Acoustic ambiguity reduction (AAR) method: an acoustic signal identification method for GNSS-A observation considering instrumental signal distortion

Abstract

Seafloor geodetic observation technology is a pivotal method for capturing plate boundary earthquakes and related phenomena. Currently, this task is performed by Global Navigation Satellite System-Acoustic ranging (GNSS-A), a technique that integrates GNSS observations with acoustic ranging. This method involves measuring the round-trip travel time of an acoustic signal between a surface platform and a preinstalled seafloor station, which is then converted into a distance for positioning. While the horizontal positioning accuracy can reach the centimeter level, the vertical accuracy tends to be loser. Recent research has revealed that equipment-dependent distortion of sound waves causes problems for accurate travel time identification, leading to a decrease in vertical component accuracy. In this paper, we conducted an analysis of distortion tendencies using water tank test data and quantitatively identified differences in distortion magnitude related to instruments, angle dependence, and directional dependence attributed to the sea surface platform. We proposed a new identification algorithm, Acoustic Ambiguity Reduction (AAR) method, using a catalog of distortions for each device, and improved the observational capabilities of the vertical component.

Graphical Abstract

1 Introduction

The Global Navigation Satellite System (GNSS)-Acoustic ranging combination technique (GNSS-A) is the most precise method for determining positions on the deep seafloor. This technique utilizes an acoustic signal that travels between a sea surface platform, whose position is determined using GNSS, and a preinstalled seafloor station (Fig. 1). The seafloor station is a device called a mirror transponder, which receives a ranging signal from a transducer on the sea surface platform and sends it back approximately 1 s later. It is placed on the seafloor with a weight attached to it, along with batteries and an electrical instrument with a glass bulb container in a protective container. Through surveys utilizing numerous round-trip travel time data values at various takeoff angles and distances, we ascertain the location of the seafloor station. More than one thousand acoustic data points are collected in one campaign observation (hereafter, this single campaign observation is called one epoch) to obtain one positioning solution. The installation of multiple stations on the seafloor allows for the refinement of ocean disturbance models (Yokota et al. 2019; Watanabe et al. 2020) and the constraint conditions (e.g., the rigid array constraint in Matsumoto et al. 2008), thereby enhancing positioning accuracy.

Fig. 1

a (Upper) Schematic diagram of GNSS-A. (center) Examples of transmitted and received 10 kHz waveforms. The ideal waveform of the signal is generated from a ninth-order M sequence and consists of 511 digits. A digit is expressed as a cluster of four waves. (bottom) When taking the normal autocorrelation of the ideal waveform, the tip of the signal becomes the top of the fourth wave. b SGO-A observation network (black circles). These figures were modified after Ishikawa et al. (2020) and Toyama (2003)

This technique was proposed in the 1980s (Spiess 1985) and put into practical use in the 2000s (Asada and Yabuki 2001; Fujita et al. 2006). Since 2015, significant progress has been made by the Seafloor Geodetic Observation-Array (SGO-A) operated by the Japan Coast Guard (JCG), which has attained a maximum observation frequency of more than four times a year (Japan Coast Guard 2024a); the root-mean-square (RMS) deviation obtained from a regression curve even using a long-term (e.g. several years) campaign data set was 1–2 cm (Japan Coast Guard 2024b). However, the vertical position time series exhibit lower accuracy (Yokota et al. 2018). Recent investigations have revealed that the vertical components are biased for each observation period and vessel. Such bias errors are contingent on artifact effects related to the sonar type and acoustic signal identification. In this study, we consider improving the performance of acoustic signal identification in GNSS-A by utilizing this kind of artifact in an inverse way.

2 Acoustic signals used in GNSS-A

First, we explain the acoustic signals used in GNSS-A. Considering that underwater acoustic signals travel several kilometers, the observation utilizes phase-shift keying (PSK) signals at approximately 10 kHz. The reception timing of the reply waveform from the seafloor station is identified through a correlation process. A higher-order M-sequence signal facilitates easier identification, but it also entails higher energy costs for transmission. The signal employed in SGO-A is modulated every four waves, following the ninth-order M-sequence at 10 kHz, with a duration of approximately 204 ms (msec) (Fig. 1) (Ishikawa et al. 2020).

The observation procedure begins with the transmission of an acoustic signal from a sea surface device to each seafloor station. To ensure accurate signal recognition and prevent the reception of erroneous replies from different seafloor stations, each seafloor station utilizes an identification header preceding the ranging signal. Following the transmission, the seafloor station returns the acoustic signal at a specific time interval after receiving it. Subsequently, the round-trip travel time is measured by identifying the signals received at the surface station. The Doppler shift of each round-trip signal is estimated and corrected during the analysis.

The selection of sonars employed for this observation method is depicted in Fig. 2. At each site, multiple seafloor stations are positioned on the seafloor. The observation employs large sonar devices capable of generating sufficient sound gain to facilitate communication over several kilometers. SGO-A has been in operation for more than 20 years, during which a diverse array of sonar types have been employed. These are depicted in Fig. 2, including the Tonpilz type and cylindrical 31-mode type. The catalog specification sheets for these devices indicate that the intensity distribution of the acoustic signal is isotropic. Additionally, a hemispherical shell type with angular dependence in the intensity distribution, as shown in Honsho et al. (2021), has also been utilized.

Fig. 2

Examples of sonar used in GNSS-A. SN: 15109 (SATR-2) manufactured by LinkQuest, Co. Ltd. (L), SN: 3482-002 (SR-2) manufactured by ITC, Co. Ltd. (I) as surface station’s sonars, a hemispherical transducer KTR-6H02 manufactured by Kaiyo Denshi, Co. Ltd. (H), a cylindrical transducer ITC-3013 manufactured by Gavial-ITC, Co. Ltd. (C), and an actual station using a hemispherical transducer JCG-401 manufactured by Kaiyo Denshi (A) as seafloor station’s sonars

To accurately capture centimeter-level deformations and centimeter-per-year plate motions, the precision of seafloor geodetic observations significantly exceeds that of other underwater acoustic surveys and aims to achieve an accuracy of millimeters. For example, at a sound speed of 1500 m/s, a misreading of just one wavelength in the 10 kHz signal introduces an error of 15 cm in distance (7.5 cm in the case of a round trip). Similar to the concept of “integer ambiguity” in GNSS, such errors have a detrimental impact on the positioning results.

The error sources in GNSS-A can be considered as analogous to those in GNSS. Similar to disturbances in the ionosphere and troposphere that negatively affect GNSS estimation, disturbances in the oceanic field constitute a source of error. Similar to the GNSS, reflected waves overlap with direct waves, creating multipath errors that cause waveform collapse and identification problems. Similar effects can be observed in the acoustic sonar of GNSS-A (Honsho et al. 2021). Furthermore, the angle dependence resulting from the instrumental features of the antenna is investigated in advance in GNSS, and analogous effects have been observed in some cases in the acoustic sonar of GNSS-A (Honsho et al. 2021; Mochizuki et al. 2006). We previously determined that the waveform was subject to distortion attributed to an electric circuit and inherent physical characteristics of the sonar (Yoshizumi et al. 2024). Although there is potential to mitigate this effect by deploying more expensive and sophisticated electric circuits and sonars in the future, the current practical need is to continue observations at a reasonable cost. Therefore, technology is required for the accurate identification of both previously obtained data and data that will be acquired from installed systems in the future. Consequently, in this study, we propose a new acoustic signal identification method using a catalog of received waveforms based on the outcomes of water tank experiments and actual data.

3 Tank experiment

We investigated water tank experimental data to quantitatively determine how waveforms are distorted by bias depending on the equipment and angle between the surface and seafloor stations.

The experimental data were acquired at the IIS Ocean Engineering Basin on the Kashiwa Campus at the Institute of Industrial Science at the University of Tokyo. The experimental setup is illustrated in Fig. 3; the data were gathered from various directions, ranging from directly above to a takeoff angle of 30°. Several shots were taken in each direction. Beyond this range, the influence of waves reflected from walls was substantial. The experiments were conducted with different combinations of devices, as depicted in Fig. 4a. The transmission and reception procedures were iterated at each position. The signal waveforms at identical points with identical combinations showed no variation. Subsequently, the combinations are denoted using abbreviations written in Fig. 4a.

Fig. 3

a IIS Ocean Engineering Basin, the University of Tokyo, where the test was conducted. b Top view of the tank. The seafloor station is fixed at a certain point, and the surface station moves. Circles indicate the points where the dolly was moved, and the transmission was performed. c Side view. The photo for the surface station is shown below

Fig. 4

a Combinations of equipment in this experiment. b POCs for received signals for L and I when the takeoff angle was 0° in the tank test. The meaning of the notation is described in a. c POCs for received signals with each takeoff angle 0°, 15°, and 30°. Each vertical line represents the expected round-trip timing of a sound wave as it propagates an underwater distance between the center surfaces of the sonars at a constant sound speed. The direction of the observation point is written at the end of the notation

In the following, we discuss the use of phase-only correlation (POC) (Kuglin and Hines 1975; Takita et al. 2003). The calculation of POC is shown in Appendix C. Figure 4b illustrates the POC waveform for a received signal for each combination of sea surface and seafloor devices under the condition that the surface station is directly positioned above the pseudo seafloor station. The device distance within the tank was accurately measured beforehand. Each vertical line represents the expected round-trip timing of a sound wave as it propagates over an underwater distance between the center surfaces of the sonars at a constant speed.

All signals shown in Fig. 4b experience a delay compared to the reception timing predicted from the actual distance. This delay arises because internal delays are introduced by circuits and sonars in the transmission and reception processes (Yoshizumi et al. 2024). In the case of L–A_0°, the timing of the large amplitude wave is delayed by one wave (0.1 ms) compared to that of I–A_0°. Since subsequent waves, influenced by electrical and mechanical factors, are simply overlaid on the preceding wave, the arrival timing of the leading wave, which is difficult to identify visually, represents the round-trip timing. When cylinder sonar was employed at the seafloor station (I–C_0°), the POC length became shorter, and the apparent timing changed, indicating differences in influence attributable to the finite size and shape of the sonar.

Figure 4c displays the POCs for the received signals for each angle (0°, 15°, and 30°). In both instances of I–H and L–H, different POC waveforms were observed for takeoff directly overhead and at 30°. However, the extent of deviation varies based on the manufacturing model of the surface station. For instance, in the case of I, the large amplitude wave at 30° was temporally advanced compared to that in the case of L. The POCs at takeoff angles of 15° and 30° in opposite positions (I–H_15°_N and I–H_30°_NE) were nearly identical. These findings suggest that sonar alone exhibits no directional dependence.

The lower section of Fig. 4c depicts the disparity between the sonar only case (L–H) and the seafloor station case (L–A). This difference highlights the body-dependent multipath effects originating from the seafloor station. Notably, a dissimilarity in waveform shape is evident at a takeoff angle of 30°, providing a quantitative assessment of the impact of multipath on the seafloor station’s surface. Honsho et al. (2021) previously suggested the potential influence of multipath from the seafloor station’s surface. However, the results of this tank experiment demonstrate that its effect is smaller than that of the angular dependence inherent in the sonar itself.

In Fig. 4b, c, the phases in the main wave segments coincide. This phenomenon arises from a trailing signal superimposed on the leading wave, predominantly at intervals corresponding to integer multiples of wavelengths (Yoshizumi et al. 2024). This results in a trailing wave that is in phase but not entirely synchronized. Consequently, consistently selecting the peak of the POC allows for the suppression of errors in the identification results to only an integer phase shift.

4 Existing signal identification methods

Before proposing a new method, we explain the existing identification method used in SGO-A observations as follows.

First, the moving cross-correlation coefficients are calculated. This method is detailed in Appendix A. In an ideal signal, the maximum peak corresponds to the fourth wave from the rising edge (Fig. 1a), but the actual waveform is distorted. The initiation of an acoustic waveform cannot be reliably identified through a straightforward correlation process. SGO-A implements an identification approach employing a modified correlation signal, as elucidated in Toyama (2003). This method is detailed in Appendix B. The rising edge of the obtained “Toyama signal” has been employed as the picking position to that is to be defined as the reception time. Considering that the true signal arrives before the maximum correlation peak owing to acoustic waveform distortion, we select the first peak exceeding a certain percentage of the maximum correlation value as the rising edge. We call this search style the “Ishikawa style.” If the waveform distortion pattern is constant during an epoch, this method can always identify the same reception timing. In SGO-A, the differences between the identified timings of transmitted and received waveforms are utilized as round-trip travel time data for an acoustic signal.

Although Toyama processing makes identification easier, misidentification cannot be avoided. As an illustration, Figure A1e displays the Toyama signal for the raw received signal shown in Figure A1c. Although the rise of the wave in Figure A1e is steeper than that in Figure A1d, which illustrates the standard cross-correlation waveform, the rise is still gradual and difficult to identify. This kind of misidentification can be determined according to the residuals between the round-trip travel times of the actual observed acoustic signal (O) and those computed in the analysis model (C). Figure 5 shows the residuals between the O–C values for all the seafloor stations. The observation data set was collected in February 2012 at the TOS1 site, and round-trip travel times were obtained using the Toyama processing. The computed travel times were calculated after optimizing the seafloor station positions using GARPOS (Watanabe et al. 2020). Here, we used the same unknown parameters as those used by Watanabe et al. (2020) with a rigid seafloor station array assumption. They are organized by the takeoff angle θ from the sea surface device. The takeoff angle θ in this paper is defined in Fig. 5. Notably, there is a bias of + 0.1 ms in the range of 0–15°. If one wavelength of 10 kHz is misread, a bias of 0.1 ms occurs. Therefore, this 0–15° bias represents a typical error associated with a one-wavelength misidentification error.

Fig. 5

Example of a takeoff–residual graph of an acoustic signal analyzed using GARPOS (February 2012 at site TOS1). The horizontal axis is the takeoff angle θ with respect to the seafloor station, and the vertical axis is a residual of travel time. Bottom figures show the definition of takeoff angle θ

5 New signal identification method

5.1 Problems with the existing method

The results of the water tank test in Sect. 3 and the actual data in Sect. 4 show that the existing method has the following problems.

The rise of the waveform is gradual, making it more difficult to distinguish the characteristics of each waveform.

Since the influence of equipment and angle dependence is not considered, integer wave biases occurred.

To solve these problems, we propose the Acoustic Ambiguity Reduction (AAR) method; it uses POC waveforms, which are sharp signals, and uses the residuals of the solution from GARPOS to correct the bias error.

5.2 Algorithm flow

The flow of the new algorithm consists of three main steps (Fig. 6). To illustrate the application of this methodology, as an example, we consider the process of correcting instrumental biases for the TOS1 site in SGO-A (as depicted in Fig. 1). Figure 7 presents the results for February 2012 (surface station: S/V Meiyo, Tonpilz type SN: 3482-001(SR-2) manufactured by ITC; seafloor station: old cylinder type M-4100A manufactured by SEA, Co. Ltd.) and June 2012 (surface station: S/V Takuyo, Tonpilz type SN: 3482A-001(IT-STR-10-1) manufactured by ITC; seafloor station: M-4100A) at site TOS1.

Fig. 6

Proposed waveform identification algorithm flow

Fig. 7

a Results of sorting in each 5° for POC waveforms for all the seafloor stations in the case of February 2012 at TOS1. Each waveform was sorted based on the existing method. The graph above is a takeoff angle–residual graph after an analysis using GARPOS. b Results when each waveform was sorted based on the proposed method. c Results in the case of June 2012 using a catalog obtained based on the proposed method. The thin and thick vertical lines indicate the timing read using the existing and proposed methods, respectively

The first step is the calculation of the POC waveforms (Fig. 6A). The raw signal data have a size of several megabytes (MBs) per shot for 200 kHz sampling and approximately 10 GB per observation epoch. However, to perform this processing, it is sufficient to extract only the main POC waveform, which has 10–100 KB of data per shot. The second step is the generation of template catalog waveforms for each pair of sea surface and seafloor devices and each takeoff angle range (Fig. 6B) and the application of a template matching method to these catalog waveforms (Fig. 6C). Given that the computer and other on-board systems might change among different observation opportunities, even if the sonar equipment remains constant, we generated a template waveform for each takeoff angle range for each observation opportunity. Owing to the similarity of waveforms in identical situations and equipment, we can apply a template matching method by minimizing residuals. In the example of Fig. 7, we stack POC waveforms from 0° to 60° in 5° increments. The selection of the angle range for stacking warrants consideration. A result for February 2012 at a seafloor station at the TOS1 site is presented in Fig. 7a. The timing, denoted by a thin line, was identified using the existing method employing the Toyama signal.

The next step is to find and correct the integer wave bias from the residuals of the GARPOS analysis results (Fig. 6D, E). Here, we use the same unknown parameters as Watanabe et al. (2020) with a rigid seafloor station array assumption, as in the final positioning process. Considering the experimental results and the takeoff–residual relationship graph, we search for the reading position with the minimum residual error by a grid search that modifies the template and repeats steps B to E. Biases can be reduced by finding the suitable timing for each pair of sea surface and seafloor devices. Figure 7b presents a result for February 2012 modified based on the catalog created through this consideration. The variations in the takeoff angle–residual relationship graph in Fig. 7b decreased, falling within the range of approximately ± 0.1 ms. In grid search, a bias is not searched for all takeoff angle range patterns, and the angle range in which the residual average exceeds the threshold is searched with greater priority. It is finally checked by the human eye. The experimental data are used as a reference in visually checking whether the template is appropriate. The threshold value varies depending on the observation site and observation epoch.

The resultant template catalogs are different among the pairs of sea surface and seafloor devices. For instance, in the case of June 2012 (Fig. 7c), contrary to the case of February 2012, in the 0°–30° range, the regions with a significant amplitude were positioned on the back side in the time direction.

Honsho et al. (2021) developed a method for creating templates like B and matching them like C. In the template creation process in Honsho et al. (2021), the correlation among POC waveform groups for each angle was calculated, and the reading position was determined so that the same part could be read continuously. In SGO-A, their method can also be applied, but occasionally the template cannot be generated correctly for long waveforms such as the angle range 45°–60° in Fig. 7b. This is thought to be the effect of the sonar dome on SGO-A observations, which will be discussed in the next section. The proposed method was designed expansively to perform proper identification for a variety of device pairs.

5.3 Direction dependency

When we investigated the takeoff angle dependence in detail, we observed that variations in the residuals were occasionally prominent only at a specific takeoff angle. In the case of June 2012, the variation is notably large only in the range of 45°–50° (as depicted in Fig. 8a). In this graph, the colors indicate the orientation of the surface station relative to the seafloor station. Specifically, when the seafloor station is positioned on the right side of the surface station (Fig. 8b), the results at 45°–50° exhibit a bias of − 0.1 ms. This bias is attributed to differences in waveforms due to direction (Fig. 8c). This dependency was not replicable in a tank experiment. There is a substantial likelihood that scattering and reflection from the sonar box itself on the bottom of the ship or a difference in scattering and reflection depending on the box position relative to the bottom shape is the cause (Fig. 8d). This effect can be rectified by establishing a catalog for direction dependency (Fig. 6F). This correction affects not only the vertical component but also the horizontal component and the estimation of the underwater sound speed field model due to its characteristics.

Fig. 8

a Takeoff–residual graph in the case of June 2012 using a catalog obtained based on the proposed method, changing the color for each direction (φ) of the seafloor station as seen from the vessel. The red and gray circles indicate the directional angle ranges of φ = 150°–210° and φ ≠ 150°–210°, respectively. b Explanation of color coding in a. c Examples of POCs when θ = 45°–50° and φ = 45° and when θ = 45°–50° and φ = 165°. The thin and thick vertical lines indicate the timing read using the existing and proposed methods, respectively. d Photo of the bottom sonar box of the surface station

5.4 Device check

When processing from A to F is completed in one epoch, a uniform bias might remain among all the travel times chosen from the POC waveforms even after the correction of A–F. There is no anomaly in the residuals, and we will not notice this by only looking at the results for a single epoch. We then compare the results with those of other sites and other epochs using the same equipment combination to confirm with the human eye that there is no bias shift (Fig. 6G, Appendix D). The waveform distortion also depends on depth as shown in Appendix D. We cannot exclude the possibility that all epoch results at each site have the same integer error, but this does not affect the determination of the relative vertical motion. Through this processing, the same position of the waveform can be recognized at any site and epoch.

5.5 Obtained position time series

Figure 9 illustrates the position time series of TOS1 from 2012 to 2018. We compared the time series obtained using the travel time data set determined by the traditional method with that derived from the data set determined by the proposed procedures. As shown in Fig. 9c, each vessel bottom sonar and transmission system is different, so the waveform distortion is different. Previous methods were unable to identify these differences, but the proposed method identifies the optimal timing for each epoch. The two horizontal components exhibit minimal modification, while the vertical component is smoother and has a smaller standard deviation.

Fig. 9

Eastward, northward, and upward time series comparison of TOS1 when read by a existing method and b proposed method. Each standard deviation around the regression line is described at the bottom right of each time series. The notation in the upward components indicates the combination of sonars and vessels in c. c Table for combination of sonars and vessels. Even with the same sonar, the whole system is calibrated/replaced at each time, so it is shown with a different number

We can improve the results at other stations as well (Appendix E). For example, with the existing method, the same vertical movements are shown in the 2016 data. It is unnatural for step-like vertical movements at completely different points to occur at the same time, and it can be determined that the vertical components obtained with the existing method are inaccurate. Considering that the standard deviation around the regression line decreases, it can be determined that the vertical movements obtained with the new method are more accurate.

6 Conclusion and future work

By incorporating the instrument characteristics derived from experiments and actual data into the process of identifying acoustic signal data in GNSS-A, it becomes feasible to improve the observation results, particularly for the vertical component. This correction method is universally applicable to equipment used not only for GNSS-A but also for similar acoustic ranging method (e.g., seafloor distance measurement) (e.g., Yamamoto et al. 2019). To implement this correction effectively, it is imperative to maintain a record of both transmitted and received signals, continuously scrutinizing instrument characteristics.

If the system can obtain waveform data, the same correction can be applied, and the scope of application of this method is not limited to SGO-A data. In addition, for systems where waveform data cannot be obtained (e.g., Sonardyne’s product), this method can be applied by using a catalog of the reading shift value instead of the waveform catalog for flow B. However, the correctness of the obtained template cannot be confirmed except by using the residuals, so it must be checked carefully.

In this study, all waveforms were used to generate the catalog. Since the actual data set contains waveforms with inappropriate errors, automatic waveform selection will be necessary to generate more accurate templates.