cs.LGOct 25, 2026
SaveConditional Diffusion Generation of DVL and Inertial Signals for Underwater Navigation
Organizations: University of Haifa, Abba Khoushy Ave 199, Haifa, 3498838, Israel
Abstract
Autonomous underwater vehicles (AUVs) navigate without satellite positioning and rely on Doppler velocity log (DVL) and inertial sensors for motion estimation. Deep learning methods for processing these sensors require training data covering the motion the AUV encounters, commonly obtained through costly sea trials. To overcome this limitation, we present a conditional diffusion framework that generates synthetic DVL and inertial signals to replace real recordings in training. The generator employs an Elucidated diffusion model conditioned on three per-channel motion descriptors. Three configurations are evaluated: DVL beams alone, inertial channels alone, and all channels jointly from one model. Across thirteen trajectories of the real dataset, the generated signals followed the requested conditions with Pearson correlations between 0.72 and 0.997, transferred to trajectories withheld from generator training, and did not replicate any training window. A BeamsNet velocity estimator trained on generated signals alone, with no real recording retained, matched the velocity error obtained with the full real training set. Replacing up to all real windows with generated ones caused no measurable loss. Thus, this approach reduces the dependence of learned AUV navigation on sea-trial data, enables training when recordings are scarce, and facilitates developing and evaluating deep learning methods for underwater navigation.
Figures & tables
Figure 1: The three Pipeline configurations. Each differs in which sensor signals are synthetic and which BeamsNet variant is trained downstream. Pipeline 1 generates the DVL beams alone and trains BeamsNetV2. Pipeline 2 generates the inertial channels alone - the dashed line marks the real DVL beams, which are supplied to BeamsNetV1 alongside the generated inertial signals. Pipeline 3 generates the DVL beams and the inertial channels jointly from a single model and trains BeamsNetV1. A separate generator is trained for each pipeline.
Figure 2: Structure of the conditional diffusion U-Net, shown for the beams-only configuration (BeamsNet V2). The four beam channels and their four peak-map channels enter together as eight input channels, and the network predicts the four beam channels alone. The scalar conditions modulate every residual block. The temporal condition is injected on the encoder side and at the bottleneck, and reaches the decoder through the skip connections.
| Experiment | P1 | P2 | P3 |
| Fully synthetic sweep | 1:1–5:1 | Not defined | 1:1–5:1 |
| Combined synthetic and real sweep | 0:1–5:1 | 0:1–1:1 | 0:1–5:1 |
| Real-to-synthetic substitution | 0–100 % | 0–100 % | 0–100 % |
| Conditioning ablation | 1:1 | 1:1 | 1:1 |
Table 1: Coverage of the four downstream experiments across the three Pipelines (P1/P2/P3). The first two experiments and the ablation vary the size of the synthetic set against the real training set and are given as ratios. The substitution experiment holds the total number of training windows fixed and is given as the fraction of real windows replaced.
Figure 3: Example peak map for one DVL beam window. Top: the beam velocity signal with detected maneuver events marked. Bottom: the resulting peak map, a sum of signed Gaussian bumps placed at the detected events.
Figure 4: Pipeline 1, DVL signals, condition adherence test. All four DVL beam velocities are shown. The requested per-channel average is plotted against the average of the generated window, over 100 windows. The dashed line is the identity. The Pearson correlation between the requested and generated averages is 0.869 on beam1 , 0.791 on beam2 , 0.774 on beam3 , and 0.718 on beam4 .
Figure 5: Pipeline 2, IMU signals, condition adherence test. Two representative channels of the six are shown: the accelerometer component ( ax ) and the gyroscope component ( gx ). The requested per-channel average is plotted against the average of the generated window. The dashed line is the identity. The Pearson correlation between the requested and generated averages is 0.997 on ax and 0.994 on gx .
Figure 6: Pipeline 3, IMU and DVL signals, condition adherence test. Three representative channels of the ten are shown, one per sensor type: the first DVL beam velocity ( beam1 ), the accelerometer component ( ax ), and the gyroscope component ( gx ). The requested per-channel average is plotted against the average of the generated window. The dashed line is the identity. The Pearson correlation between the requested and generated averages is 0.960 on beam1 , 0.988 on ax , and 0.895 on gx .
Figure 7: Pipeline 1, held-out conditioning transfer. All four beam channels are shown over a single 206-sample window. The conditioning statistics were taken from trajectory T8, withheld from training.
Figure 8: Pipeline 2, held-out conditioning transfer. The conditioning statistics were taken from trajectory T13, withheld from training. Two representative channels of the six are shown, the accelerometer component ( ax ) and the gyroscope component ( gx ), together with the gyroscope component ( gz ), a channel whose real signal contains no local extrema and for which the peak map is empty.
Figure 9: Pipeline 3, held-out conditioning transfer. The conditioning statistics were taken from trajectory T5, withheld from training. Four representative channels of the ten are shown: a DVL beam velocity ( beam1 ), the accelerometer component ( ax ), and the and gyroscope components ( gx and gz ). The gyroscope shows the largest level divergence observed across the six inertial channels.
Figure 10: Example of draw-to-draw diversity in Pipeline 3, under fixed conditioning. Two channels are shown, the accelerometer component ( ax ) and the gyroscope component ( gx ). Several independent samples were generated from a single conditioning vector and are shown together with the real window that vector was computed from.
Figure 11: Nearest-neighbour replication test. For each window, the L2 distance to the closest window in the real training set is computed on per-channel windows. Green: real training windows measured against all other training windows, excluding themselves. This gives the natural nearest-neighbour scale of real data, since no real window is a copy of another, and it is the reference against which the synthetic distances are read. Red: synthetic windows measured against the real training set.
| Training set | Pipeline 1 | Pipeline 2 | Pipeline 3 | |||
| RMSE [m/s] | Improv. | RMSE [m/s] | Improv. | RMSE [m/s] | Improv. | |
| Real only (baseline) | 0.0039 | – | 0.0036 | – | 0.0036 | – |
| Real + synthetic 1:1 | 0.0036 | 7.7 % | 0.0035 | 2.5 % | 0.0036 | 1.7 % |
| Synthetic only 5:1 | 0.0035 | 10.3 % | – | – | 0.0036 | 1.5 % |
Table 2: Downstream velocity RMSE on the held-out real trajectories for the three Pipelines, under three training set compositions. Improvement is relative to the real-only baseline of the same Pipeline. Pipeline 2 has no fully synthetic entry and cannot exceed a 1:1 ratio. It generates the inertial channels alone, and each synthetic inertial window is paired with a real DVL window, so every training window contains real beams and no more synthetic windows can be produced than there are real DVL windows.
Figure 12: RMSE improvement of a downstream model trained entirely on synthetic data, as a function of synthetic data size, relative to a real-only baseline.
Figure 13: RMSE improvement when synthetic data is added to the full real training data, as a function of the amount of synthetic data added.
Figure 14: RMSE improvement when a fraction of the real training data is replaced by an equal amount of synthetic data, from (real-only baseline) to (fully synthetic, same size as the real-only dataset).
| Conditioning | Pipeline 1 | Pipeline 2 | Pipeline 3 | |||
| RMSE [m/s] | Change | RMSE [m/s] | Change | RMSE [m/s] | Change | |
| Full conditioning | 0.003712 | 0% | 0.003525 | 0% | 0.003608 | 0% |
| No conditioning | 0.9622 | 0.003526 | 0.262380 | |||
| No peak map | 0.0043 | 0.003526 | 0.003626 | |||
| No mean and STD | 1.009 | 0.003526 | 0.178263 | |||
Table 3: Conditioning ablation across the three Pipelines. Downstream velocity RMSE for the corresponding downstream model trained on synthetic data at a one-to-one ratio to real data, for each conditioning variant. Change is relative to the full conditioning of the same Pipeline.
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