Research on Sonar Motion Compensation Method Based on Acoustic Calibration System

The influence of sonar motion error restricts the improvement of sonar imaging resolution. High-precision sonar motion compensation is an important guarantee for high-quality imaging. In this paper, a sonar motion compensation method based on acoustic calibration system is proposed, and the imaging results are compared with those based on the traditional combined inertial guidance measurement method. Experimental results show that the sonar motion compensation method based on acoustic calibration system plays a crucial role in imaging, which proves that acoustic calibration method is an effective means to improve the resolution of sonar imaging.


Introduction
3D imaging sonar is generally mounted on underwater ROV (Remote Operated Vehicle), AUV (Autonomous Underwater Vehicle), or fixed to the bottom of the ship.Due to the influence of dynamic factors such as wind, waves, and tidal currents, as well as the limited control ability of the carrier's motion, the carrier's motion will inevitably deviate from the set trajectory, making it difficult to accurately obtain the position coordinates of hydrophone elements and sound sources during the motion process.According to theoretical analysis, when the motion error exceeds 1/8 wavelength, it will significantly affect the quality of 3D imaging [1].Common methods for compensating carrier motion errors include coarse error compensation based on motion sensors and motion error compensation based on sonar echo data [2][3][4][5].
The coarse error compensation based on motion sensors measures the motion state of the carrier by installing motion sensors such as accelerometers and gyroscopes, and then calculates the displacement, velocity, and acceleration information of the carrier's motion based on the motion model, thereby performing error compensation.The compensation accuracy of this method depends on the performance of the sensor, and it is usually unable to compensate for sub wavelength level motion errors [6][7].Therefore, this method is commonly used in the coarse error compensation stage.In addition, in the case of low-speed motion, the results obtained by the coarse error compensation method based on motion sensors may be unstable.In the fine compensation stage, motion compensation methods based on sonar echo data are generally used.By conducting time-frequency analysis and phase matching on sonar echo data, corresponding motion compensation is performed [8][9].This method has high compensation accuracy and does not require additional sensors, but it requires high processing requirements for sonar echo data, often requiring data conversion processing, and can only compensate for phase errors in specific directions [10].In addition, high-precision acoustic methods are currently mainly applied in the field of carrier positioning, and acoustic positioning systems can accurately measure the position and attitude information of carriers.This article proposes a high-precision motion error compensation method for motion synthesis imaging of linear array sonar, based on a real-time acoustic calibration system with cable connection, and applies it to the field of down looking 3D imaging.

Method
During imaging, the sound source periodically emits pulse signals.Using a chirp signal as a transmit signal, the signal expression can be written: Where () rect represents the rectangular wave envelope, r T is the signal pulse width, c f is the carrier center frequency, r K is the modulation frequency of the chirp signal, and r B is the signal bandwidth.When the signal transmitted by the sound source is reflected by the target and then received by the hydrophone, the expression of the target reflected echo signal received by a single hydrophone primitive is [11]: The time delay is the round-trip delay time from the sound source to the target and the hydrophone.It can be calculated from equation ( 3 Where c is the speed of sound in the water, TS R is the distance from the target to the sound source, and TA R is the distance from the target to a hydrophone primitive.In order to obtain the high resolution of the 3D acoustic image in the cross-navigation direction, it is necessary to pulse the echo data of each channel before 3D imaging.After pulse compression, the two-dimensional sonar echo signal received by the system can be recorded as , () NM st .The Back Projection (BP) algorithm is an accurate time-domain point-by-point search imaging method.For the target point ( , , )  Gx Gy Gz , the imaging result of this point is the accumulation of the delay of the echo signal amplitude received by each hydrophone primitive in each frame.The imaging results for this point can be expressed as follows: The latter three motion attitude error components will mainly affect the directivity of the sound source and hydrophone primitives, and only affect the detection performance of the sonar system.The first three motion position error components will mainly affect the calculation of the distance from the sound source and hydrophone primitives to the target, resulting in inaccurate delay and phase estimation of the echo signal received by the hydrophone, which will have a significant impact on the imaging results.The motion error compensation method studied in this paper focuses on the first three motion position error components by precise positioning.
This paper proposes a real-time acoustic calibration method: the hydrophone primitive of the downward view 3D imaging line array sonar not only receives the target scattered echo signal, but also receives the calibration signal from the underwater preset calibration sound source.This signal is strictly synchronized with the imaging sound source and the receiving hydrophone through the cable mode.The use of calibration signal for echo ranging can accurately measure the position of each hydrophone primitive and carrier sound source and compensate for the motion of the echo signal.The specific process is as follows: Step 1: Select the hydrophone primitive for positioning In order to achieve good results in acoustic positioning through geometric relationships, when selecting the primitives of hydrophones, it is necessary to ensure that the selected primitive configuration has better spatial characteristics as much as possible.
Step 2: Calculates the distance from the selected hydrophone primitive to the calibration sound source For the calibration signal after pulse compression, the sampling point corresponding to the maximum amplitude of the calibration signal can be taken.Then calculate the distance from the hydrophone primitive that receives the calibration signal to the calibration sound source: x y z .Obtaining the distance from the three selected hydrophone primitives to the calibrated sound source allows the relative position coordinates of the calibrated sound source to be solved using the following system of equations: Step 4: Calculate the absolute coordinates of the hydrophone primitives and sound sources Coordinates in relative coordinate systems can be converted to coordinates in absolute coordinate systems by linear transformation.After the system is deployed, the absolute position coordinates of the calibration sound source are determined.
Step 5: Calculate the motion error compensation value The ideal distance from the hydrophone primitive to the calibration sound source can be calculated by the following equation: After that, the compensation value for the sonar motion error can be obtained by the following equation:

EXPERIMENTS
In this paper, the data collected by the 64-element line-of-sight array imaging sonar system in the lake test are used to verify the motion compensation method.In the process of lake test, in addition to the use of acoustic calibration method proposed in this paper for motion compensation, GPS and inertial navigation system are also equipped on the downward imaging sonar carrier in combination with the calibration sound source system.In the data processing, a combination of different auxiliary measurement methods is selected to verify the effectiveness of the sonar motion compensation method based on high-precision real-time acoustic calibration proposed in this paper.
In the experiment, the center frequency of the sound source emission signal is 85kHz, the bandwidth is 30kHz, the sound pulse width is 1ms, and the emission sound period is 1s.The relevant parameters of the target at the bottom of the lake are as follows: the target depth is 17m, the diameter of the disc point target on the target is 3cm, and the interval between the point targets is 5cm.The target shape is shown in Figure 2:  In this frame of pulse echo data, there is a strong echo signal between 15,000 and 17,000 sampling points.This signal is a calibration signal and can be extracted from the echo signal.It is possible to choose whether to use acoustic calibration for imaging to compare the imaging effect before and after motion compensation.Figure 4 shows a comparison of imaging results using different auxiliary measurement methods.In Figure 4, comparing figures (a) and (d), it can be seen that after using the motion error compensation algorithm based on high-precision real-time acoustic calibration proposed in this paper, the focused imaging effect of the acoustic image has been significantly improved.Comparing figures (a) and (c), it can be seen that when only GPS positioning and inertial navigation systems are used, effective sound maps cannot be obtained; After using a high-precision real-time acoustic calibration system alone for sonar pose measurement and motion error compensation, clear imaging results can already be obtained.It can be seen that between the GPS combined inertial guidance measurement method and the motion error compensation algorithm based on high-precision real-time calibration sound source, it is the latter that plays a decisive role in the imaging results.
Comparing figures (b) and (c), it can be seen that if only acoustic calibration is used to measure sonar pose without motion error compensation, even if recognizable imaging results can be obtained, the sound map quality is not good.This shows the importance of motion error compensation after sonar pose measurement.

Conclusion
Motion error compensation is a problem that must be solved for downward looking 3D imaging sonar towards engineering applications.In this paper, the high-precision real-time acoustic calibration system is used to not only accurately measure the position coordinates of the sonar system, but also compensate for the motion of sub-wavelength echo signals received by each hydrophone primitive.The experimental results show that compared with the combined inertial navigation measurement method, the quality of the focused sonogram obtained by downward view 3D imaging sonar is significantly improved after using the motion error compensation method based on high-precision real-time acoustic calibration proposed in this paper.

3 :
is the sampling point corresponding to the maximum amplitude of the calibration signal, start N is the number of delay points of channel transmission, and delay N is the number of delay points of the calibration sound source.Step Calculates the relative position coordinates of the calibration sound source In a frame, the relative coordinate of the calibration sound source is recorded as ( , , ) bj bj bj

Figure 2 .
Figure 2. Optical photograph of the underwater target.In the experiment, the time-domain echo signal of a frame after pulse compression is shown in the figure 3 below:

Figure 3 .
Figure 3. Optical photograph of the underwater target.In this frame of pulse echo data, there is a strong echo signal between 15,000 and 17,000 sampling points.This signal is a calibration signal and can be extracted from the echo signal.It is possible to choose whether to use acoustic calibration for imaging to compare the imaging effect before and after motion compensation.Figure4shows a comparison of imaging results using different auxiliary measurement methods.

Figure 4 .
Figure 4. Comparison of imaging results.(a) GPS combined inertial guidance.(b) Acoustic position without motion compensation.(c) Acoustic position with motion compensation.(d)GPS combined inertial guidance and using acoustic position with motion compensation.In Figure4, comparing figures (a) and (d), it can be seen that after using the motion error compensation algorithm based on high-precision real-time acoustic calibration proposed in this paper, the focused imaging effect of the acoustic image has been significantly improved.Comparing figures (a) and (c), it can be seen that when only GPS positioning and inertial navigation systems are used, effective sound maps cannot be obtained; After using a high-precision real-time acoustic calibration system alone for sonar pose measurement and motion error compensation, clear imaging results can already be obtained.It can be seen that between the GPS combined inertial guidance measurement method and the motion error compensation algorithm based on high-precision real-time calibration sound source, it is the latter that plays a decisive role in the imaging results.Comparing figures (b) and (c), it can be seen that if only acoustic calibration is used to measure sonar pose without motion error compensation, even if recognizable imaging results can be obtained, the sound map quality is not good.This shows the importance of motion error compensation after sonar pose measurement. )