An Embedded Tactical Decision Aid Framework for Environmentally Adaptive Autonomous Underwater Vehicle Communication and Navigation

Motivated by a changing acoustic environment in the Arctic Beaufort Sea, in this article, we present a tactical decision aid framework for a human decision-maker collaborating with an autonomous underwater vehicle (AUV) to integrate the vertical sound-speed profile for underwater navigation and communication. In a predeployment phase, using modeled and real oceanographic data, we load basis function representations of the sound-speed perturbations onto one or more AUVs on deck, where a handful of weights can estimate a sound-speed profile. During deployment, these weights are updated on an AUV through a digital acoustic message to improve navigation and reciprocal communication throughout the duration of an under-ice mission. Field work applying this framework in the Beaufort Sea is presented, highlighting key decisions regarding predeployment oceanographic data assimilation, CTD cast collection, and in situ weight choice. Selected examples evaluate the framework’s ability to adapt to a depth-limited CTD cast and the appearance of an anomalous microlens feature in the profile. We show that the framework effectively balances the need to adapt in a changing acoustic environment in real time while maintaining operator trust in an AUV’s embedded intelligence.


I. INTRODUCTION
A UTONOMOUS underwater vehicles (AUVs) are an increasingly popular platform to explore and sample the ocean, particularly for remote or dangerous environments. Lightweight, mobile, and inexpensive compared to mannedand ship-based systems, these vehicles are becoming more capable with smaller payload sensors, faster computing power, and smarter embedded intelligence [1], [2]. But a major hurdle in considering AUVs as reliable and standard tools for oceanographic research is navigation uncertainty. While land and air-based robots utilize satellite-based global positioning system (GPS) to achieve stunning location accuracy and precision throughout the duration of their missions, AUVs cannot access GPS while underwater due to the rapid attenuation of electromagnetic waves [3]. A vehicle can stall on the surface to receive a GPS fix, but this foolproof method of repositioning is inaccessible in an ice-covered environment or other GPS-denied situations.
Much work has been done in underwater vehicle navigation, which relies on any combination of dead reckoning, hydrodynamic models, inertial navigation systems (INS), doppler velocity logs (DVL), GPS fixes, and/or acoustic baseline navigation systems [4]. In particular, the long baseline (LBL) navigation system is the most similar in scale and style to GPS, and most appropriate for mitigating drift in underwater vehicle localization without overburdening computation on the vehicle [5]. Multiple distributed transponders, in fixed positions on the order of hundreds of meters to several kilometers, listen for vehicle range requests. They can send a message back such that the AUV can self-localize via two-way travel time ranging and trilateration. The advent of the WHOI micromodem [6] and synchronized chip scale atomic clocks [7] enabled ranging via one-way travel time (OWTT) [8]- [11].
For both one-way and two-way travel time configurations, however, accuracy in the range estimate in an LBL paradigm is limited by the environmentally sensitive relationship between range, travel time, and the sound-speed profile. For mesoscale (tens to hundreds of kilometers) navigation or localization efforts, a deterministic [12] or through-the-sensor [13] value for sound speed is used. Some postprocessing methods account for the depth dependence [14], spatio-temporal variability in the sound-speed profile to minimize error [12], [15], or specific ray paths [15]. Short range (less than ten kilometer) navigation efforts, on the other hand, can accurately rely on a nominal sound speed value and achieve minimal navigation error [9], [10], [16]. But this assumption breaks down in complex propagation environments such as the multipath incurred by the Beaufort Lens [17].
The Beaufort Lens is as a warm water intrusion in an intensely stratified water mass, creating a local temperature (and sound speed) maximum around 50-60 m. From the surface down, there is less saline surface water via ice melt; warm, saline Pacific Summer Water (forming the lens); cold Pacific Winter Water; warm, saline Atlantic water; and then Arctic Deep This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Water [18], [19]. This stratification creates a unique double ducted environment that has drastic consequences for acoustic communication, sensing, and navigation compared to historical conditions of a monotonically increasing sound speed [20]. The upper duct, at the surface, keeps transmission loss low but severely degenerates signal coherence due to a higher degree of surface interacting paths. The lower duct, approximately between 50 and 200 m in depth, effectively traps sound above 300 Hz and can propagate sound at near-basin scales [21]. Here, we distinguish the lens as an oceanographic feature-the local temperature/sound-speed maximum, its variability, and effect on surrounding water masses-and the ducts as acoustic features dependent on source depth and frequency.
While the duct has been exploited for long range transmissions [13], [22], short range transmissions are marred by an acoustic shadow zone. This shadow zone is a predominant feature from 2 to 6 km in range for source depths of 33-200 m [21], engulfing the operational ranges and depths for AUV deployments. Furthermore, the strength of the duct is highly variable and not captured by publicly available models like hybrid coordinate ocean model (HYCOM) [23], a sea-ice coupled, three-hour resolution, 1/12 • resolution model well used by the ocean acoustics and naval intelligence communities [24]. A custom high resolution and daily surface forced MITgcm [25] modeling effort was able to represent the warm water layer as a persistent, widespread, but discontinuous feature [26], [27]. Long-term mooring deployments in the Beaufort Sea have shown that the largest observed sound-speed variability is in between 50 and 100 m in depth, due to warmer and saltier (spicier) water [28]. This work is motivated by under-ice AUV operations with four GPS-aided micromodem buoys, during the Ice Exercise 2020 (ICEX20), in March, in the Beaufort Sea. Environmentally driven AUV behavior was central to mission success given the total under-ice environment (necessitating accurate return to home) and the Beaufort Lens (obfuscating short-range propagation). The spatio-temporal variability of the Beaufort Lens predicates a locally updatable sound-speed profile for the integrated communication and navigation network [29], [30] depth-dependent adaption [21] and real-time acoustic ranging [24], [31].
In this article, we introduce a decision-making framework to facilitate robust environmental awareness in the Beaufort Sea, where profiler data reveals a complex acoustic propagation environment due to variable warming in the upper 100 m. We use a basis function representation of the sound speed to estimate a local sound-speed profile observation and compress the message content to a handful of weights; we call this the Virtual Ocean (VO). We also design and evaluate tactical decision aids (TDAs) to convey the joint environmental realism and acoustic utility for the various combinations of weights, i.e., various VO estimates from the basis function representation. We then communicate these weights to the vehicle via acoustic message to update its internal sound-speed estimate, which informs the navigation and communication behaviors. This framework was successfully deployed during Ice Exercise 2020 (ICEX20) from March 8-12, 2020, where multiple messages were sent from a topside transponder to submerged assets to synchronize updated sound-speed information.
The rest of this article is organized as follows. Section II covers background material and reviews relevant literature. Section III introduces a generalized procedure for modular and robust environmental autonomy, and Section IV details experimental conditions for ICEX20. Section V presents selected results to demonstrate how the framework created guided decision-making. Finally, Section VI concludes this article.

II. RELATED WORK
This section will cover the relevant literature in empirical orthogonal function (EOF) analysis, tactical decision aid (TDA) development, and vehicle deployments in the Arctic. In this work, we use EOF analysis to create a basis function representation of the sound speed, which serve as the feature space for TDAs to assess the environmental realism and acoustic utility for vehicle communication and navigation.

A. Empirical Orthogonal Function Analysis
EOF analysis seeks to reduce a large data set but capture its underlying, characteristic variability. It is often associated with principal component analysis (PCA), which finds the power behind each characteristic feature to estimate the initial data set, and singular value decomposition (SVD), which is the decomposition of any rectangular matrix [32]. As these eigenmethods are numerically driven, with no parametric distributions or underpinning physics, it is important to not ascribe scientifically meaning structures in the data without additional evidence, testing, or insight.
Consider a demeaned n × p data matrix X describing p measurements of the same variable at n times. In our case, each row of X contains an observed sound-speed profile assimilated to p different depths. An EOF analysis calculates the eigendecomposition of C xx , the associated autocovariance of the demeaned data matrix, which is by definition square This solves for E, a p × p orthonormal matrix, detailing column eigenvectors e i (also known as modes or EOFs), and Λ, the diagonal matrix of eigenvalues. The sum of all eigenvalues, or the trace of Λ, is equal to the total auto-covariance of the data. Dividing each eigenvalue λ i over the trace of Λ indicates how much variance is explained by the ith EOF.
Importantly, the EOFs are mutually uncorrelated in space. The time evolution of each EOF, also referred to as principal components or weights, β i , are similarly mutually uncorrelated in time. The weights pertaining to any EOF are found by projecting X onto the EOF; the unit of the initial measurement is preserved in the weights, not the EOFs. For the first EOF Thus, the demeaned data matrix X can be represented exactly as a sum of p weighted EOFs but can be estimated with a subset of the first j EOFs, where j p. It is computationally efficient to perform an EOF analysis through an SVD analysis. The former must compute the autocovariance matrix; the latter solves for a reduced amount of eigenvectors and values, at most j ≤ min n,p . An SVD analysis is factored as where U is a n × n orthogonal matrix, V is a p × p orthogonal matrix, and S is n × p diagonal matrix with j singular values. The column vectors of V are the EOFs; the column vectors of U are the normalized weights associated with each EOF. The eigenvectors and weights are linked by the singular values of S, which are the square root of the eigenvalues from C xx . Given a 2-D data set, where one represents the dimension in which we want to represent structure, and the other represents the dimension realizations of this structure have been sampled, eigenmethods generated a weighted feature space to explain the maximum amount of variance in the data. Their applications for sound-speed variability are diverse: creating a sound-speed "data bank" [33]; modeling sound speed and current fields for tomography [34]; merging multiple partial depth data time-series to better approximated the mixed layer compared to extrapolation [35]; classifying acoustically stable areas [36]; and reconstructing internal wave trains for acoustic study [37].

B. Tactical Decision Aids
TDAs, while used in the US Navy as early as 1972 to support mine countermeasures [38], rose to the forefront after a cruiser misidentified a civilian plane as a hostile military aircraft [39]. Wagner [40] distills the essence of a TDA-to assist a decision-maker by "assimilation and convenient presentation of data" and "analysis of the tactical problem beyond what is feasible by humans in a timely fashion." By 1989, four TDAs with predominantly environmental inputs and tactical outputs-Navy Search and Rescue (NAVSAR), Environmental Strike Planning Aid (ESPA), Tactical Environmental Ship Routing System (TESR), and Chaff Planning and Prediction System (CHAPPS)-were designed specifically to assist decision-makers in stressful and/or complex scenarios. TDA development for AUVs plays a natural analogue for submarine operations. More recent TDAs optimize for multivehicle path planning [41], prepare an acoustic battlefield [42], and implement fuzzy logic to digest qualitative and quantitative wave height descriptions [43].
The root idea of TDAs-communicating information across digital and human boundaries while leveraging computation of the former and the heuristic judgment of the latter-drives advances in fields as far as interactive architectural design [44] and, closer to home, human-robot interaction [45]- [47]. Thus, TDAs serve as organic documentation between human and AI decision-makers. The TDAs we present here are framed as operational guidance that modify robot behavior; they build on previous successful elements like text-and graphic-based recommendations, user-entered bounds, cost functions, and dynamic programming.

C. Autonomous Vehicle Deployments in the Arctic
We refer the interested reader to [48] and [49] for a thorough historical review of vehicle operations in polar environments. Here, we focus on how comparable recent autonomous vehicle deployments in the Arctic have not needed to consider the soundspeed profile in real-time for successful navigation and recovery.
Most AUV deployments under-ice in the Arctic have observed the historical, upward refracting sound-speed profile, where the isovelocity assumption does not introduce large error for short-range operations. AUV deployments in the summer of 2007 near the Gakkel Ridge observed greatly varying open ice leads, which posed challenges for a vehicle to surface [50]. But because the LBL beacons sat 150 m above the seafloor, and the majority of the vehicle's mission was below 2000 m, slant ranges were accurately calculated using a depth-averaged sound speed [51]. Cross-shore transects taken under coastal sea ice relied on an ultrashort baseline homing system to ensnare the AUV in a net [52], [53].
Other AUV missions have demonstrated success in partial or ice-free conditions with inherently higher tolerance for navigation error. Vehicles have been applied to map several important oceanographic processes including glacially modified waters [54], horizontal density structure [55], and surface fronts [56]. It was not until glider deployments in September 2014, in the northern Chukchi and Beaufort Seas, that a vehicle operated in the Beaufort Lens' double ducted environment. The initial experiment exploited the lower duct for highly accurate long-range transmissions, but acoustic navigation was untenable outside of the duct [13], [22]. In September 2017, a follow-up glider deployment showed that glider renavigation using an acoustic arrival method and the average sound-speed profile from the gliders reduced positioning error by a factor between four and five depending on the dive [12].

III. GENERALIZED VIRTUAL OCEAN FRAMEWORK
This section will introduce a generalized framework for environmentally adaptive behavior in the VO paradigm. A schematic detailing the operational procedure into four steps is shown in Fig. 1.

A. Predeployment Phase
First, in the predeployment phase [see Fig. 1(a)], multiple sound-speed training sets are formed. Each training set can be populated by any set of relevant models and/or observations, assimilated to the same depth grid, and demeaned with a depth-dependent sound-speed mean. The depth-dependent sound-speed mean is used, opposed to a scalar value, such that a series of null weights would be somewhat realistic. The EOF shapes are smoothed with a small spatial filter to encourage sound-speed continuity at the cost of perfect orthogonality. Custom VO files are created and preloaded onto the vehicle, where each one contains the depth-dependent sound-speed mean; an EOF basis set; a corresponding depth vector; and kernel density estimates (KDE) for the weights for every EOF from the training set. By the nature of EOF analysis, the resulting sound-speed estimates have no knowledge of bathymetry or bottom properties. A companion bathymetric file with 1-min resolution is supplied [57] and bottom properties are set manually.

B. Interactive Tactical Decision Aids
Next, just before vehicle deployment, an initial external conductivity, temperature, and depth (CTD) cast is taken to get a local observation of the sound-speed profile in the deployment area [see Fig. 1(b)]. Through the TDA framework, a decision-maker compares this real sound-speed profile to the training sets and chooses an initial VO file and weights to best estimate the desired sound speed while preserving historical variability. The basis set is confirmed for the mission duration, and the initial weights are sent to the vehicle via an acoustic message as it begins its mission. In the scenario where no EOF set accurately described the sound-speed profile, a backdoor was built in to modify the base sound-speed value directly. This would impose previously studied variability onto a new mean. The vehicle would begin its mission with all EOF weights set to zero; these weights could be updated accordingly throughout the mission, with reference to the initial anomalous CTD cast.
With this first ground truth CTD (or a subsequent one, if enough time has passed), a decision algorithm distills the environmental and acoustic realism for various EOF SSP estimates. The sound-speed estimates are least squares projections of the observed sound-speed perturbation with respect to the EOF basis; the decision algorithm iterates through every possible combination of weights. Fig. 2 sketches out the TDA data and simulation pipeline.
The environmental realism is assessed by the mean absolute error between the desired sound-speed profile from the CTD c z , and the estimate from the EOFsĉ z , in the interpolated depth grid from the EOFs to the maximum depth of the CTD. The environmental penalty c is as follows: Acoustic penalties directly derive from timefronts along rays to align with timing and positioning mechanisms for navigation. The ray tracing solution implemented here is custom built [58] to be more computationally efficient than BELLHOP [59] for this use case, as it does not produce any binary files and only reports the outputs necessary to drive the acoustic metrics. Because our operations are on small scales and the Arctic is a generally upward refracting environment, bottom interactions are simplified with a constant bathymetry. However, it would be trivial to include a 2-D bathymetry in a region where bottom effects were pronounced. Scattering from the ice surface is ignored to maintain interpretability of the acoustic penalties.
The raytracing function Γ, inputs c, a sound-speed profile; θ, a list of ray launch angles; t max , the maximum travel time desired; and z max , a nominal water column depth. It outputs ray positions in range and depth, P rz , indexed by launch angle and list of travel times The raytracing function is run for both c z andĉ z , with all other parameters defined the same. We define ray shift as the difference of the timefront locations of rays of the same launch angle between the desired and estimated sound speeds. The first acoustic penalty rz looks at the magnitude of the error in Euclidean space. The second acoustic penalty σ is simply the standard deviation of the ray shift, where n θ,t is the total number of launch angles multiplied by the total number of interpolated travel times. Both preserve the units of distance in meters To normalize the differences in scale and units across all penalties, each is converted to a z-score, to minimize the overall cost function J The cost function returns an initial ranking of sound-speed estimates. The ranking is not a greedy estimator-more EOFs do not always perform better, as shown in Appendix A.
Sorting the cost function J produces an initial ranking of sound-speed estimates for the user. The top choice is automatically loaded into all the graphical interpretations distilling the environmental and acoustic penalties (discussed in Section V). The user can investigate any other ranking through a prompted entry, which updates the graphical components accordingly. Eventually, a ranking can be selected which preserves the simulation state, visual elements, and initializes (but does not send) the command to update weights on the submerged AUV. Thus, the responsibilty for any tactical choice remains with the authoritative decision-maker.

C. Acoustic Message
While the VO file is chosen once per mission, weights can be resent at any time given another CTD cast, at the discretion of the topside decision-maker [see Fig. 1(c)]. These updates are marshaled via lightweight messages comprised of bounded basic variable types, necessitated and designed for a low bandwidth acoustic channel [60], and are sent via a WHOI micromodem [6] with a 10-kHz carrier frequency, 5-kHz bandwidth, and phaseshift keying modulation; they were received on the AUV with the same micromodem.

D. Environmentally Adaptive Communication and Navigation Behaviors
The VO estimation interfaces directly into acoustic models to inform communication and navigation. The acoustic models [59] included 2-D bathymetry from the VO bathymetry file as well as a roughness parameter for ice scattering.
For navigation, the sound-speed information was used to estimate an effective horizontal group speed for each transmission path between an AUV and the four GPS-aided modem buoys [24], [31]. This ensured a reliable, physics-based method of converting OWTT to range that resulted in navigation accuracy on the order of meters.
For communication, the sound-speed information from the VO was used to seed depth adaptive behaviors. The vehicle inputted SSP, navigation message content (source depth, estimated position), and its self-position estimate into an onboard acoustic model to maintain optimal depth for communication [61]. Each LBL modem contained receive channels at 30 and 90 m in depth and a transmit channel at 30 or 90 m in depth. A synergistic self-adapting behavior determined what receive and transmit elements should be active [30].

IV. EXECUTION OF TDA FRAMEWORK DURING ICEX20
This section details the performance of the Virtual Ocean and interactive TDA framework for ICEX20. This begins with predeployment data assimilation to make an EOF basis, covers the CTD casts and the corresponding weights, and ends with a retrospective analysis on the environmental and acoustic penalties. The communication and navigation performance is beyond the scope of this article and has been initially covered by related work [24], [30], [31], [61].
In our field tests, the cost function J was solved for within two minutes, roughly scaling to a second per synthetic sound-speed estimate on a 8-core, 16-GiB RAM laptop. Additionally, colors and linestyles were chosen to be distinct for deuteranomaly, a visual disability that affects roughly 5% of men [62]; those colors are preserved here.

A. Data Assimilation and EOF=Analysis
To isolate different snapshots of sound-speed variability, six total tuned EOF sets were created using modeled and real data from March of 2013, 2019, and 2020. The latter two years, 2019 and 2020, were chosen for temporal proximity; 2013 was chosen for its similarity to trends in Northern Hemisphere sea ice extent provided by the National Snow and Ice Data Center [63] a few days before ICEX20. Fig. 3 details the spatial information for the modeled and real data inputs over the Beaufort Sea as well as the location for ice camps during 2016 and 2020, Camp Sargo and Seadragon, respectively. Model outputs were provided by the Hybrid Coordinate Ocean Model (HYCOM) Global Ocean Forecast (GOFS) 3.1 [64]. The model output was downloaded from March 4-13 with a three hour time step, from 71 to 73 N and 141 to 146 W, a few days before ICEX20. The exact location of Camp Seadragon was not known when downloading the HYCOM outputs, just that it was southwest of the ICEX16 location. It is important to note that the HYCOM output for 2013 is "reanalysis" data, which assimilates the HYCOM "analysis" with observed temperature and salinity profiles. The HYCOM output for 2019 and 2020 is simply "analysis" data.
Data outputs were provided by the Woods Hole Oceanographic Institution's Ice Tethered Profiler (ITP) program [65], [66]. Data from all ITP profilers were filtered within 70 to 76 N and 140 to 160 W, around March of each year. The profiles, with depth sampling every two meters, were assimilated to the 40-point standard depth grid from HYCOM to capture the overall impression, not the microstructure, of the sound-speed profile. Due to sea ice, profilers rarely reach the surface. Due to instrument operating depth, profilers do not exceed 800 m. Profiles with valid data above 20 m were linearly extrapolated to the surface. Profiles with valid data below 600 m were continued to the maximum depth of HYCOM (4000 m) with the hydrostatic sound-speed gradient of 0.0167 m/s/m. The HYCOM depth grid ensured that the number of unique profiles was much greater than the number of depth grid points (n p). In hindsight, we recommend that n should be at least an order of magnitude greater than p.
Half of the sets were trained only on modeled data and the other half blended real data and k-means clusters from models in a 4:1 ratio. Modeled data were necessary in every training set to populate the full water column. Fig. 4 shows Fig. 4. Base values for sound speed across the training sets show a variety of duct strengths and heights. The "ITP" label indicates those that were trained on models and data; the "HYCOM" label indicates those that were trained on model output only. the depth-dependent sound-speed mean for each training set; the ones trained with ITP data show a Beaufort Lens feature of varying strength, whereas the ones trained without data are reminiscent of the classical Arctic sound-speed profile. Fig. 5 shows the first 7-EOF shapes with the cumulative variance explained and Fig. 6 shows the kernel density estimate for the ITP 2013 set. Together, these figures demonstrate that as the variance explained begins to plateau, the associated weight KDE begins to look more Gaussian and zero-centered. The VO files were truncated to 7 EOFs based on this insight, as higher order EOFs after this may be encoding more noise than signal.

B. Choosing a Mission EOF Set
A single EOF set is chosen to parameterize the entire mission's Virtual Ocean based off a driving CTD (the second CTD in Fig. 7). We assume this CTD is representative enough of the ocean state for short, small-scale operations. The tuned EOF sets from ITP 2013 and HYCOM 2019 both estimated the driving CTD with less than c ≤ 0.5m/s. Ultimately the ITP 2013 set was chosen because it had better visual agreement and its baseline profile included a duct. Taking multiple CTD profiles in the week before deployment would have allowed this choice to be more quantitatively than qualitatively driven.
While we included the 2013 data based on first-order interactions between sea ice melt and growing heat content in the Pacific Summer Water [67], it is an oversimplification to claim that the sea ice extent explains the variability with the Beaufort Lens variability, especially since it is also the most populated data set. This EOF set was most valid for our observed conditions; at another location and/or time, a different one may have performed best.
Interpreting the impact of the choices of initial databases on SSP estimation is not straightforward, especially with only four days of CTD data. The data-blended EOF sets tended to outperform the model-driven ones, likely because HYCOM has a high degree of redundancy and does not capture ducted conditions well.
Though the ITP 2013 EOF set was successful in SSP tracking over the course of ICEX20, it would not have been difficult to include an EOF set for March-like conditions of every year since 2010, or use statistical or machine learning methods to make EOF sets based on different degrees of ducting.

C. All ICEX20 CTDs
Ten CTDs were cast from an ice hole over the three-and-ahalf-day experiment, roughly 250 km northeast of Sagavanirktok (Prudhoe Bay), Alaska. As shown in Fig. 7, the first five were from the RBR Concerto 3 (RBR), a retrievable plastic sensor that was operated on a manual winch down to a maximum of 400 m; the latter five were from the Lockheed Martin XCTD-1 (XCTD), which is expendable but goes to much greater depth. The accuracy of the XCTD is about an order of magnitude less than the RBR for temperature, conductivity, and pressure, but more than accurate to match the standard depth grid HYCOM provides. The top two meters from all CTD casts were discarded to eliminate observations that drifted warmer due to sensor stagnation in a heated ice hut.
Concurrent modeling or data assimilation set is a realistic benchmark for the EOF system. The HYCOM reanalysis was interpolated to the exact time, latitude, and longitude of the CTD casts. The reanalysis drastically mischaracterizes the soundspeed conditions as the classical Arctic conditions, as there is not a duct nor any significant changes in the sound-speed profile throughout the experiment.
The nearest ITP data, weighted by space and time, were retrieved shortly after ICEX20. These profiles capture a duct but the lens is 20-30 m deeper than those of the CTDs. There is better fit in the maximum sound speed of the observed duct, but naturally, due to the sparse nature of ITP observations, they are not sensitive to the local ICEX20 duct weakening, most evidenced from March 11 0630 onward.
The chosen EOF weights, drawn in a dotted black line, more accurately represent the local sound-speed conditions and produce reasonable estimates for sound speed beyond the CTD depth as well. The "dominant" sound-speed profile for ICEX20, observed in all RBR casts and the first XCTD cast, is extremely well fitted by the EOF set. There is some mismatch around 175 m, where the depth grid spacing loses resolution-from 100, 125, 150, and then 200 m.
From March 11 0630 onward, the duct develops a microlens that continues to shift in later observations. This feature is fairly unstable and not well characterized by the EOF set. Going through each of the four relevant CTDs, the chosen weights ignore the microlens; match the microlens by misfitting at 150 m; match a weaker duct because of no observed microlens; and ignore the microlens. Eventually, the tactical choice, enabled by The initial plan was for a CTD cast every three hours to match HYCOM's temporal resolution; due to technical difficulties, we took ten over the course of three and a half days, with two different sensors. All times are Alaska time.
the TDA, was to ignore an unstable and acoustically minimal microlens. Overall, each sound speed is matched with a mean absolute error no greater than 1 m/s. The fluctuations across the ten CTDs provide strong narrative evidence that frequent CTD casts are necessary, even for short-term deployments, as the duct changes overnight between March 10th and 11th. The duct changing more likely represents the environment changing as a function of space and time than camp moving into new water given that the ice drift was unprecedentedly small, less than one cm/s. The final CTD was roughly only 2 km south of the first one.

D. Chosen Weights
Knowing that the sound-speed profile was overall well represented, we were interested to see how "predictable" these sound speeds could have been. A comparison of the discrete weights chosen for ICEX20 CTDs w compared to the distribution of weights from the training set β, as shown in Fig. 8, indicates that a bootstrapping technique would have likely captured the sound-speed profiles observed.
For all chosen weights, only β 6 and β 7 go beyond the a priori distribution when matching the microlens, further suggesting that it is an anomalous feature. The majority of chosen weights for all observations fall within the a priori distribution such that a probability distribution encoding may be of practical use [68]. The exceptions to this pattern, most evident in β 6 , may be easily remedied by extending the encoding domain.
When looking at the temporal spread of chosen weights, we see a consistency in the first five CTDs. The first CTD, which only went down to 50 m, is a narrow exception, as it only uses the first two weights. This was a tactical choice to not overfit the data provided. The sixth CTD, the first of the XCTDs, has slightly different weight mapping even though the sound-speed profile is similar; this is because the CTD cast itself is deeper, so the weighting is influenced by a different basis. Future work could add an element of interactivity to the TDA to modify the default uniform weighting of depth grid points. The chosen weights for the rest of the XCTDs are not as consistent, due to ill-fitting of the microens, but show the efficacy of a minimal message to update the internal sound-speed estimate on a submerged asset.
As expected, all of the chosen weights use w 1 . But the natural extension of that, that less dominant EOFs might be used less, is not strictly observed as β increases. For example, w 2 is skipped twice; w 3 is skipped thrice; w 4 is only skipped once. A simple rank sum for each CTD, across all the estimates that performed better than the mean ranking, finds that the second EOF was the most consistent driver behind the first eight CTDs; the sixth EOF governed the last two CTDs.

E. Correlation Between Acoustic and Environmental Penalties
Lastly, a comparison of environmental and acoustic penalties demonstrates the nonlinear relationship between the two, and by extension, the necessity for a TDA to convey a joint utility when estimating the sound speed. Fig. 9 shows c , the mean absolute error of the sound speed, on the x-axis, and rz , the ray shift, on the y-axis.
The chosen weights for the first CTD, which has very little depth information, were initially ranked fiftieth. The ranking algorithm does not reward using fewer weights, but presents the information in an easy enough way to find them in the case of a lack of data or mistrust of sensor data. The other ranks chosen have a mode of 1 and a median of 5, so the ranking algorithm is aligning with decision-maker agreement. Rarely are the chosen ranks the minimal environmental and acoustic penalties. In addition to the mismatch between top ranks, there was a strong instinctual element in the decision-maker's process, i.e., simply not liking the shape of a particular sound-speed perturbation at a depth of interest, or a preference for acoustic parameters over profile shape in certain operational scenarios. At the same time, the decision-maker also settled for some ranks using all EOFs when the difference between top ranks appeared minimal.
There is no singular correlation when examining the relationship between the acoustic and environmental penalty for all CTDs. We can disregard the pattern from the first CTD due to insufficient depth information, though it raises important questions for through-the-sensor mechanisms. The second CTD shows an overall positive correlation, but there are two clusters; the second cluster shows a wide range of acoustic error with little variance in sound-speed error. These clusters are the dominant features for the next four CTDs; the first cluster has a positive correlation and the second cluster has a negative one. The negative correlation here most likely stems from turning points in multiple surface-interacting rays realigning back to the original CTD pattern. The remaining XCTDs show weak positive correlations between the two penalties, with the exception of the one on March 11 1300, which uniquely has seemingly no correlation.
Overall, this shows the counterintuitive result that a minimal acoustic penalty can be driven by a varying range of environmental penalties. This information was rarely exploited by a human decision-maker for any individual CTD, as they were risk-averse in choosing an environmentally different but acoustically similar environment. The corollary, that minimal environmental penalties could produce a wide range of acoustic penalties, is technically true but is generally not possible because of how the EOFs reconstitute sound speed. These penalties are, of course, a function of the source depth and other parameters in the TDA configuration. Continued tactical simulations with the Virtual Ocean for vehicle operations will garner more data about this relationship.

V. SELECTED RESULTS
This section will explore three CTD casts to demonstrate the graphical TDAs, with a focus on the environmental and acoustic TDAs, respectively. The first case study uses the first Fig. 9. Relationship between acoustic and environmental penalties for all ICEX20 CTDs. The x-axis shows the mean absolute error of the sound-speed c and the y-axis shows the mean absolute error of the timefront eigenray shift, rz . The black × indicates the chosen sound-speed estimate's penalties, where its rank is displayed in the top right corner. Fig. 10. Comparison of the first graphical TDA that shows all the combinations of sound-speed estimates (gray) compared to the desired sound speed (purple) and the chosen sound speed, rank, and weights (teal). On the left is the pipeline test CTD down to 50 m; on the right is the driving CTD that chose the EOF set.
two CTDs (RBR March 8 2051 and RBR March 9 0605); the second uses the seventh (XCTD March 11 0630). Code to demo the TDAs for any CTD cast is provided as a GitHub repository in Appendix VI.

A. Environmental TDAs
The first CTD taken on site tested the sensor functionality and the data pipeline; the cast only went down to 50 m. While not used in the field, it, and the CTD cast 10 h later, provide an excellent window into sound-speed estimation beyond sensor depth, and the environmental TDAs. Fig. 10 demonstrates the first TDA visualization of the soundspeed information. This TDA digests a user-entered sound speed and allows a user to match it to various EOF fits. The test CTD conjures several improbable sound-speed estimates because it overfits the minimal data available; the chosen rank is 50. The driving CTD for the mission, which was 10 h later, Fig. 11. This TDA shows a priori weight distribution from the EOF training set in black. Purple lines show the weights driving all sound-speed estimates and a teal line shows the weight for the chosen rank. The purple dashed line refers to weights that were manually tapped out as null.
corroborates the sound-speed estimate from the previous test CTD. The updated weights modify the first two from before and add the third, fourth, and seventh EOFs to the mix. This better reflects the data, especially between 50 and 100 m; and the TDA decision algorithm does a much better job suggesting this fit, with a rank of 5. The variation in sound speed fits at the surface encode different warming in the mixed layer; the variation from 50 to 100 m strangely encodes two different duct shapes (and strengths). At depths greater than 100 m, the window of the sound-speed estimates at any given depth is roughly 5 m/s. The second environmental TDA, shown in Fig. 11, presents the discrete weights for all sound-speed estimates w versus the weight distribution from the training set β. Decision-makers were interested in sending the weights that most heavily and consistently deviated from the maximum likelihood. This is seen quite clearly for w 1 , w 2 , and w 7 , where the weights have little standard deviation and are located in a tail of the distribution. Less importance was attributed to a weight like w 3 , where the estimates spanned the full distribution (suggesting little impact), or w 5 , heavily centered at 0 (suggesting unnecessary forcing).
Overall, these two TDAs characterized the local Beaufort Lens and the error in the sound-speed estimation while contextualizing the estimate relative to the training distribution.

B. Acoustic TDAs
The second case study examines a weaker duct with the microlens around 45 m. This particular CTD is a compelling case study for the two acoustic TDAs because the chosen weights do not try to fit the microlens.
The first acoustic TDA visualizes the ray geometries between the ground truth SSP from the CTD and the estimated SSP from the VO. The user-entered time fronts are highlighted with increasing color to visualize the spread, but will be communicated with more granularity by the second acoustic TDA. The ray comparison by color and transparency is more intuitive than comparing color as an indicator for transmission loss differences, which has little bearing on navigation. In Fig. 12, one can see very little ray shift throughout the water column, even though the microlens is not considered. The multipath is well preserved; the rays that bound the shadow zone are slightly extended but not in any way to mislead position. The deeper rays are also preserved but were generally not considered to be of high importance because of our small operational domain. Thus, these ray geometries provide some insight as to what spatial scales of sound-speed features may impact downstream performance.
The second acoustic TDA delineates the relative ray shift over all launch angles by the suggested timefronts, as shown in Fig. 13. For rays represented by Γ(ĉ, θ), we define a unitless ray shift percentage where r is the range component of rz and P r (c, t, θ) is the range component of P rz . Effectively, range is normalized by the distance the ray has traveled and depth is normalized by the maximum water depth. The orange dot, referencing the desired ray position, centers the ray shift with no error. The numerous teal dots indicate the ray shift for all prescribed launch angles. Fig. 13. This TDA displays the relative timefront eigenray shift as a percentage. The x-axis is the range error relative to the range traveled and the y-axis is the depth error relative to the water column depth. The gray dots show the relative ray shift for all sound-speed estimates and are darker for regions that have higher probability. The teal dots show the relative ray shift for the chosen sound-speed estimate for each launch angle. The orange dot is centered at 0, 0 , as this is the reference from the CTD.
The transparencies of the gray dots, referencing the ray shifts for all other sound-speed estimates, are weighted by the proximity to other ray shift estimates. The relative ray shift allows for a strategic interpretation of range localization error sorted by pre-selected travel times. For example, if the user knows the vehicle is roughly a kilometer away and returning home, reducing the ray shift structure for 0.6 and 1.3 s may be more tactically important than the others. Alternatively, if the vehicle is at the same location and just starting its mission, the user may prioritize tightening the ray shift structure for larger travel times. Ultimately the second acoustic TDA provides a more granular approach to the relationship between mismatches in the sound-speed structure and their acoustic significance at times of interest. A byproduct of the relative ray shift, given the reliability of onboard pressure sensors, is a nominal estimate for the navigation error based on the acoustic propagation itself.
The major limitation for this interpretation is of course spatiotemporal variability in the water column. Given this is a fairly untenable problem for in situ observations or modeling, we assume that an updatable range independent sound-speed profile is representative enough for small operational regions.
It should be noted that the observed range shift is almost always positive because the SSP estimate tends to be slightly greater than that of the SSP from the CTD. This is most obvious near the surface and may even be true beyond the depth of the CTD. The time delay observed may be attributed to any ray's turning points in these overestimated regions. Ray shift plots for other CTDs show a more balanced negative and positive range shift.

VI. CONCLUSION
Based on our demonstration in the ice-covered Beaufort Sea, we conclude that this framework sufficiently addresses the need to consider the acoustic impact of a locally changing sound-speed profile in current underwater navigation paradigms. We have demonstrated that this tactical decision aid succinctly and effectively enables the use of an updatable, full water column profile rather than a single deterministic value for sound speed. From left to right: Rank is the z-score sorting of the metrics; EOF subset is which functions are used to generate the estimate; SspError is the mean absolute sound-speed error compared to the sound speed derived from the CTD; RayError is the Euclidean distance of specified eigenray timefronts between the CTD sound speed and the EOF estimate; raySTD is the standard deviation of the directional distance of the specified eigenray timefronts.
In doing so, our approach enables a human decision-maker to oversee an AUV in a way that promotes environmental awareness and trust in its autonomous capabilities. Future iterations of this framework could provide collaboration between submerged assets for enhanced spatiotemporal environmental awareness.
While EOF analysis is widely adopted for sound-speed reconstruction for its simplicity and effectiveness in capturing variability, it would behoove researchers to be cognizant of its acoustic implications. In this work, we smooth EOFs to encourage sound-speed continuity. One method to mitigate this manual smoothing, currently under investigation, is to include depth-dependent sound-speed gradients in the training feature space. To prioritize acoustic performance, we implement a realtime acoustic simulations and metrics in addition to the usual environmental fit in assessing weights. The lesson learned on this subject is that while a certain set of weights may produce a sound-speed profile that is visually dissimilar to a desired one, the acoustic properties may be a closer match. To make this distinction clear to the human decision-maker, some pretraining on the impact of the acoustic parameters will be required before use. An improvement to this work would diversify the acoustic penalties into the communication realm without adding significant latency in the decision algorithm.
Given the Arctic's heightened sensitivity toward global climate change, we expect the spatio-temporal variability of the Beaufort Lens to continue to be a focus for oceanographers, acousticians, and roboticists alike. The approach presented here, which adapts to temporal changes in the sound speed, should be expanded to account for spatial variability-especially for long range applications. One can impose stochastic internal waves or encode 2-D probability distributions [69]. In addition, machine learning techniques like dictionary learning [70] may simplify weight finding and even reduce message size. In light of the sound-speed profile estimation mismatch at 150 to 200 m in depth, there is a need to understand what depth grid resolution encodes variability optimally given the tradeoffs of limited source data and abundant microstructure.
It is also of extreme importance to maintain the quality of data garnered in the Canada Basin to continue to study the potential interactions between sea ice and the Beaufort Lens [67]. Because satellite ice cover data can be at daily resolution, linking the two may be a way to leverage the information disparity to further study warming of subsurface Arctic waters. More broadly speaking, the sea ice thickness dictates when these experiments can be done safely (generally only in March); but the Arctic's sensitivity to warming threatens these types of efforts and even invites a different ambient acoustic environment [71], [72].
This framework serves as a proof of concept for how we can leverage minimal acoustic communication to advance autonomy and is easily extendable to other underwater platforms and applications. For example, gliders would disproportionately benefit from not only the coupled environmentally adaptive communication and navigation paradigm but also from an updatable basis function representation to account for currents in the water column while path planning. Encoding other oceanographic parameters of interest, like temperature, salinity, or oxygen concentration, can create human-assisted feedback loops for more informed vehicle sampling to curate data sets of scientific value. This would be paradigm shifting for autonomous vehicle deployments where the data are of utmost scientific value and cannot easily be gathered any other way, such as a recent application where an AUV was constrained to fixed altitude paths to characterize warm water pathways underneath Thwaites Glacier [73].
As we seek to transition from teams of humans supervising a single vehicle toward teams of vehicles collaborating with little human supervision, a key focus of this work is building and maintaining operator trust in embedded AUV intelligence. TDAs are just one pathway to shift decision spaces into increasingly automated domains. Operations in the Beaufort Lens provided an excellent testbed to develop and demonstrate a type of information sharing that significantly improved autonomous navigation and communication behaviors. We hope this to continue this work to enable more intelligent multivehicle sampling, with geolocating oceanographic observations, to better understand the evolution and dynamics of oceanographically sensitive and acoustically complex environments.

A2: Table of Initial Ranking
See Table I.