1. Introduction
Under water autonomous vehicles (AUVs, ROVs) are employed in GPS-denied conditions where pose estimation could be crucial in navigation, inspection and mapping. The single sensor does not meet the fine accuracy, strong, and broad coverage requirements:
- Inertial Measurement Units (IMUs) provide data at high-rates (angular-velocity and linear acceleration) with drifts in their integration throughout time.
- Acoustic sonars (imaging sonar, multibeam, Doppler-velocity-log (DVL)) offer absolute range or velocity data, which are resistant to visual impairment, but have low resolution, multipath effects and acoustic noise.
Combining these complementary modalities alleviates the individual inabilities and produces a system of navigation which is both continuous (the IMU) and bounded (sonar).
2. Sensor Characteristics
| Sensor | Typical Output | Strengths | Limitations |
|---|---|---|---|
| IMU (accelerometer, gyroscope, magnetometer(optional)) | 3-axis acceleration, 3-axis angular rate, (optional) magnetic field | Higher update rate (≥200Hz), can operate in any lighting environment or turbidity environment | Error of bias drift, scale factor, cumulative integration error |
| Imaging Sonar (e.g. forward-looking, side scan) | 2 dimensional image of acoustic intensity, range bearing points | Functions in dark environments, goes through scattering media | Poor spatial resolution, and speckle noise as well as poor field -of-view |
| Multibeam / Scanning Sonar | This range measurements are dense, forming a point cloud. | Maps have a metric depth provided. | Calibration of beam-pattern critically required. |
| DVL | Speed in respect to sea floor or column of water | Direct velocity measurement, which is applicable to dead-reckoning correction. | Limited range, dependent on bottom reflectivity. |
The recent literature underlines that high frequency IMU data is important to predict short term motion and acoustic range/velocity data is important to predict long term correction1.
3. Fusion Architectures
3.1 Loose (Loosely‑Coupled) Fusion
- Each sensor has its own estimator (e.g. IMU dead -reliance, sonar odometry).
- A secondary filter (which is normally an EKF) combines high-level pose estimates.
- Easier to apply and leaves no use of raw measurement correlations.
3.2 Tight (Tightly-Coupled) Fusion
- The sonar and raw IMU measurements are simultaneously introduced into one state-estimation model.
- Common approaches:
| Method | Core Idea | Typical Use |
|---|---|---|
| Extended Kalman Filter (EKF) | Linearize motion and measurement models; propagate IMU state, correct with sonar ranges/velocities | Early underwater SLAM systems |
| Unscented Kalman Filter (UKF) | Propagate sigma points to capture non-linearities; used for IMU + DVL fusion | Higher accuracy with modest computational load |
| Factor-Graph / Graph-Optimization | Build a pose graph where IMU pre-integration and sonar constraints are edges; solve via non-linear least squares (e.g., g2o, Ceres) | State-of-the-art SLAM (SVIn2, SVIn2-plus) |
| Particle Filter | Sample-based representation for highly non-Gaussian noise; applied in cluttered acoustic environments | Research prototypes |
Tight coupling makes it possible to continuously fix errors and provide more control over asynchronous sensor streams.
4. State‑Estimation Formulation
An example of continuous-time state vector of an AUV is \[ \mathbf{x}_k = \begin{bmatrix} \mathbf{p}_k \\ \mathbf{v}_k \\ \mathbf{q}_k \\ \mathbf{b}_a \\ \mathbf{b}_g \end{bmatrix} \]
- \( \mathbf{p}_k \ \) – position, \( \mathbf{v}_k \ – velocity, \mathbf{q}_k \ \) – orientation quaternion
- \( \mathbf{b}_a \ , \mathbf{b}_g \ \) – accelerometer and gyroscope biases
IMU propagation makes use of discrete pre-integration (e.g. Forster et al.) to compute a constraint of motion between two keyframes.
Sonar measurement models:
- Range-only: \( r = \| \mathbf{p}_k – \mathbf{s}_i \| + n_r \) where \( \mathbf{s}_i \ \) is the beacon or position of a feature of sonar.
- Imaging-sonar feature: Once salient acoustic landmarks have been extracted (e.g., through edge detector or ICP), a 2-D bearing θ and range r are obtained and incorporated as a bearing‑range constraint.
The residuals are piled up into a cost function \[ \min_{\mathbf{x}} \sum_k \left\| \mathbf{r}_k^{\text{IMU}} \right\|_{\Sigma_{\text{IMU}}}^2 + \sum_j \left\| \mathbf{r}_j^{\text{sonar}} \right\|_{\Sigma_{\text{sonar}}}^2 \]
and it is related to solved using an iterative method.
5. Data Pre‑Processing
- IMU Calibration – statical bias, scale-factor and temperature compensation.
- Sonar Image Enhancement – Speckle reduction (median/anisotropic diffusion), contrast stretching, edge extraction.
- Feature Extraction – by acoustic corners, by intensity gradients, or point cloud registration (ICP).
- Temporal Alignment – High-rate IMU and low-rate Sonar temporal alignment via hardware timestamps and/or software temporal interpolation.
Recently a study was carried out to demonstrate a sonar-inertial filter-odometer which integrates ICP-based pose increments with IMU propagation with a sub-meter RMS error in both structured ports and lakes with weak texture.
6. Calibration of Spatial Extrinsics
The condition requires correct knowledge of the rigid transform \( \mathbf{T}_{\text{sonar}}^{\text{imu}} \). Common strategies:
- Calibration of the hand-eye offline with the help of a calibration block, where the vehicle is moved and IMU and sonar coordinated data are measured simultaneously.
- Online self-calibration within the factor-graph with the extrinsic parameters being the variables and optimized along with the trajectory.
7. Implementation Considerations
| Aspect | Recommendation |
|---|---|
| Real-time feasibility | IMU pre-integration Canada This step helps to minimize the optimization variables; run a sliding-window optimizer (e.g. 10-20 keyframes). |
| Computational load | Off load the heavy Sonar Image processing to GPU, leave the filter core for the CPU. |
| Robustness to outliers | Gating Mahalanobis sonar residules, robust ones in graph optimization (Huber, Cauchy) |
| Failure detection | Keep track of innovation metrics; revert to pure IMU dead-reckoning as the sonar quality goes bad (e.g. high reverberation). |
8. Benefits and Challenges
Benefits
- Drift minimization – sonar has definite limits restricting IMU integration error.
- All weather operation – acoustic sensing can operate in turbid and dark water where visual SLAM does not work.
- Better quality of map – sonar-based depth readings enhance reconstructions of 3-D especially in feature-deprived scenes.
Challenges
- Low resolution & noisy – acoustic measurements are crude; complex feature extraction and outlier rejection is needed.
- Multipath & reverberation – May cause biased estimate of range, Modeling of Acoustic propagation helps.
- Temporal asynchrony – IMU can operate at frequencies above 200Hz and sonar can utilize a lower frequency of up to 10Hz; interpolation is required.
9. Representative Applications
| Application | The benefits of Sonar-Inertial Fusion |
|---|---|
| Hull inspection | Accurate pose estimation makes it possible to reconstruct ship hulls with high resolution in 3-D with low light conditions. |
| Cave / wreck exploration | Where GPS and visual data are missing, sonar provides geometry: IMU provides a continuous line between the shots of sonar. |
| Pipeline / cable following | DVL’s style of acoustic velocity in combination with IMU reduces dead reckoning quite well on long linear structures. |
| Seafloor mapping | Multibeam sonar carries with it a dense bathymetry; IMU carries with it an attitude to allow an accurate georeferencing. |
10. Future Trends
- Learning based sensor models – Deep networks that are meant to learn aspects of sonar measurement noise from raw sonar echoes to better weight filters.
- Hybrid acoustic-visual-inertial SLAM – Systems such as the SVIn2 are already contributing sonar, cameras, IMU, and pressure sensors; further effort is desired to incorporate further tightness and to introduce semantic meaning. 2
- Edge-computing platforms – Specialized ASICs to IMU pre-integration and sonar image processing will be able to perform the complete on-board functionality in real time.
- Adaptive fusion technologies – Context-based weighting of a strategy that automatically decreases the use of sonar during less favorable acoustic conditions (e.g. high reverberation levels).
11. Summary
Sonar-inertial fusion is a technology that relies upon the merits of inertial measurement rate and high-quality acoustic ranging in order to provide a wide-band, real-time inside-the-water-robot navigation. A tightly tightly coupled estimation framework, combined with carefully preprocessed and calibrated measurements with outlier rejection can typically be offered by EKF/UKF or Factor-graph optimizer has an important role in providing reliability in the challenging marine environment. Currently, there is activity in the direction of more closely integrated systems and models better optimized to support learning as well as real-time edge systems, making sonar-inertial fusion one of the pillars on which future generation autonomous underwater systems will be built.
References
- Fomekong Fomekong Rachel Merveille, Baozhu Jia, Zhizun Xu, and Bissih Fred. “Advancements in Sensor Fusion for Underwater SLAM: A Review on Enhanced Navigation and Environmental Perception.” P. 3, Sensors, vol. 24, no. 23, 2024, p. 7490. MDPI, https://doi.org/10.3390/s24237490
- Sharmin Rahman , Alberto Quattrini Li, and Ioannis Rekleitis. “SVIn2: Sonar Visual-Inertial SLAM with Loop Closure for Underwater Navigation.” arXiv, 7 Oct. 2018, https://arxiv.org/abs/1810.03200.