Navigation Solution Research Articles

From Algorithm to Module: Adaptive and Energy-Efficient Quantization Method for Edge Artificial Intelligence in IoT Society

Next-generation industrial edge artificial intelligence (AI) applications will undoubtedly emerge on energy-efficient, highly-integrated platforms incorporating various sensors, processors, and functional modules. Effectively bridging sensor data captured from a microprocessor or central processing unit with dedicated processing modules is still being studied in academia and industry. Therefore, embedding the data quantization module onto edge AI chips, connecting sensors, processors, and functional modules, is critical to achieving adaptive transformation of diverse data representation formats. This paper proposes a novel adaptive and low-power quantization technique and systematically validates its effectiveness from algorithm to hardware module for industrial IoT applications, covering precise navigation for autonomous vehicles and accurate classification utilizing deep neural networks (DNNs). The proposed quantization method merges an adaptive conversion function from floating-point to fixed-point binaries and an adaptive radix-point determination function, ensuring adequate resolution and minimal error loss of the fixed-point inputs to the edge AI modules. The experimental results demonstrate that the quantization error in the proposed quantization technique contributes negligible errors to the navigation solutions of the strapdown inertial navigation system and the DNNs' top-1 and top-5 classification accuracy (on the order of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-8}$</tex-math></inline-formula> and 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-7}$</tex-math></inline-formula> ). Moreover, a quantization-on-multiplier (QoM) hardware module is designed, synthesized, and routed in accordance with the proposed quantization technique. The simulation results indicate that the QoM's power consumption and area are 0.1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$mW$</tex-math></inline-formula> and 649.552 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu m^{2}$</tex-math></inline-formula> , accounting for 5% and 14.15% of its total energy consumption and area, respectively. With our proposed on-chip quantization technique, the time required to quantize the parameters of DNNs is up to 1142 times shorter than with the existing benchmark off-chip quantization approaches.

A Secure ZUPT-Aided Indoor Navigation System Using Blockchain in GNSS-Denied Environments.

This paper proposes a novel Blockchain-based indoor navigation system that combines a foot-mounted dual-inertial measurement unit (IMU) setup and a zero-velocity update (ZUPT) algorithm for secure and accurate indoor navigation in GNSS-denied environments. The system estimates the user's position and orientation by fusing the data from two IMUs using an extended Kalman filter (EKF). The ZUPT algorithm is employed to detect and correct the error introduced by sensor drift during zero-velocity intervals, thus enhancing the accuracy of the position estimate. The proposed Low SWaP-C blockchain-based decentralized architecture ensures the security and trustworthiness of the system by providing an immutable and distributed ledger to store and verify the sensor data and navigation solutions. The proposed system is suitable for various indoor navigation applications, including autonomous vehicles, robots, and human tracking. The experimental results provide clear and compelling evidence of the effectiveness of the proposed system in ensuring the integrity, privacy, and security of navigation data through the utilization of blockchain technology. The system exhibits an impressive ability to process more than 680 transactions per second within the Hyperledger-Fabric framework. Furthermore, it demonstrates exceptional accuracy and robustness, with a mean RMSE error of 1.2 m and a peak RMSE of 3.2 during a 20 min test. By eliminating the reliance on external signals or infrastructure, the system offers an innovative, practical, and secure solution for indoor navigation in environments where GNSS signals are unavailable.

Rapid and Accurate INS Transfer Alignment for Air Launched Tactical Missile Using Kalman Filter

An Inertial Navigation System (INS) independently measures the Position, Velocity, and Attitude (PVA) of thevehicle to navigate it towards the target. Since INS is a dead-reckoning system, it requires accurate initialization toprovide the navigation (PVA) solution. In the case of an air-launched tactical missile, the aircraft navigation system(Master INS) information is used to initialize accurately the missile INS (Slave INS). Rapid transfer alignment isneeded in today’s combat operation to converge slave INS initialization in the shortest possible time using aircraftnavigation information. The transfer alignment consists of first initializing the missile INS and establishing anavigation solution (PVA) using the missile IMU rates and accelerations, then a Kalman filter is used to, estimatethe errors between the Slave INS and Master INS. The proposed method’s simulation results show that a tacticalmissile INS can be aligned to an acceptable accuracy in a very short time based on the aircraft’s attitude information and with natural maneuvers experienced during aircraft take-off.

Survey of Relative Navigation Methods for Multi-Agent Unmanned Aerial Vehicle Systems

Multi-agent Unmanned Aerial Vehicle (UAV) systems require stable and high-precision navigation. The existing navigation solutions, such as global navigation satellite systems (GNSS) and inertial navigation systems, may perform inefficiently in some application scenarios. The relative navigation methods can help solve this problem. Relative navigation enables UAVs to precisely estimate their positions relative to each other, as opposed to absolute navigation, which calculates the UAVs’ position relative to the Earth. Despite the abundance of relative navigation articles, there are no systematic reviews of relative navigation methods. Additionally, various articles on relative navigation use a variety of terms for comparable concepts, which makes it more difficult to understand the subject. Therefore, this review comprehensively studies systematizes relative navigation methods, and analyzes their strengths and weaknesses. We categorize relative navigation methods appropriate for multi-UAV systems, compare them, and make conclusions based on our findings. The relative navigation methods discussed in this review include differential GNSS, radio-frequency-based, visual, and their combinations. We evaluate the achievable accuracy and range for each type of method according to related studies. We also describe the limitations and vulnerabilities of each method. As a result, we outline relative navigation’s primary capabilities and assess its condition now.

A Hybrid CNN-LSTM-Based Approach for Pedestrian Dead Reckoning Using Multi-Sensor-Equipped Backpack

Researchers in academics and companies working on location-based services (LBS) are paying close attention to indoor localization based on pedestrian dead reckoning (PDR) because of its infrastructure-free localization method. PDR is the fundamental localization technique that utilize human motion to perform localization in a relative sense with respect to the initial position. The size, weight, and power consumption of micromechanical systems (MEMS) embedded into smartphones are remarkably low, making them appropriate for localization and positioning. Traditional pedestrian PDR methods predict position and orientation using stride length and continuous integration of acceleration in step and heading system (SHS)-based PDR and inertial navigation system (INS)-PDR, respectively. However, these two approaches provide accumulations of error and do not effectively leverage the inertial measurement unit (IMU) sequences. The PDR navigation solution relays on the standard of the MEMS, which yields PDR with the acceleration and angular velocity from the accelerometer and gyroscope, respectively. However, low-cost small MEMSs endure enormous error sources such as bias and noise. Hence, MEMS assessments lead to navigation solution drifts when utilized as inputs to the PDR. As a consequence, numerous methods have been proposed to mitigate and model the errors related to MEMS. Deep learning-based dead reckoning algorithms are provided to address aforementioned issues owing to the end-to-end learning framework. This paper proposes a hybrid convolutional neural network (CNN) and long short-term memory network (LSTM)-based inertial PDR system that extracts inertial measurement units (IMU) sequence features. The end-to-end learning framework is introduced to leverage the efficiency of low-cost MEMS because data-driven solutions provide more complete knowledge of the ever-increasing data volume and computational power over the filtering model approach. A CNN-LSTM model was employed to capture local spatial and temporal features. Experiments conducted on odometry datasets collected from multi-sensor backpack devices demonstrated that the proposed architecture outperformed previous traditional PDR methods, demonstrating that the root mean square error (RMSE) for the best user was 0.52 m. On the handheld smartphone-only dataset the best achieved R2 metric was 0.49.

The Use of Artificial Intelligence Approaches for Performance Improvement of Low-Cost Integrated Navigation Systems.

In this paper, the authors investigate the possibility of applying artificial intelligence algorithms to the outputs of a low-cost Kalman filter-based navigation solution in order to achieve performance similar to that of high-end MEMS inertial sensors. To further improve the results of the prototype and simultaneously lighten filter requirements, different AI models are compared in this paper to determine their performance in terms of complexity and accuracy. By overcoming some known limitations (e.g., sensitivity on the dimension of input data from inertial sensors) and starting from Kalman filter applications (whose raw noise parameter estimates were obtained from a simple analysis of sensor specifications), such a solution presents an intermediate behavior compared to the current state of the art. It allows the exploitation of the power of AI models. Different Neural Network models have been taken into account and compared in terms of measurement accuracy and a number of model parameters; in particular, Dense, 1-Dimension Convolutional, and Long Short Term Memory Neural networks. As can be excepted, the higher the NN complexity, the higher the measurement accuracy; the models' performance has been assessed by means of the root-mean-square error (RMSE) between the target and predicted values of all the navigation parameters.

Semantic-Aware Path Planning with Hexagonal Grids and Vehicle Dynamic Constraints

The article presents a navigation system that utilizes a semantic map created on a hexagonal grid. The system plans the path by incorporating semantic and metric information while considering the vehicle’s dynamic constraints. The article concludes by discussing a low-level control algorithm used in the system. This solution’s advantages include using a semantic map on a hexagonal grid, which enables more efficient and accurate navigation. Creating a map of allowable speeds based on the semantic map provides an additional layer of information that can help optimize the vehicle’s trajectory. Incorporating both semantic and metric information in the path-planning process leads to a more precise and tailored navigation solution that accounts for the vehicle’s capabilities and the environment it is operating in. Finally, the low-level control algorithm ensures that the vehicle follows the planned trajectory while considering real-time sensor data and other factors affecting its movement. Through this article, we aim to provide insights into the cutting-edge advancements in path planning techniques and shed light on the potential of combining hexagonal grids, vehicle dynamics constraints, and semantic awareness. These innovations have the potential to revolutionize autonomous navigation systems, enabling vehicles to navigate complex environments with greater efficiency, safety, and adaptability.

Enhanced Autonomous Vehicle Positioning Using a Loosely Coupled INS/GNSS-Based Invariant-EKF Integration.

High-precision navigation solutions are a main requirement for autonomous vehicle (AV) applications. Global navigation satellite systems (GNSSs) are the prime source of navigation information for such applications. However, some places such as tunnels, underpasses, inside parking garages, and urban high-rise buildings suffer from GNSS signal degradation or unavailability. Therefore, another system is required to provide a continuous navigation solution, such as the inertial navigation system (INS). The vehicle's onboard inertial measuring unit (IMU) is the main INS input measurement source. However, the INS solution drifts over time due to IMU-associated errors and the mechanization process itself. Therefore, INS/GNSS integration is the proper solution for both systems' drawbacks. Traditionally, a linearized Kalman filter (LKF) such as the extended Kalman filter (EKF) is utilized as a navigation filter. The EKF deals only with the linearized errors and suppresses the higher orders using the Taylor expansion up to the first order. This paper introduces a loosely coupled INS/GNSS integration scheme using the invariant extended Kalman filter (IEKF). The IEKF state estimate is independent of the Jacobians that are derived in the EKF; instead, it uses the matrix Lie group. The proposed INS/GNSS integration using IEKF is applied to a real road trajectory for performance validation. The results show a significant enhancement when using the proposed system compared to the traditional INS/GNSS integrated system that uses EKF in both GNSS signal presence and blockage cases. The overall trajectory 2D-position RMS error reduced from 19.4 m to 3.3 m with 82.98% improvement and the 2D-position max error reduced from 73.9 m to 14.2 m with 80.78% improvement.

Satellite navigation method based on high-speed frequency hopping signal

Global navigation satellite system has been widely used, but it is vulnerable to jamming. In military satellite communications, frequency hopping (FH) signal is usually used for anti-jamming communications. If the FH signal can be used in satellite navigation, the anti-jamming ability of satellite navigation can be improved. Although a recently proposed time-frequency matrix ranging method (TFMR) can use FH signals to realize pseudorange measurement, it cannot transmit navigation messages using the ranging signal which is crucial for satellite navigation. In this article, we propose dual-tone binary frequency shift keying-based TFMR (DBFSK-TFMR). DBFSK-TFMR designs an extended time-frequency matrix (ETFM) and its generation algorithm, which can use the frequency differences in different dual-tone signals in ETFM to modulate data and eliminate the negative impact of data modulation on pseudorange measurement. Using ETFM, DBFSK-TFMR not only realizes the navigation message transmission but also ensures the precision and unambiguous measurement range of pseudorange measurement. DBFSK-TFMR can be used as an integrated solution for anti-jamming communication and navigation based on FH signals. Simulation results show that DBFSK-TFMR has almost the same ranging performance as TFMR.

Low-Cost Onboard Multisensor State Estimator Based on Global Mixed Sampling Optimization Filter

Long-term convergent and accurate state estimation( attitude, velocity, and position) is critical to unmanned aerial vehicles (UAVs). However, the measurement accuracy and noise of multiple low-cost sensors onboard are poorer compared to high-precision sensors. To improve the solution accuracy and reliability of UAVs state estimation based on the low-cost sensors, a two-step multi-sensor fusion estimator (federated mixed-sampling Kalman filter, FMSKF) is proposed. Firstly, a multi-sensor integrated navigation model array is designed depending on the different sensors, including the gyroscope, accelerometer, magnetometer, GPS module, and barometer. Then, a three-stage mixed sampling Kalman filter is proposed to obtain the local convergent state vector, which is difficult to meet the flight accuracy requirements. Therefore, a multi-sensor global information optimization filter is proposed to obtain the global convergent navigation solution parameters. Finally, the simulation and flight experimental results and detailed analysis demonstrate that the proposed algorithm can improve the state estimation accuracy, filtering robustness, and obtain desirable navigation performance.

Data-driven denoising of stationary accelerometer signals

Modern navigation solutions are largely dependent on the performances of the standalone inertial sensors, especially at times when no external sources are available. During these outages, the inertial navigation solution is likely to degrade over time due to instrumental noises sources, particularly when using consumer low-cost inertial sensors. Conventionally, model-based estimation algorithms are employed to reduce noise levels and enhance meaningful information, thus improving the navigation solution directly. However, guaranteeing their optimality often proves to be challenging as sensors performance differ in manufacturing quality, process noise modeling, and calibration precision. In the literature, most inertial denoising models are model-based when recently several data-driven approaches were suggested primarily for gyroscope measurements denoising. Data-driven approaches for accelerometer denoising task are more challenging due to the unknown gravity projection on the accelerometer axes. To fill this gap, we propose several learning-based approaches and compare their performances with prominent denoising algorithms, in terms of pure noise removal, followed by stationary coarse alignment procedure. Based on the benchmarking results, obtained in field experiments, we show that the learning-based models outperform traditional signal processing filtering in terms of pure inertial signal reconstruction. Moreover, they are shown to improve angular errors by one order of magnitude, given a navigation-related task.

Weight Factor Graph Co-Location Method for UAV Formation Based on Navigation Performance Evaluation

At present, multiple unmanned aerial vehicles (UAVs) collaboration have attracted people’s more and more attention. The abundant relative distance information in UAV cooperative network can be employed to further improve UAV’s positioning accuracy. However, the traditional distance-based cooperative localization (CL) algorithm does not consider the performance of cooperative navigation information. Cooperative information with poor navigation performance will affect follower UAV’s state estimation accuracy. Thus, this paper proposes a weight factor graph CL method based on navigation performance evaluation. A novel navigation performance evaluation strategy based on Fisher information and relative entropy is proposed. The distance observations and cooperative nodes’ positions with higher estimation accuracy and contribution are selected to estimate follower UAV’s position. Considering the difference contributions of the selected cooperative information to follower UAV’s state estimation, we employ the information weight processing to achieve higher state estimation accuracy. Based on the selected cooperative information and weight coefficient, a multi-UAVs cooperative optimization graph model based on navigation performance is constructed. The global optimization cost function is constructed using relative distance constraints from the current time to historical time in the sliding window. The global optimal navigation solution of follower UAV is achieved using iterative weighted least squares method. Simulation and experiment results show that the proposed navigation performance evaluation strategy can effectively screen cooperative information with higher estimation accuracy and contribution for CL. Using the selected high-quality cooperative information, the system computational complexity is reduced without significantly affecting system positioning accuracy.

Performance evaluation of coarse alignment methods for autonomous underwater vehicles in mooring conditions

The coarse alignment stage of inertial navigation systems (INS) is a step of paramount importance, specially for vehicles that employ the latter as a reference navigation solution, as is the case of autonomous underwater vehicles (AUVs). For such class of vehicles, the alignment has encumbrances that goes beyond those usually reported for terrestrial and aerial systems, as AUVs generally align at non benign environments (e.g., under swaying and mooring conditions) and have limited auxiliary navigation sensors. This work, hence, proposes a comparative analysis of the most representative coarse alignment methods applied to AUVs in mooring condition. The alignment approach herein explored, throughout its optimized and non-optimized versions, is the attitude decomposition-based initial alignment (ADIA) method, and the proposed comparison procedure tests different types of observation vectors resolved in the frames of interest. Experimental tests are conducted, which are based on kinematic data collected from an unmanned marine vehicle representing the typical swaying and attitude oscillations of AUVs in the mooring state, i.e., when subject to wave induced disturbances. Results lead to practical conclusions that can be applied to the AUV initial attitude estimation and are related to autonomy, accuracy and precision of the methods, as well as to their convergence rate and computational effort.

Improving Self-Consistency in Underwater Mapping Through Laser-Based Loop Closure

Accurate, self-consistent bathymetric maps are needed to monitor changes in subsea environments and infrastructure. These maps are increasingly collected by underwater vehicles, and mapping requires an accurate vehicle navigation solution. Commercial off-the-shelf (COTS) navigation solutions for underwater vehicles often rely on external acoustic sensors for localization; however, survey-grade acoustic sensors are expensive to deploy and limit the range of the vehicle. Techniques from the field of simultaneous localization and mapping, particularly loop closures, can improve the quality of the navigation solution over dead reckoning, but are difficult to integrate into COTS navigation systems. This article presents a method to improve the self-consistency of bathymetric maps by smoothly integrating loop-closure measurements into the state estimate produced by a commercial subsea navigation system. Integration is done using a white-noise-on-acceleration motion prior, without access to raw sensor measurements or proprietary models. Improvements in map self-consistency are shown for both simulated and experimental datasets, including a 3-D scan of an underwater shipwreck in Wiarton, ON, Canada.

SBAS-based navigation system for precision approach in CAT II LVC

Due to lack of advanced navigation systems, secondary airports are normally unable to support instrument approaches in low visibility conditions (LVC) more adverse than Category (CAT) I, making them inaccessible during such conditions. Incoming flights are then delayed, diverted to adjacent airports, or cancelled before take-off. This paper presents an onboard navigation solution, under development in scope of SESAR 2020 Solution PJ02-W2- 17.2, which focuses on technology development to mitigate these traffic disruptions by enabling instrument approaches in CAT II LVC with minimum airport and air navigation service provider investments. The concept builds upon global navigation satellite systems (Global Positioning System L1 frequency – GPS L1, satellite-based augmentation system), which currently enables Localizer Performance with Vertical guidance (LPV) operation down to LPV 200 minima. The designed system includes radio altimeter-based aiding and innovative integrity algorithm to improve navigation performance in support of operations below 200ft down to CAT II / LPV 100 minima. As no such requirements have yet been officially published, authors also defined sets of candidates based on Instrument Landing System Collision Risk Model and other sources. The team developed and verified a Monte-Carlo fast-time simulation toolset to enable representative and statistically significant evaluation of the concept feasibility via its availability throughout Europe, as well as sensitivity to proposed sets of alert limits. Also, flight data collection and a developed software prototype allow for further validations. Simulations demonstrated over 95% average availability with the best results achieving level of 99% depending on used set of requirements. The solution enabling operations in LVC allows unlocking various benefits to business/airline operators (e.g., avoided extra costs, increased predictability), passengers (avoided opportunity loss) and airports (retained profit from flights, less traffic at diversion airports). Technology development also marks an important step towards gate-to-gate autonomous operations.

Hybrid Navigation Prototype for Small Aircraft Transportation Vehicles

The Small Aircraft Transportation (SAT) segment represented mainly by helicopters, piston fixed-wing aircraft, turboprop aircraft, and business jets requires a reliable source of navigation information with an appropriate price. This paper describes the research and development activity funded by Clean Sky 2 Cost Optimized Avionic Systems (COAST) development program targeting affordable hybrid navigation solutions. The affordability is driven by size, weight, and power consumption (SWAP) requirements. The desired level of accuracy, integrity, and availability is being achieved by a hybrid navigation solution based on GPS/INS fusion extended by other navigation sensors. The hybrid core of the systems uses GPS with SBAS augmentation to outperform standard tightly coupled GPS-based hybrid systems. The purpose of this article is to describe the current state, algorithmic structure, and hardware maturity of the navigation system prototype. The paper describes individual hardware components, points to the resulting prototype, and summarizes tests in a representative environment. The ultimate goal is to demonstrate the overall performance of the hybrid system based on a low-cost micro-electro-mechanical system (MEMS) Inertial Measurement Unit (IMU). The low-cost inertial sensor is one of the key components securing the affordability of the proposed system, so its testing plays important role. Another assumption considered in the system design was integration of standardly-used onboard sensors. For this purpose, the hardware prototype was tested in a demonstrative and outdoor environment. The results of this exercise are summarized in this paper.

Know What You Don't Know: Consistency in Sliding Window Filtering With Unobservable States Applied to Visual-Inertial SLAM

Estimation algorithms, such as the sliding window filter, produce an estimate and uncertainty of desired states. This task becomes challenging when the problem involves unobservable states. In these situations, it is critical for the algorithm to “know what it doesn't know”, meaning that it must maintain the unobservable states as unobservable during algorithm deployment. This letter presents general requirements for maintaining consistency in sliding window filters involving unobservable states. The value of these requirements for designing navigation solutions is experimentally shown within the context of visual-inertial SLAM making use of IMU preintegration.

Development and testing of a navigation solution for Autonomous Underwater Vehicles based on stereo vision

Autonomous Underwater Vehicles (AUVs) employed for inspection and monitoring applications require a reliable estimate of their navigation status to successfully accomplish the scheduled mission. Considering that they are typically endowed with vision systems to collect images of the surveyed environment, approaches based on Visual Odometry (VO) allow to utilise the optical payload also to perform robot navigation. Despite a large body of prior research, the topic of navigation based on stereo vision is still an open problem in the marine domain. Within this context, this paper proposes an underwater navigation framework utilising a stereo camera as a linear velocity sensor. The purpose is to assess the potentiality of a stereo vision system to indirectly measure the linear velocity of an AUV, and provide this information to the navigation framework of the vehicle. The proposed strategy consists in a visual inertial odometry solution fusing linear velocity estimates, derived from optical information, with attitude and depth measurements to retrieve the robot navigation status. Such linear velocity estimates are computed exploiting a stereo VO algorithm, relying on a 3D-to-2D approach, whose source code is made available online. The developed strategy is evaluated on real underwater datasets acquired during monitoring surveys performed by an AUV equipped with Doppler Velocity Log (DVL), bottom-looking stereo camera, inertial unit, and depth sensor. The results, obtained through a comparison with the DVL taken as benchmark, confirm the approach as feasible and exploitable in underwater inspection and monitoring contexts.

Exploring Sign System Design for a Medical Facility: A Virtual Environment Study on Wayfinding Behaviors

The National Taiwan University Hospital (NTUH) is a significant institution in modern medicine in Taiwan. Its West Campus, the oldest medical center in the country, has been recognized as a municipal historic site due to its architectural and historical importance. However, visitors have faced navigation difficulties for a long time. To address this issue, a study was conducted to find navigation solutions within the constraints of architectural structure, hardware, and busy crowds. Blender and Unity were used to recreate the environment, and interactive virtual wayfinding experiments were conducted with 64 participants divided into two groups. Each group completed 12 tasks in two scenarios, and their task performance, wayfinding behavior, and questionnaire responses were collected to evaluate the overall environment. The pretest helped identify problems in the existing signage system and weak areas, leading to redesigning of a new signage system. The main objective of the posttest was to evaluate the new design’s effectiveness. Our research contributes to future signage system layout design references, enhancing readability and information coherence while recommending locations within medical facilities. We set specific design standards to facilitate wayfinding signage systems in complex environments.

Drift Reduction in Underwater Egomotion Computation by Axial Camera Modeling

Localization of autonomous underwater vehicles is essential for underwater exploration, environmental monitoring, and infrastructure inspections, as only a few examples. As wirelessly transmitted data cannot be used in underwater navigation, and equivalent sensors are costly and not readily deployable, the use of cameras as a localization aid offers an attractive alternative. Nonetheless, the utilization of cameras for underwater navigation is hindered by medium-induced visual deterioration and refraction of the incident ray. While most research has been focusing on addressing the radiometric deterioration effects, we demonstrate that the introduction of a physically aware model of the refraction effect can significantly improve the platform localization. Specifically, we develop a refraction-aware continuous formulation of the egomotion model, which computes the translational and rotational velocities using optical flow measurements. We also demonstrate that a linear model can be reached despite the nonlinear ray's path. Results show an improved navigation solution echoed by a significant reduction in the drift with more than tenfold improvement in the estimated position and angular quantities compared to state-of-the-art methods. They demonstrate the benefit of exact modeling in underwater navigation.