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When a synthetic aperture sonar (SAS) system operates under low-frequency broadband conditions, the azimuth range coupling of the point target reference spectrum (PTRS) is severe, and the high-resolution imaging range is limited. To solve the above issue, we first convert multi-receivers’ signal into the equivalent monostatic signal and then divide the equivalent monostatic signal into range subblocks and the range frequency subbands within each range subblock in order. The azimuth range coupling terms are converted into linear terms based on piece-wise linear approximation (PLA), and the phase error of the PTRS within each subband is less than π/4. Then, we use the chirp-z transform (CZT) to correct range cell migration (RCM) to obtain low-resolution results for different subbands. After RCM correction, the subbands’ signals are coherently summed in the range frequency domain to obtain a high-resolution image. Finally, different subblocks are concatenated in the range time domain to obtain the final result of the whole swath. The processing of different subblocks and different subbands can be implemented in parallel. Computer simulation experiments and field data have verified the superiority of the proposed method over existing methods.

For a multi-hydrophone synthetic aperture sonar (SAS), the instability of the platform and underwater turbulence easily lead to two-dimensional (2-D) space-variant (SV) motion errors. Such errors can cause serious imaging problems and are very difficult to compensate for. In this study, we propose a 2-D SV motion compensation algorithm for a multi-hydrophone SAS based on sub-beam compensation. The proposed algorithm is implemented using the following four-step process: (1) The motion error of each sub-beam is obtained by substituting the sonar’s motion parameters measured in the exact motion error model established in this study. (2) The sub-beam’s targets of all targets are compensated for motion error by implementing two-phase multiplications on the raw data of the multiple-hydrophone SAS in the order of hydrophone by hydrophone. (3) The data of the sub-beam’s target compensated motion error are extracted from the raw data by utilizing the mapping relationship between the azimuth angle and the Doppler frequency. (4) The imaging result of each sub-beam is obtained by performing a monostatic imaging algorithm on each sub-beam’s data and coherently added to obtain high-resolution imaging results. Finally, the validity of the proposed algorithm was tested using simulation and real data.

The existing multi-receiver synthetic aperture sonar (SAS) imaging algorithms are suitable for narrow-beam width, which will lead to a decrease in imaging quality under wide-beam condition and are not in line with the development needs of SAS. We propose a non-linear chirp scaling algorithm (NCSA) for wide beam multi-receiver SAS. Firstly, the point target reference spectrum (PTRS) of each receiver is obtained by the Lagrange inversion theorem (LIT), and then the under-sampled signal in the azimuth frequency domain is obtained through azimuth spectrum extension; Then, considering the cubic term of range frequency in the PTRS and the linear variation of equivalent frequency modulation slope with range, each receiver is imaged using the NCSA, and coherent superposition is performed in the azimuth frequency domain to eliminate spectrum aliasing caused by azimuth spectrum extension; Finally, the azimuth inverse transform is performed on the superimposed signal to obtain the focusing imaging. Computer simulation experiments and field data verify that this method is superior to the existing SAS imaging algorithm, improving the quality of wide-beam imaging, avoiding the interpolation operation of the traditional range-Doppler algorithm, and saving computation cost.

Two-dimensional phase unwrapping (2-D PU) is the process of converting the measured phase into the real phase in interferometric signal processing. Reliable unwrapping results are critical for digital elevation model generation using interferometric synthetic aperture radar (InSAR) and interferometric synthetic aperture sonar (InSAS). The majority of previous research has concentrated on accuracy, whereas the computational efficiency must be taken into account for the interferometric measurement system that requires real-time processing. This article proposes a low-time-consuming algorithm that can accomplish high-precision 2-D PU for this application scenario. The neural network and a new path-based 2-D PU algorithm make up this algorithm. First, the incorrect region in the gradient field is predicted and corrected using the neural network. The output channelwise variance is then calculated and used to generate the quality maps. Finally, to achieve phase reconstruction, the path-based algorithm performs path planning and flooding integral according to quality maps and compensated gradient. This article also provides a recommended data structure implementation to ensure the algorithm's high efficiency. Experimental results using InSAR and InSAS data show that the proposed algorithm is highly efficient and accurate.

Abstract The quality of interferogram, which is limited by various phase noise, will greatly influence the subsequent processes of interferometric synthetic aperture sonar (InSAS), such as phase unwrapping and digital elevation model (DEM) estimation. Therefore, phase filtering is an essential step in signal processing for InSAS. In this paper, an adaptive filtering method combined with quality map is proposed to suppress the phase noise while preserving the fringe edges. The main advantage of the new approach is the size of filtering window can be adaptively selected according to the quality map. A function between window size and quality map is established, which controls the strength of filtering. In the area of high quality, the window size is large to remove noise, otherwise, in the low quality area, the window size is small to keep edge details. The effectiveness of the proposed method is validated via some illustrative simulated experiment and the real InSAS data.

To improve the imaging quality of conventional imaging algorithms without motion compensation (MOCO) and the efficiency of point-by-point MOCO algorithms for multiple-receiver synthetic aperture sonar (SAS) with azimuth-invariant six-degree of freedom (DOF) motion errors, an azimuth-invariant MOCO and imaging chirp scaling (CS) algorithm is presented in this paper. Taylor series approximation is used to process the range history in double square root form, while considering the fourth-order and inner terms with respect to the azimuth time. Using the method of series reversion and Fourier transform (FT) properties, the analytical two-dimensional frequency spectrum of the point target response of each receiver is derived. On this basis, the azimuth-invariant MOCO and imaging CS algorithm is proposed for six-DOF motion error compensation and multiple-receiver SAS imaging. Because it considers the azimuth-invariant six-DOF motion errors, the proposed algorithm has better imaging quality than conventional imaging algorithms without MOCO. Additionally, it has a significantly higher efficiency than point-by-point MOCO algorithms because the CS algorithm is a fast FT-based algorithm and does not require interpolation processing. The imaging simulation and experimental results verified the effectiveness and efficiency of the proposed algorithm.

Precise orientation information facilitates target recognition of sonar images. Traditional orientation estimation methods, including the Hough transform method, have poor antinoise abilities, so they cannot achieve high estimation precision for sonar images, which usually have low signal-to-noise ratios. The convolutional neural network (CNN) regression method is sensitive to image affine transformations and requires extensive computation, so it cannot achieve strong robustness or high speed. To achieve high-precision, high-speed, and robust orientation estimation of sonar image targets, we present a novel orientation estimation method via the wavelet subimage energy ratio (WSER). The WSER varies with the rotation angles of images and has the highest value when the long axes of targets are vertical. It is translational and scale invariant and does not need supervised training. Therefore, we propose estimating orientations of sonar image targets by finding the max of the WSER to achieve high precision, high speed, and strong robustness to the translation and scale transformations of images. The results of experiments on a self-made sonar image dataset show that the mean absolute error (MAE) of the proposed method is 7.9°, while the MAEs of the CNN regression method and traditional methods are 10.1 and 22.9°, respectively. In addition, the proposed method is six times faster than the CNN regression method. The proposed orientation estimation method has also been applied to align the orientation of sonar images and CNN can achieve state-of-the-art performance for rotated target recognition using the aligned images. Data and codes are publicly available.

The compensation of slant range motion errors needs to be carried out after range pulse compression in the signal processing of multiple-receiver synthetic aperture sonar (SAS). Whereas range pulse compression cannot be performed as the first step in multiple-receiver SAS chirp scaling (CS) algorithm, as it requires the transmitted signal to be linearly frequency modulated. For this reason, it is difficult to combine CS algorithm with motion compensation. Besides, those imaging algorithms based on interpolation, such as range-Doppler algorithm and wavenumber domain algorithm, have plenty of computation load and large phase errors. Aimed at these problems, a CZT algorithm for multiple-receiver SAS in the non-stop-hop-stop mode is proposed in this paper. The proposed algorithm can correct range cell migration utilizing chirp-z transform, which avoids interpolation. Furthermore, the algorithm is easily combined with motion compensation as it can process pulse-compressed data directly. This paper describes the algorithm in 9 key steps, including the principle of correcting range cell migration utilizing chirp-z transform in discrete domain. In the simulation and sea trial data processing, the proposed algorithm provides image quality equal to the CS algorithm, and the algorithm is slightly more efficient than CS algorithm when combined with motion compensation.

The convolutional neural network (CNN) has achieved good performance in object classification due to its inherent translation equivariance, but its scale equivariance is poor. A Scale-Aware Network (SA Net) with scale equivariance is proposed to estimate the scale during classification. The SA Net only learns samples of one scale in the training stage; in the testing stage, the unknown-scale testing samples are up-sampled and down-sampled, and a group of image copies with different scales are generated to form the image pyramid. The up-sampling adopts interpolation, and the down-sampling adopts interpolation combined with wavelet transform to avoid spectrum aliasing. The generated test samples with different scales are sent to the Siamese network with weight sharing for inferencing. According to the position of the maximum value of the classification-score matrix, the testing samples can be classified and the scale can be estimated simultaneously. The results on the MNIST and FMNIST datasets show that the SA Net has better performance than the existing methods. When the scale is larger than 4, the SA Net has higher classification accuracy than other methods. In the scale-estimation experiment, the SA Net can achieve low relative RMSE on any scale. The SA Net has potential for effective use in remote sensing, optical image recognition and medical diagnosis in cytohistology.

Purpose: This paper aims at defining the value creation mechanism and income distribution strategies of product-service integration in order to promote product-service integration of a firm.Design/methodology/approach: This paper conducts researches quantitatively on the coordination mechanism of product-service integration by using game theory, and uses the methods of Shapley value and Equal growth rate to further discuss income distribution strategies of product-service integration.Findings: Product-service integration increases the total income of a firm and the added value of the income decreases as the unit price demand variation coefficient of products and services increases, while decreases as the marginal cost of products increases, decreases as the marginal cost of services increases. Moreover, the findings suggest that both income distribution strategies of product-service integration based on Shapley value method and Equal growth rate method can make the product department and service department of a firm win-win and realize the pareto improvement. The choice of what kind of distribution strategy to coordinate the actions between departments depends on the department playing dominant role in the firm. Generally speaking, for a firm at the center of market, when the product department is the main contributor to firm income, the service department will choose the income distribution strategy of product-service integration based on Shapley value method; when the service department is the main contributor to firm income, the service department will choose the income distribution strategy of product-service integration based on Equal growth rate method.Research limitations/implications: This paper makes some strict assumptions such as complete information, risk neutral, linear cost function and so on and the discussion is limited to the simple relationship between product department and service department.Practical implications: Product-service integration enables a firm to improve its total income. A firm should take appropriate income distribution strategies in order to promote the its product-service integration.Originality/value: This paper introduces game theory into the research of product-service integration for the first time and it has reached some valuable conclusions, which has opened up a new field of study in the product-service area.

A correction approach for the inclined array of hydrophones is proposed to prevent decline of the image quality in SAS. In this approach, the 2-way exact acoustic propagation path of the inclined array is transformed into the sum of a single root term and an offset term, where the single root term is the 2-way ideal propagation path and the offset term contains all errors cause by the inclined array. The correction for the offset term is separated into two steps: phase correction and delay correction. The phase correction is performed on the echo signal of each receiving hydrophone in the 2-D time domain by a phase multiplication and the delay correction is performed on the echo signal of each receiving hydrophone in the range frequency domain by a phase multiplication with a linear function of range frequency at the reference range. Finally, the effectiveness of the proposed approach is examined by the simulation experiments.