needs to enumerate all possible incident angles. Assuming the incident range of the incident angle is [ ] ,    , the distance between each baseline and the reference baseline 0 A is 1 2 , , , N D D D . The frequency of the incoming wave is f. If the correct estimation of DOA is defined as the 0 1  deviation of the 0 A 1 A 2 A