Dual band CSAS system and processing adaptation

 

Malte Sommer, Holger Schmaljohann, Blair Bonnett, et al.

 

Citation: Proc. Mtgs. Acoust. 47, 070014 (2022); doi: 10.1121/2.0001614

 

View online: https://doi.org/10.1121/2.0001614

 

View Table of Contents: https://asa.scitation.org/toc/pma/47/1

 

Published by the Acoustical Society of America

 

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Dual band CSAS system and processing adaptation

 

Malte Sommer

 

Hochfrequenztechnik, Fakultät für Elektrotechnik, Helmut-Schmidt-Universitat Universitat der Bundeswehr Hamburg, Hamburg, 22043, GERMANY; sommerma@hsu-hh.de

 

Holger Schmaljohann

 

Bundeswehr Wehrtechnische Dienststelle für Schiffe und Marinewaffen Maritime Technologie und Forschung, Kiel, Schleswig-Holstein, 24148, GERMANY; HolgerSchmaljohann@bundeswehr.org

 

Blair Bonnett and Thomas Fickenscher

 

Hochfrequenztechnik, Fakult¨at f¨ur Elektrotechnik, Helmut-Schmidt-Universitat Universitat der Bundeswehr Hamburg, Hamburg, 22043, GERMANY; blair.bonnett@ieee.org; tfi@hsu-hh.de

 

The resolution potential of circular synthetic aperture sonar (CSAS) requires a navigation accuracy not provided by the motion compensation techniques used for linear SAS. Thus, a class of post-image formation data-driven autofocus (AF) algorithms have been previously developed using phase information of the backscattered hydroacoustic data to reduce phase errors due to errors in the platform trajectory. These algorithms work within the full-view area (FVA) of the image, i.e., the area where the scene has been viewed from all aspects. This area is smaller at higher frequencies due to the narrower opening angle of the transducers. In this work, we detail the optimisation of the tilt angles of the MF and HF bands of our SAS system (Atlas Elektronik SeaOtter AUV with Vision1200 SAS sensors) to ensure the maximum overlap between the FVAs of the bands. The impact of crabbing is shown. We then show that AF corrections determined with one band can be applied to the other band. Of particular interest is the application of corrections determined from the larger MF FVA to an HF image.

 

1. INTRODUCTION

 

The resolution potential of synthetic aperture sonar (SAS) can vastly be improved by circular SAS (CSAS), where the vehicle encircles the target region and, thus, gathers backscattered data from all aspects.¹ Navigation accuracy of high end inertial navigation systems (INS) is not sufficient for linear SAS. To determine well focused linear SAS images the DPCA algorithm has to be applied, but even then blurring in CSAS imagery is usually present. To further improve the navigation accuracy, backscattered acoustic data of the image can be used, leading to a class of autofocus (AF) algorithms.^2,3 These algorithms work only for data backscattered within the full view area (FVA), the region covered by the beam from all aspects along the circular trajectory.

 

 

Figure 1: The ideal trajectory (black) differs from the true one (red). The common full view area (FVA) of HF and MF bands (FVA_HF/MF ) follows from the overlap of both beams and the true, full trajectory (whole circle including errors like crabbing and roll).

 

In Fig. 1, a typical CSAS scenario is shown. We use an AUV SeaOtter from A tlas Electronic equipped with a Vision 1200 sonar using two bands, high frequency (HF) and medium frequency (MF). The vehicle moves along a circle, but due to navigation errors, the true trajectory (red) differs from the assumed trajectory (black) due to drift and limitations in the INS as well as in the DPCA processing. Furthermore, in practice the heading of the vehicle differs from the tangential direction of the trajectory, known as crabbing. This leads to a translation and shrinking of the FVA. The width of the HF beam is much smaller than the one of MF beam, thus, FVA of the HF beam (FVA_HF ) is smaller than the one of the MF beam, FVA_MF.

 

The aim of this publication is to shown ways how to deal with those challenges. Since the system was originally designed for linear SAS, we first show its optimization for the dual band application of CSAS. The impact of crabbing on CSAS missions is described and shown, how to deal with it. Adaptation of the system to increase the FVA for CSAS in dual band operation is presented. We briefly summarize the AF algorithm implemented for navigation correction and validate the performance of the algorithm for different levels of navigation errors. Finally, we show that the AF corrected CSAS images of both frequency bands lead to comparable improvements in sharpness. This holds even when we apply the correction obtained with the MF band to the HF CSAS image or vice versa.

 

2. MODIFICATIONS FOR DUAL BAND CSAS APPLICATION

 

Since the vertical beam elevation has originally been optimized for linear SAS, we modified it to be optimal for CSAS. This is achieved by maximizing the overlap of HF and MF beams within the range of the system, to maximize the common FVA.

 

The beams emitted by the vehicles transmitters are characterized by their frequency bands (HF & MF), their beamwidths ( Θ_HF/MF ) and the tilt angles of the transducers ( γ _HF/MF ). This is a superposition of:

 

 

In its original configuration, the system was designed to maximize the covered range. Thus, we have to change the transmitter in vertical direction to optimize the FVA for CSAS for both frequency bands. The washer is a wedge that can be used to modify the tilt of the transducers. The "beam offset angle" changes the beam direction by refraction and is only installed inside the MF transducer. The beam sectors are depicted in Fig. 2 for different combinations of wedges. A constant roll of the vehicle modifies the direction as well. The radial ground range (D) of the area of seafloor, covered by a single beam, is described by the tilt angle γ_over and the angular width Θ_over :

 

 

with h_hog being the height over ground, γ the tild angle of the transmitter (from the horizontal direction downwards), and beam width Θ .

 

In case of two overlapping sectors, the overlap forms itself a sector described by:

 

 

Inserting eq.(4) and eq.(3) into eq.(2) yields the radial ground range of the overlapping sector. The washer offsets can be removed or turned around in a way optimizing the overlap of the beams for CSAS as depicted in Fig. 2.

 

 

Figure 2: Beam coverage for the Vision 1200 system. The HF beam is shown in blue, the MF in red. The figure is normalized to a height over ground (hog) of one. The blue arrow indicates the range of suitable data. Top: The MF-washer is removed. The data shown in this paper, are all gather for this scenario. Bottom: The washer of the HF transmitter is turned around, thus it shows 2 ^◦ downwards.

 

In the first sketch, the MF washer was removed, causing an overlap of the beams. This is the scenarion used for the data shown in this paper. In the last sketch, the HF washer is turned around (2^◦ downwards), and the MF washer is turned upward (5^◦) causing the beams to overlap completly.

 

3. IMPACT OF CRABBING ON SIZE AND POSITION OF THE FVA

 

The performance of the autofocus approach strongly depends on the patch selected within the FVA. Its size and position is dependent on the vehicles motion behaviour. In case of a current, the vehicle has to steer into current direction to keep on track and its heading differs from its course over ground. This angular deviation is known as crabbing. As a consequence, the beam will not point towards the centre of the trajectory circle, and the radius of the full view area ( r_FVA ) will be reduced. Since the crabbing is known from the logging of heading and position data, the change in size and location of the FVA can be derived geometrically.

 

 

Figure 3: Impact of current on crabbing along circular trajectory. The black arrows drawn on the circular trajectory indicate the heading of the vehicle. The beams (blue, dashed), radiated perpendicularly to the heading, pointing towards a beam convergence centre (BCC) off centre of the trajectory centre.

 

The position of the beam convergence centre (BCC) can be described by the polar coordinates Θ_c and r_c , with the geometric center of the trajectory as origin as depicted in Fig. 3. The crabbing angle Θ_crab varies of sinusoidaly along the track of a full circle:³

 

 

with C being the maximal crabbing angle, Θ_AUV the aspect angle of the vehicles position and Θ_{of fset} can be interpreted as the constant crabbing angle, occuring even without current due to the steering behaviour of the vehicle. Thus, Θ_c can be calculated from the phase ϕ of the crabbing over a full circle and correction by the vehicles starting position Θ ^start_AUV :

 

 

The radius r_c can be found by the maximal crabbing C in radians and the radius of the trajectory r_tj :

 

 

 

Figure 4: Measured crabbing along a full circle gathered in the presence of current (blue, solid). A sinusoidial curve is fitted to the crabbing (orange, dashed), with the period fixed to one, in order to determine the position of the FVA.

 

In Fig. 4, measured crabbing data are shown. A sine is fitted to determine the BCC. The constant crabbing angle Θ_{of fset} will result in a reduction of the r_{FV A} , according to:

 

 

with Θ_beam being the beamwidth and r the distance between transmitter and scatterer, thus    with h being the height over ground of the vehicle.

 

During a measurement campaign, about 140 trajectories have been gathered inside Kiel Arsenal harbour. Since it can be assumed that there is no current, they can be used to determine the constant crabbing angle and thus, by applying eq.(8), the radius of the FVA in absence of current for different radii of the trajectory as depicted in Fig. 5 for the beamwidth of MF and HF.

 

 

Figure 5: Impact of constant crabbing (without current) on radius of full view area for MF (left) and HF (right).

 

Figure 5 reveals that the FVA almost vanishes for HF, due to crabbing. This information is of high relevance for the application of AF algorithms.

 

4. SUMMARY OF THE AUTOFOCUS ALGORITHM AFTER T. MARSTON

 

The goal of the autofocus algorithm is to locally optimize the contrast of the CSAS image.² It utilizes the circumstance that a geometric displacement ( ϵ_sway , ϵ_heave ) of the trajectory causes a phase error ϕ_e in the backscattered data:

 

 

with k being the wave-number, and g the slant range error, also refered to as the slope of a slice. It is dependent on the heave and sway by the angle Θ AUV between receiver and backscatterer. Thus, the phase information can be used to adjust the trajectory of the AUV. 2 Eq.(9) can be arranged in a way that it is dependent on the aspect angle ψ between the AUV and the scene:

 

 

g(ψ) is a range error causing the erroneous phase shift ϕ_e. It represents a slice at angle ψ through a two dimensional surface ϕ_e(k_x,k_y) in wave-number space as depicted in Fig.6.

 

 

Figure 6: Cones described by eq.(9) represented in polar ( Ψ , k ) and cartesian ( k_x , k_y ) coordinates. In this image, k is truncated at k = 1.

 

Thus, the coordinates of ϕ_e can be represented either using polar coordinates k and ψ or Cartesian coordinates k_x and k_y :

 

 

This surface, following eq.(10), is called a "generalized cone".

 

A focusing correction can be applied in the frequency domain to an image ˜u (x, y) by multiplying its spec- trum ˜U(k_x , k_y) with Φ_Zcor such that the corrected image u(x, y) is⁴

 

 

Or the other way around, the actual corrupted image can be represented by a manipulation of the spectra of the uncorrupted image

 

 

while the Φ_e is actually the phase shift in the wave-number space caused by navigation inaccuracies

 

 

The algorithm basically loops through the N aspects angles of a full circle

 

 

cuts a sector 

 

 

and finds by a line search algorithm the corre- sponding slope g (Ψ) that maximizes the contrast, defined as the standart deviation σ (...) over the mean ¯... of the image of this sector. Thus,

 

 

with

 

 

The spectral sector width is determined by:

 

 

where f_c is the carrier frequency and B is the bandwidth. But so far, the scewing component ζ_n( k, Ψ) of the cone has been ignored and instead of g (Ψ_n ) , the radial slope of the unscewed component cone D_n is computed. The scewed component cone is formed by the superposition of a circular cone ^ˇϕ_n (k) with the scewing component:

 

 

with

 

 

Thus, the radial slope of the unscewed component cone D_n can be shown to be connected with the slope of the error cone g(Ψ) by the differential equation²

 

 

which can be solved by

 

 

In practice, the first sinusodial has to be removed as well from g (Ψ) , to avoid positional shifts in the scene. Finally, the image is reconstructed according to eq.(12).

 

5. AUTO FOCUS RESULTS FOR SIMULATED DATA

 

In order to validate the performance of the AF algorithm, it has been tested on synthetic data. An ideal trajectory has been perturbated by inducing a known radial shift on its coordinates. For this perturbed trajectory a raw dataset has been simulated, while the processing was done for the ideal trajectory. This depicts the scenario of processing real data, where the error in the trajectory is not known. The shift correction computed by the AF algorithm was compared with the induced one, as shown in Fig. 7 and Fig. 8, for a perturbation function, scaled with a factor ranging from 0.0 cm to 24.0 cm.

 

 

Figure 7: Calculated radial shift correction (red, δ ) for a simulated dataset corresponding to our system configuration. The trajectory perturbation is induced with known navigation error (black,ˆδ ). From this the residual error can be found (dashed blue). Corrections are shown for several applications on the same image (iterations).

 

 

Figure 8: Mean of the absolute value of the difference between the induced error and the corrections computed by the AF algorithm.

 

The AF algorithm has been applied up to five times on the image. In Fig. 7, the induced shift (black, solid) and the estimated corrections of the AF algorithm (red, solid), as well as the residual error (blue, dashed) is shown. The lower figures show the corrections after five iterations. Obviously, the algorithm works better for small perturbations and the results will be improved for several applications of the AF algorithm on the image. In Fig. 8, the mean of the absolute value of the residual error (blue, dashed) is shown for increasing perturbation levels and multiple AF algorithm applications (AF iterations). The corresponding perturbation functions are shown by a,b,c and d. Several AF interations improve the results up to a perturbation of 13 cm. Until this level, we see a smaller residual error in the radial shift after five iterations.

 

6. RESULTS AND CONCLUSIONS

 

Here, we apply the AF algorithm to the same CSAS patch in both frequency bands and get radial shift corrections for HF and MF. These AF corrections of those frequency bands have been applied to a MF and HF snippet.

 

 

Figure 9: HF images are depicted in the left column, while the MF images are depicted in the right column. The top row shows images without AF processing, while the middle shows images after AF processing based on HF data inside FVA HF and the bottom row depicts corrections from MF data inside FVA_MF.

 

Figure 9 shows HF (left column) and MF (right column) images before application of the AF algorithm (top row), by applying HF corrections on the image (middle row) and by applying MF corrections on the images (bottom row). The diameter of the FVA of the HF beam is 2.5m while the diameter of the FVA of the MF beam is 9.5m. Theirs centers are located at 0.6m north and 2.0m east.

 

Figure 9 demonstrates that the AF corrections from the MF image can be used to corrected the HF data and vice versa, without downgrading of the image quality. To get a proper correction for the whole CSAS scene the AF algorithm has to be applied on different locations.³ For our setup this is more likely to be realized with the MF band, due to its larger FVA. The results shown give us some confidence that well focused HF CSAS images may be obtained with AF corrections based on the MF band, following the multilateran

 

REFERENCES

 

1. B. Bonnett, H. Schmaljohann, T. Fickenscher, and U. Herter, “Seafloor segmentation using multi-band SAS: initial results,” Proc. Meet. Acoust. 44 (1), 070015 (2021).
2. Timothy M. Marston, Jermaine L. Kennedy, Philip L. Marston, “Autofocusing circular synthetic aperture sonar imagery using phase corrections modeled as generalized cones,” J. Acoust. Soc. Am. 136 (2), 614– 622 (2014).
3. Timothy Marston, Jermaine Kennedy, “Spatially variant autofocus for circular synthetic aperture sonar,” J. Acoust. Soc. Am. 149 (6), 4078–4093 (2021).
4. M. Soumekh, “Reconnaissance with slant place circular SAR imaging,” IEEE Trans. Image Process. 5 (8), 1252–1265 (1996).