# Research on Passive Ranging Technology of Moving Ship Based on Vertical Hydrophone Array
## 1 Introduction  
Range localization is a significant component of the Sound Navigation and Ranging (SONAR) system in the field of underwater target detection. Currently, the most popular methods for ranging are three subarrays, the matched field processing (MFP) and the waveguide invariant method. The three subarray passive ranging method mainly uses the principle of the curvature of the spherical wavefront. The target range is estimated by measuring the relative time delay of the received signal on each of the three subarrays [1]. However, this method is easily affected by the time delay estimation accuracy, whose error cannot be ignored, especially in the complex ocean environment [2]. The matching field passive positioning technology is an environment-dependent method based on ocean channel modelling [3]. The copy sound field is first calculated through the ocean channel model, and the matching processing is applied in the copy field and signals received by the hydrophone array. We can obtain the range and depth information of the sound source after the parameter search processing [4; 5]. However, the mismatch problem of the ocean channel environment cannot be solved effectively in practice, and thus the matching field positioning accuracy becomes poor. Comparatively, the waveguide invariant technology is more tolerant of the environmental demands, which is an importantparameter to describe the range-frequency interference structure phenomenon of the ocean sound field. [PERSON] [6] adopted the waveguide invariant technology to estimate the range of a broadband sound source by using a single hydrophone. This method requires only a little prior knowledge of the environment and acquires a higher estimation accuracy. Reference [7] developed a method to achieve range localization in shallow water and a range-independent environment when the time interval of the pressure field was ascertained. [PERSON] et al. [8] adopted the waveguide invariant theory to achieve the orientation by quantifying the intensity interference fringes in the range-frequency domain. Furthermore, the waveguide invariant parameter is the core of the spectral analysis that is involved in the range estimation. The signal transmitted from cargo ships can be used to estimate both the time-varying source-receiver range and the receiver position [9]. Further, many robust algorithms have been developed to improve range estimation precision. [PERSON] [10] employed the Low Frequency Analysis Record (LOFAR) spectrum of the vector sensor linear array to record the parabolic striations of the wide-band target passing the CPA point. Then, the image processing technology was used to obtain the waveguide invariance and realize the range estimation of the target. [PERSON] et al. [11] combined the waveguide invariant with the beam-time migration technology to achieve a range estimation by a vertical or horizontal array. Generally, the sound sources mentioned in the above literature mostly radiate narrowband or broadband signals. In comparison with the wideband ship noise, the narrowband ship noise is more extensively applied in the range estimation field. However, the low-frequency line spectrum of the broadband ship noise is usually unstable, and it needs to be preprocessed by signal processing technology in order to obtain a high SNR narrowband signal. The Detection of Envelope Modulation on Noise (DEMON) spectrum method is widely used in the analysis of broadband ship noise, and the low-frequency characteristic spectrum can be obtained by demodulating the high-frequency components of the receiving signal [12; 13; 14]. Due to the poor ranging accuracy of a single hydrophone, researchers developed multi-sensor data fusion technology. Data fusion is defined as a technology that combines data from multiple sensors with information from related databases to achieve a higher precision [15].