An Analysis Method for Solving Ambiguity in Direction Finding with Phase Interferometers
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An Analysis Method for Solving Ambiguity in Direction Finding with Phase Interferometers Lutao Liu1 · Tao Yu1 Received: 4 January 2020 / Revised: 22 August 2020 / Accepted: 24 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The phase interferometer is an effective direction finding (DF) method. It is widely utilized in various electronic reconnaissance systems due to its advantages of fast operation and high precision. In a wideband system, the combination of long and short baselines, or even multi-level baselines, is applied in an interferometer to solve the contradiction between accuracy and phase ambiguity for DF. In this paper, a novel analysis method is proposed to obtain the probability of successfully solving ambiguity based on mathematical statistics. According to the length ratio between short and long baselines, the joint density function of phase errors can be derived. Then, the probability can be achieved under different signal-to-noise ratios (SNRs) by integrating the joint density function in a specific interval. Furthermore, the formula of phase measurement error is adjusted by the least square method to improve computational accuracy in low SNR during the process. Under different baseline configurations, the strategy can provide the theoretical probability of successfully solving ambiguity, thus guiding the baseline design for obtaining a maximum probability without impacting the specified DF accuracy. Simulation results show that the mathematical model is efficient in some complex cases. Keywords Phase interferometer · Phase ambiguity · Solving ambiguity · Direction finding (DF) · Mathematical statistics
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Tao Yu [email protected] Lutao Liu [email protected]
1
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
Circuits, Systems, and Signal Processing
1 Introduction Due to the importance of target azimuth, direction finding (DF) technology occupies an essential position in the field of modern signal reconnaissance. It is the key to the basic means to position radiation signals [8,23]. The azimuth angle of a radiation source delivers significant intelligence, since it cannot be camouflaged compared with other parameters. Amplitude-comparison methods, phase-comparison methods, spatial spectrum estimation methods, and compressed sensing estimation methods are currently the main classifications for DF. Among them, amplitude-comparison methods require high requirements for antenna beams, but have poor estimation accuracy in wideband situations. The Bartlett beamformer and Capon’s beamformer are two typical examples. More importantly, they suffer from the Rayleigh resolution limit [13]. Multiple signal classification (MUSIC) and the estimation of parameters by rotational invariant techniques (ESPRIT) are basic algorithms for spatial spectrum estimation methods. They are superresolution algorithms and apply to multi-target DF. However, the cost is high computational complexity. They need the cov
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