Proceedings of the Institute of Acoustics

 

Long-range interferometric synthetic aperture sonar

 

Torstein O. Sæbø, Norwegian Defence Research Establishment (FFI), Kjeller, Norway
Roy E. Hansen, Norwegian Defence Research Establishment (FFI), Kjeller, Norway
Ole J. Lorentzen, Norwegian Defence Research Establishment (FFI), Kjeller, Norway

 

1 INTRODUCTION

 

Synthetic aperture sonar (SAS) interferometry is a processing technique that provides very high-resolution images and bathymetric maps of the seabed over large swaths¹. Typically, the sensor platform is an autonomous underwater vehicle (AUV) moving in straight lines at an altitude of a few tens of meters above the seabed. The imaging swath is typically limited to no more than a few hundred meters to each side. For deep-water bathymetric mapping, there usually is enough signal energy to achieve sufficient signal-to-noise ratio (SNR) also out to maximum range². Due to sonar beampatterns and the geometry limited principle of interferometric processing, there is a blind zone called the nadir gap directly below the AUV and out to a maximum grazing angle, where the seabed cannot be mapped. The theoretical maximum area coverage rate of a interferometric SAS system alone is therefore two times the maximum ground range, minus the nadir gap, multiplied with the AUV speed through the water³.

 

By increasing the length of the receiver array, the imaging swath increases correspondingly. However, for a typical sonar frequency and sonar signal energy, the SNR then becomes marginal, or even too low, for accurate bathymetric mapping out to maximum range⁴. One solution is to increase the spatial averaging in the phase estimation filter⁵.

 

In this paper, we suggest an alternative solution, where we optimize the collection geometry and the signal energy, by customizing the AUV altitude. We use the sonar equation together with scattering theory to establish a set of relations that predicts the area coverage rate, given criteria for horizontal resolution and variance of the interferometric estimates. We do this for both a single pass, where we assume that a multibeam echosounder covers the blind zone below the AUV, and for a lawnmower pattern, where adjacent tracks are used to fill in the nadir gap.

 

We test and evaluate our suggested method both on simulated data and on experimental data from a Kongsberg HISAS 1032 Dual Rx system, with almost 500 meters range per side for typical AUV speed⁶. We show that there is potential for significant increase in effective area coverage rate by optimizing AUV and sonar parameters. This is especially important for long-range systems, since the optimal AUV and sonar parameters are strongly dependent on the maximum range of the sonar.

 

2 THEORETICAL MAPPING PERFORMANCE

 

The sonar / radar equation is the tool to investigate the power budget and predict the SNR^7,8. In this paper, we investigate the effect of sensing geometry on a fixed system. Our goal is to model the observed performance, using a simple model that links scattering physics through SNR calculations and thereby theoretical performance. Following^9,10, we simplify the power budget equation into writing the SNR ρ as

 

 

 

Figure 1: Geometry for interferometric SAS.

 

where C is a constant containing the non-varying terms such as center frequency, band width, element sizes, transmit power and pulse length. N₀ is the additive noise level, D_t and D_r are the transmitter and receiver element directivity in the vertical plane, φ is the direction of arrival relative to the interferometer, η is the range dependent absorption loss, R is range and φ_g is the grazing angle (see Fig. 1). σ⁰is the backscattering coefficient per unit area on the seabed. Note that the SNR is equivalent for sidescan (SSS) processing and SAS processing when using the same hardware and setup for a distributed scatterer (e.g. the seabed) and in the pulse-limited case. Synthetic aperture synthesis only changes resolution, not SNR. See¹¹ for details.

 

The seabed backscattering coefficient σ⁰is strongly dependent of acoustic frequency and the grazing angle¹². The general result is that lower grazing angles gives lower backscattering coefficient, especially when reaching grazing incidence. We use the model described in¹³. In this paper, all the results are produced using medium sand as the seabed type.

 

The seabed is rarely a perfectly flat surface. Small seabed slope variations cause variations in the grazing angle, which again lead to variations in the backscattering coefficient. A simple way of modeling this is to calculate the average backscattering coefficient from a distribution of grazing angles around the nominal grazing angle given by the flat seabed¹⁰. Fig. 2 shows the backscattering coefficient for an unperturbed flat seabed (blue) compared with the average backscattering coefficient when using a Gaussian distribution of grazing angles with 5 degrees standard deviation (yellow). In addition, we compare with a modified backscattering coefficient that uses a lower limit of five degrees grazing angle (red).

 

Interferometric SAS is the process of estimating direction of arrival from two or more vertically displaced SAS receivers arrays^2,14. Assume two receivers a distance D apart forming an interferometer, with a baseline direction φ_b relative to the vertical axis. This is illustrated in Fig. 1. From the estimated time difference of arrival t_d, the direction of arrival φ relative to the interferometer can be calculated

 

 

 

Figure 2: Average backscattering coefficient with slope perturbations for medium sand.

 

giving a relative depth of the seabed compared to the platform

 

 

where R is slant range. A more detailed geometrical description can be found in¹⁴,². It should be noted that the tilt of the baseline φ_b only affects the interferometer, and should not be confused with the mechanical and electronical tilt of the transducers, which defines the vertical beampatterns D_t and D_r to be used in the power budget.

 

The standard deviation of the depth estimate, or rather the lower bound, can be approximated using the Cramer-Rao lower bound for time delay estimation in combination with the geometry terms as²

 

 

Here BT is time-bandwidth product, equal to the number of independent samples used in the time delay estimation, and ρ is the generalized SNR (GSNR) related to the interferometric coherence γ as¹⁴

 

 

under the assumption that uncorrelated noise is the only source for decorrelation. In the following, we will assume that the actual SNR given by the power budget is the only source for decorrelation, and therefore GSNR = SNR.

 

3 THE EXPERIMENT

 

To verify the modeled SNR and variance of the estimated seabed depths, we use data from an experiment in February 2022, with a Kongsberg HISAS 1032 Dual Rx System⁶, mounted on an HUGIN AUV. Each receiver arrays of the Dual Rx is 64 elements and 2.4 meters along track, with an interferometric baseline D = 30 cm. The center frequency is 122 kHz and the bandwidth is 36 kHz.

 

In the experiment, the AUV travelled six identical 4700 meters tracks with different altitudes, at 200 meters water depth outside Horten, Norway. The altitudes varied between the tracks, from 15 meters to 90 meters in 15 meters steps, and the recorded slant range was 370 meters. All other parameters than the altitudes were fixed between the tracks.

 

Interferometric processing is performed both by SSS swath bathymetric processing, using a 1D range correlation window of a few meters and by SAS interferometric processing using an 18 × 18 cm ground range 2D correlation window. We have verified that SSS and SAS interferometric processing on average give the same coherence estimates when the spatial averaging is equal, confirming that the synthetic aperture synthesis only changes resolution, not SNR.

 

4 RESULTS

 

By studying (1) it is clear that the dominating effects of increasing the altitude over a flat seabed are: 1) an increased SNR at long range due to an increased grazing angle, 2) a decreased SNR at short range due to the steep fall in the vertical beampattern, and 3) a decreased SNR at long range due to the range dependent absorption loss and the spreading of the transmitted energy.

 

Fig. 3 shows the SAS and SSS coherences of an example 50×370 meters flat seabed with trawl marks. The two upper panels are with 15 meters altitude and the two lower panels with 90 meters altitude. Clearly, the nadir blidzone increases with altitude, but so does the maximum valid ground range. The figure also shows that SSS and SAS coherence are very similar (the difference at long range for 15 meters altitude is due to the longer range correlation window for SSS). The figure also shows the strong dependence between coherence (and thus SNR) and grazing angle. This can be most easily seen in the second panel from the top, where there is high variability in the coherence everywhere the trawl marks cause changes in the grazing angle.

 

In Fig. 4 we have studied the SNR as a function of ground range and altitude. The figure shows the SNR averaged over 1000 pings for both sonar sides. The seabed for the selected pings are mostly flat, except for small perturbations in depth caused by trawl marks. In addition to the measured SNR the figure shows the SNR modeled using (1). The additive noise term N₀ is adjusted such that the modeled SNR approximately fits the measured SNR at long range. The clear discrepancy between model and measurement at near range is due to too simplistic directivity functions D_t and D_r in the model and decorrelation due to other sources than additive noise. The discrepancy at long range for the lowest altitudes is most likely due to a too simple correction for the non-flat seabed (due to the trawl marks). However, in general the model is a good fit of the measurements and captures the most important systematic effects, which confirms that the proposed model can be successfully used to predict the SNR and thus the variance of the seabed depth estimates.

 

In Fig. 4 we have marked the 10 dB SNR crossing point at both short and long range. Typically, we use a SNR threshold of 3 dB to separate between valid and invalid estimates, but since we only have 370 meters range in these data, some of the long range effects are not captured with a 3 dB threshold. By defining R_max as the 10 dB crossing at long range and R_min as the 10 dB crossing at short range, we may study the swath width R_max − R_min as a function of altitude. Fig. 5 shows the swath width for both the measurements and the model. The figure also shows the nadir blind zone 2R_min. Clearly, the model fit the measurements very well for both the swath width and the blind zone.

 

From Fig. 5 it is clear that the swath width is largest for an altitude of around 60 meters.

 

 

Figure 3: Coherence estimates for a 50 × 360 m scene. Upper to lower: SSS coherence with h = 15 m, SAS coherence with h = 15 m, SSS coherence with h = 90 m and SAS coherence with h = 90 m. The stripe with coherence loss in the SSS coherence with h = 90 m is due to acoustic interference. The dynamic range is from 0 (blue) to 1 (red).

 

At lower altitudes, there is insufficient SNR at long range, and at higher altitudes, the blind zone increases while the attenuation lowers the long range SNR. So for this experiment, 60 meters altitude would provide the largest area coverage rate, provided that only a single track is used or that the blind zone could be covered by e.g. a multibeam echosounder.

 

The SAS sensor may be used to map the entire scene rather than merging data from a multibeam echosounder. Then the nadir blind zone is covered by running in a lawnmower pattern with overlap. Building on³ we consider the effective area coverage rate. Assume an AUV velocity v, and R_min > 0 (i. e. that there is a nadir blind-zone) and R_max > 3R_min (i. e. that the one-sided swath can cover the two-sided nadir blind-zone in a single pass). The effective area coverage rate A becomes

 

 

Intuitively, the most effective seabed mapping is achieved when the nadir blind zone is equal to the one-sided valid swath, since there is no redundancy in the data. This happens when R_max = 3R_min and (6) then collapses to

 

 

R_min and R_max are both nonlinear functions of the altitude and thus not independent, making (6) difficult to solve in the general case. From Fig. 5, it is clear that our fitted model in (1) gives us a possibility to numerically optimize the effective area coverage rate.

 

 

Figure 4: Estimated SSS GSNR (solid lines) compared with a model fit (dotted lines).

 

 

Figure 5: Modeled and measured ground range swath width.

 

To better visualize the SAS seabed mapping performance of this system as a function of altitude we have selected a 35 × 50 meters scene with flat seabed, trawl marks and a rock formation. Fig. 6 shows the estimated coherence and the estimated depth maps for the six different altitudes. The rock formation is at around 245 meters ground range and it can be easily seen that the three lowest altitudes provide inferior depth maps relative to the three highest altitudes.

 

5 SUMMARY

 

In this paper, we have studied the performance of a long-range SAS mapping system. For long range systems, traditional geometry provides very low grazing angles at maximum range, which again leads to insufficient SNR for accurate seabed mapping. On the other hand, increasing the altitude increases the nadir blind zone and also increases the range dependent attenuation and energy spreading loss.

 

 

Figure 6: Coherence (left) and estimated bathymetry (right) for a 35 × 50 meters scene with flat seabed and a rock formation. The dynamic range is from 0 (blue) to 1 (red) in the coherence plots and with one meter depth variation in the bathymetry plots. Upper left to lower right: h = 15, 30, 45, 60, 75 and 90 m.

 

We have suggested a simplified model to predict the SNR of the interferometric estimates and thus also the variance of the interferometric estimates. We have compared this model to experimental data using a HISAS 1032 Dual Rx system and found that the model relatively accurately describes the minimum and maximum valid mapping range.

 

We have also described the relationship between the minimum and maximum range and the effective area coverage rate, when the SAS sensor covers its own blind zone in a lawnmover pattern. Future work will continue the study of this relationship and establish a framework for predicting the optimum altitude for long range seabed mapping. A future study will also consider other parameters than the altitude, like the direction of the vertical beamp patterns, the vehicle speed and the seabed properties.

 

6 ACKNOWLEDGEMENTS

 

The authors thanks Darrel Jackson from Applied Physics Laboratory at University of Washington, Seattle, for providing code to produce the sediment backscatter model used in this study. The authors also thanks Anthony Lyons from Center for Coastal and Ocean Map ping / Joint Hydrographic Center at University of New Hampshire for valuable discussions on seabed backscatter. Finally, the authors thank Kongsberg Discovery for providing data for the study.

 

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