Position Estimation Research Articles

Sensorless Position Control in High-Speed Domain of PMSM Based on Improved Adaptive Sliding Mode Observer

To improve the speed buffering and position tracking accuracy of medium–high-speed permanent magnet synchronous motor (PMSM), a sensorless control method based on an improved sliding mode observer is proposed. By the mathematical model of the built-in PMSM, an improved adaptive super-twisting sliding mode observer is constructed. Based on the LSTA-SMO with a linear term of observation error, a sliding mode coefficient can be adjusted in real time according to the change in rotational speed. In view of the high harmonic content of the output back electromotive force, the adaptive adjustment strategy for the back electromotive force is adopted. In addition, in order to improve the estimation accuracy and resistance ability of the observer, the rotor position error was taken as the disturbance term, and the third-order extended state observer (ESO) was constructed to estimate the rotational speed and rotor position through the motor mechanical motion equation. The proposed method is validated in Matlab and compared with the conventional linear super twisted observer. The simulation results show that the proposed method enables the observer to operate stably in a wide velocity domain and reduces the velocity estimation error to 6.7 rpm and the position estimation accuracy error to 0.0005 rad at high speeds, which improves the anti-interference capability.

Pseudorandom high‐frequency injection synchronous reluctance motor sensorless control with parameter variation consideration

AbstractThe sensorless control of synchronous reluctance motor (SynRM) in the zero and low‐speed domain using the traditional high‐frequency injection method has the problems of audible noise caused by the high‐frequency injection and high‐frequency loss caused by the change of working conditions, which limits the practical application of SynRM in the industrial field. To solve the problem of high‐frequency noise and loss, a pseudo‐random high‐frequency injection method considering parameter variation is proposed in this paper. Firstly, the signal injection form was adjusted to expand the power spectral density of the high‐frequency current, and the current energy spike was suppressed to reduce high‐frequency noise. Secondly, the current demodulation was combined with the flux map model to complete the injection voltage amplitude adjustment, so that the response current was kept constant under multiple operating conditions to reduce the high‐frequency loss. At the same time, the flux map model is applied to the observer to reduce the rotor position estimation error caused by the cross‐coupling effect. Under the condition of satisfying the dynamic and steady performance requirements of sensorless control, the high‐frequency loss and sharp noise caused by the high‐frequency injection method are effectively suppressed. Finally, experiments were carried out on a 1.5 kW SynRM drive platform to verify the feasibility and effectiveness of the sensorless control scheme in this paper.

Differential Positioning with Bluetooth Low Energy (BLE) Beacons for UAS Indoor Operations: Analysis and Results

Localization of unmanned aircraft systems (UASs) in indoor scenarios and GNSS-denied environments is a difficult problem, particularly in dynamic scenarios where traditional on-board equipment (such as LiDAR, radar, sonar, camera) may fail. In the framework of autonomous UAS missions, precise feedback on real-time aircraft position is very important, and several technologies alternative to GNSS-based approaches for UAS positioning in indoor navigation have been recently explored. In this paper, we propose a low-cost IPS for UAVs, based on Bluetooth low energy (BLE) beacons, which exploits the RSSI (received signal strength indicator) for distance estimation and positioning. Distance information from measured RSSI values can be degraded by multipath, reflection, and fading that cause unpredictable variability of the RSSI and may lead to poor-quality measurements. To enhance the accuracy of the position estimation, this work applies a differential distance correction (DDC) technique, similar to differential GNSS (DGNSS) and real-time kinematic (RTK) positioning. The method uses differential information from a reference station positioned at known coordinates to correct the position of the rover station. A mathematical model was established to analyze the relation between the RSSI and the distance from Bluetooth devices (Eddystone BLE beacons) placed in the indoor operation field. The master reference station was a Raspberry Pi 4 model B, and the rover (unknown target) was an Arduino Nano 33 BLE microcontroller, which was mounted on-board a UAV. Position estimation was achieved by trilateration, and the extended Kalman filter (EKF) was applied, considering the nonlinear propriety of beacon signals to correct data from noise, drift, and bias errors. Experimental results and system performance analysis show the feasibility of this methodology, as well as the reduction of position uncertainty obtained by the DCC technique.

Tightly Coupled LIDAR/IMU/UWB Fusion via Resilient Factor Graph for Quadruped Robot Positioning

Continuous accurate positioning in global navigation satellite system (GNSS)-denied environments is essential for robot navigation. Significant advances have been made with light detection and ranging (LiDAR)-inertial measurement unit (IMU) techniques, especially in challenging environments with varying lighting and other complexities. However, the LiDAR/IMU method relies on a recursive positioning principle, resulting in the gradual accumulation and dispersion of errors over time. To address these challenges, this study proposes a tightly coupled LiDAR/IMU/UWB fusion approach that integrates an ultra-wideband (UWB) positioning technique. First, a lightweight point cloud segmentation and constraint algorithm is designed to minimize elevation errors and reduce computational demands. Second, a multi-decision non-line-of-sight (NLOS) recognition module using information entropy is employed to mitigate NLOS errors. Finally, a tightly coupled framework via a resilient mechanism is proposed to achieve reliable position estimation for quadruped robots. Experimental results demonstrate that our system provides robust positioning results even in LiDAR-limited and NLOS conditions, maintaining low time costs.

An Algorithm for Affordable Vision-Based GNSS-Denied Strapdown Celestial Navigation

Celestial navigation is rarely seen in modern Uncrewed Aerial Vehicles (UAVs). The size and weight of a stabilized imaging system, and the lack of precision, tend to be at odds with the operational requirements of the aircraft. Nonetheless, celestial navigation is one of the few non-emissive modalities that enables global navigation over the ocean at night in Global Navigation Satellite System (GNSS) denied environments. This study demonstrates a modular, low cost, lightweight strapdown celestial navigation solution that is utilized in conjunction with Ardupilot running on a Cube Orange to produce position estimates to within 4 km. By performing an orbit through a full rotation of compass heading and averaging the position output, we demonstrate that the biases present in a strapdown imaging system can be nullified to drastically improve the position estimate. Furthermore, an iterative method is presented which enables the geometric alignment of the camera with the Attitude and Heading Reference System (AHRS) in-flight without an external position input. The algorithm is tested using real flight data captured from a fixed wing aircraft. The results from this study offer promise for the application of low cost celestial navigation as a redundant navigation modality in affordable, lightweight drones.

Experimental assessment of IMU data processing techniques for a backpack mobile laser scanning system

Abstract. Positioning techniques are fundamental in many automation tasks with several applications. In GNSS-denied environments like in dense forests, other alternatives are required, such as inertial and visual navigation. However, Inertial Measurement Units (IMUs) data, mainly those from microelectromechanical-system (MEMS), are noisy, which affects the orientation estimation. MEMS IMUs have been employed in mobile laser scanning systems due to their compact design and low-cost solutions for short-term navigation. In this paper, we have compared three IMU processing techniques freely available: MAH (Mahony et al., 2009), MAD (Madgwick et al., 2011) and DCM (Hyyti and Visala, 2015). These techniques implemented different approaches to estimate the attitude. They were experimentally assessed with data from a backpack mobile laser scanning system, which is composed of an OS0-128 Ouster LiDAR equipped with an internal IMU. We have used data from a 5-second trajectory segment aiming to evaluate the attitude and position estimation for a local path. The results showed that the DCM algorithm maintained a consistent velocity for 5 seconds, achieving a positional error of 1.4 m, 0.06 m, and 1.05 m along the X-, Y- and Z-axis, respectively. In contrast, MAD and MAH showed a position error over 20 m, 7 m and 3 m along the X-, Y- and Z-axis, respectively, which was affected by the velocity drift.

3D in-system calibration method for PET detectors.

Light-sharing detector designs for positron emission tomography (PET) systems have sparked interest in the scientific community. Particularly, (semi-)monoliths show generally good performance characteristics regarding 2D positioning, energy-, and timing resolution, as well as readout area. This is combined with intrinsic depth-of-interaction (DOI) capability to ensure a homogeneous spatial resolution across the entire field of view (FoV). However, complex positioning calibration processes limit their use in PET systems, especially in large-scale clinical systems. This work proposes a new 3D positioning in-system calibration method for fast and convenient (re-)calibration and quality control of assembled PET scanners. The method targets all kinds of PET detectors that achieve the best performance with individual calibration, including complex segmented detector designs. The in-system calibration method is evaluated and empirically compared to a state-of-the-art fan-beam calibration for a small-diameter proof of concept (PoC) scanner. A simulation study evaluates the method's applicability to different scanner geometries. A PoC scanner geometry of 120mm inner diameter and 150mm axial extent was set up consisting of five identical finely segmented slab detectors (one detector under test and four collimation detectors). A 2 2Na point source was moved in a circular path inside the FoV. Utilizing virtual collimation and by selecting gamma rays incident approximately perpendicular to the detector normal of the detector under test, training data was created for the training of a 2D positioning model with the machine-learning technique gradient tree boosting (GTB). Data with oblique ray angles was acquired in the same measurement for subsequent angular DOI calibration. For this, a 2D position estimate in the detector under test was calculated first. On this basis, the DOI label was calculated geometrically from the ray path within the detector to finally establish up to 3D training data. With a mean absolute error (MAE) of 0.8 and 1.19mm full-width at half maximum (FWHM) along the planar-monolithic slab dimension, the in-system methods performed similarly within 1% to the fan-beam collimator results. The DOI performance was at ∼90% with 1.13mm MAE and 2.47mm FWHM to the fan-beam collimator. Analytical calculations suggest an improved performance for larger scanner geometries. The functionality of the 3D in-system positioning calibration method was successfully demonstrated with the measurements within a PoC scanner configuration with similar positioning performance as the bench-top fan-beam setup. The in-system calibration method can be used to calibrate and test fully assembled PET systems to enable more complex light-sharing detector architectures in, for example, large PET systems with many detectors. The acquired data can further be used for more complex energy and time calibrations.

Pulse position encoded RZ-OOK transmission for free-space optical communications

This paper proposes a pulse position encoded return-to-zero on-off keying (PP-RZ-OOK) transmission for free space optical (FSO) communications. At the transmitter end, PP-RZ-OOK signal is modulated by encoding the pulse position of RZ-OOK in the symbol duration. At the receiver end, PP-RZ-OOK signal is demodulated by symbol-by-symbol signal estimation. First, the existence of pulse is distinguished by adaptive threshold decision using the channel state information (CSI). Then, with respect to the symbol with the pulse, the knowledge of pulse position is estimated by slot-by-slot pulse power comparison. Finally, PP-RZ-OOK signal is effectively demodulated by both pulse existence and pulse position estimation. Therefore, the spectral efficiency of RZ-OOK is increased by the proposed pulse position encoding technique. The performance of the proposed PP-RZ-OOK modulation was verified through simulations under different turbulence channels and pulse durations, and it was compared with non-return-to-zero OOK (NRZ-OOK) and RZ-OOK modulations. The simulation results demonstrated that the capability of scintillation effect compensation was significantly enhanced compared with NRZ-OOK due to the pulse power increasing. Besides, the spectral efficiency was improved compared with RZ-OOK due to the additional pulse position encoding.

Vehicle trajectory extraction with interacting multiple model for low-channel roadside LiDAR

High-precision and consistent vehicle trajectories encompass microscopic traffic parameters, mesoscopic traffic flow characteristics, and macroscopic traffic flow features, which is the cornerstone of innovation in data-driven traffic management and control applications. However, occlusion and trajectory interruption remain challenging in multivehicle tracking under complex traffic environments using low-channel roadside LiDAR. To address the challenge, a novel framework for vehicle trajectory extraction using low-channel roadside LiDAR was proposed. First, the geometric features of the cluster and its L-shape bounding box were used to address the over-segmentation in vehicle detection arising from occlusion and point cloud sparse. Then, objects within adjacent point cloud frames were associated by developing an improved Hungarian algorithm integrated with an adaptive distance threshold to solve the mismatching problem caused by objects entrancing and exiting in a new point cloud frame. Finally, an improved interacting multiple model by considering vehicle driving patterns was deployed to predict the location of missing vehicles and connect the interrupted trajectories. Experimental results showed that the proposed methods achieve 98.76 % of vehicle detection accuracy and 97.40 % of data association precision. The mean absolute error (MAE) and mean square error (MSE) of the vehicle position estimation are 0.2252 m and 0.0729 m2, respectively. The trajectory extraction precision outperforms most of the state-of-the-art algorithms.

Statistical resolution analysis of microwave computational imaging

AbstractThis letter presents a model based on the Cramér–Rao bound theory for calculating the theoretical lower limit of imaging resolution of microwave computational imaging aided by re‐configurable metasurface. The model takes into account two crucial parameters: the signal‐to‐noise ratio and the number of measurements in the imaging process. By simultaneously considering the signal‐to‐noise ratio and the number of measurements, as well as other parameters, the model allows for a comprehensive assessment of the imaging resolution of the imaging system. In addition, both position estimation and intensity estimation are considered, and a new composite statistical resolution concept is proposed, which is more suitable for microwave computational imaging.

Optimizing Swim Pose Estimation and Performance Analysis Using AI and Predictive Analytics

Swim position estimation and performance analysis are critical for improving training outcomes and minimizing injury rates among swimmers of all skill levels. Traditional approaches rely heavily on manual video processing, which is timeconsuming and prone to human error, as well as biomechanical evaluations. Recent advances in artificial intelligence (AI) and predictive analytics have created new prospects for automating and improving these operations. The goal of this project is to create an artificial intelligence-powered swim position evaluation system that utilizes machine learning and computer vision techniques. The device monitors swimmers' activities in real time and gives exact feedback on technique, posture, and stroke efficiency. Predictive analytics improves this technique by predicting future trends and potential areas for development based on performance indicators and historical data. To provide precise, non-invasive human movement tracking in water, the proposed system employs biomechanical studies, deep learning models, and 3D pose estimation techniques

A New Intraocular Lens Power Formula Integrating an Artificial Intelligence-Powered Estimation for Effective Lens Position Based on Chinese Eyes.

To develop and evaluate a new intraocular lens (IOL) formula based on Chinese eyes. A training dataset of 709 eyes undergoing uneventful cataract surgery was used to train the algorithm for effective lens position estimation. The algorithm was then integrated with Gaussian optics to develop the new IOL formula (Jin-AI). From the same center, 177 eyes served as an internal test dataset. An independent dataset of 557 eyes served as an external test dataset. The standard deviation (SD) of prediction errors was compared among the Jin-AI formula, traditional third-generation formulas (SRK/T, Holladay 1, Hoffer Q), and newer generation formulas (Kane, Barrett Universal II [BUII], Hill-radial basis function [RBF] 3.0, and PEARL-DGS). In the internal test dataset, the Jin-AI formula showed the lowest SD (0.25 D), followed by the BUII (0.31 D), Kane (0.33 D), and PEARL-DGS (0.33 D) formulas. In the external test dataset, the Jin-AI, Kane, and PEARL-DGS formulas had the lowest SD (0.38 D), followed by the BUII (0.39 D), Hill-RBF 3.0 (0.39 D), SRK/T (0.45 D), Holladay 1 (0.48 D), and Hoffer Q (0.48 D) formulas. The SD of the Jin-AI formula was significantly lower than the third-generation formulas and comparable to the four newer generation formulas. Predictive accuracy of the Jin-AI formula was similar to the newer generation formulas across all axial length, keratometry, and anterior chamber depth ranges. The new formula has exhibited good performance in predicting postoperative refractions. Its overall predictive accuracy was better than the third-generation formulas and comparable to the newer generation ones. The Jin-AI formula could be a reliable alternative for IOL power calculation in Chinese.

Influence of Ocean Current Features on the Performance of Machine Learning and Dynamic Tracking Methods in Predicting Marine Drifter Trajectories

Accurately and rapidly predicting marine drifter trajectories under conditions of information scarcity is critical for addressing maritime emergencies and conducting marine surveys with resource-limited unmanned vessels. Machine learning-based tracking methods, such as Long Short-Term Memory networks (LSTM), offer a promising approach for trajectory prediction in such scenarios. This study combines satellite observations and idealized simulations to compare the predictive performance of LSTM with a resource-dependent dynamic tracking method (DT). The results indicate that when driven solely by historical drifter paths, LSTM achieves better trajectory predictions when trained and tested on relative trajectory intervals rather than the absolute positions of individual trajectory points. In general, LSTM provides a more accurate geometric pattern of trajectories at the initial stages of forecasting, while DT offers superior accuracy in predicting specific trajectory positions. The velocity and curvature of ocean currents jointly influence the prediction quality of both methods. In regions characterized by active sub-mesoscale dynamics, such as the fast-flowing and meandering Kuroshio Current and Kuroshio Current Extension, DT predicts more reliable trajectory patterns but lacks precision in detailed position estimates compared to LSTM. However, in areas dominated by the fast but relatively straight North Equatorial Current, the performance of the two methods reverses. The two methods also demonstrate different tolerances for noise and sampling intervals. This study establishes a baseline for selecting machine learning methods for marine drifter prediction and highlights the limitations of AI-based predictions under data-scarce and resource-constrained conditions.

An Improved Velocity-Aided Method for Smartphone Single-Frequency Code Positioning in Real-World Driving Scenarios

The availability of Global Navigation Satellite System (GNSS) raw observations in smartphones has driven research into low-cost GNSS solutions, especially in challenging urban environments, which have garnered significant attention from scholars in recent years. This study proposes an improved smartphone-based velocity-aided positioning method and conducts vehicle-mounted experiments in urban roads representing typical scenarios. The results show that when transitioning from low- to high-multipath environments, the number of visible satellites and carrier phase observations are highly sensitive to environmental factors, with frequent multipath effects. The introduction of robust pre-fit and post-fit residual algorithms has proven to be an effective quality control method. Additionally, using more refined observation models and appropriate parameter estimation algorithms led to a slight 6% improvement in velocity performance. The improved Kalman filter position estimation model (KFSPP-P) strategy, by incorporating velocity uncertainty into the state estimation process, overcomes the limitations of conventional velocity-aided smartphone positioning methods (KFSPP-V) in complex urban environments. In low-multipath environments, the accuracy of the KFSPP-P strategy is comparable to that of KFSPP-V, with an approximate 8% improvement in horizontal accuracy. However, in more challenging environments, such as tree-lined roads and urban environments, the KFSPP-P strategy shows significant improvements, particularly enhancing horizontal positioning accuracy by approximately 50%. These advancements demonstrate the potential of using smartphones to provide reliable positioning services in complex urban environments.

An estimation method for vision-based autonomous landing system for fixed wing aircraft

In this paper, we propose a vision-based estimation method for autonomous landing of fixed-wing aircraft for Advanced Air Mobility. The concept of autonomous flight with minimal human intervention has gained significant interest with a particular focus on autonomous landing. The goal is to overcome the limitations of existing instrument landing systems and reduce reliance on GNSS during aircraft landing. The proposed system leverages the following techniques for high-performance and real-time operations in various real-world environments and during all stages of landing. A deep learning segmentation model was directly learned, created, and used for robust runway recognition performance against environmental changes around the runway. Algorithms were designed to adapt to different flight stages considering the varying information offered by image data when the aircraft is in mid-air and on the ground. The relative lateral position from the aircraft to the runway was estimated using bird’s-eye-view conversion and inverse projection techniques instead of conventional perspective-n-point methods for reducing the recognition error occurring from the conversion between 2D image and 3D world. Finally, the mixed-precision technique was used for the segmentation model to improve inference speed and ensure real-time operation in real-world deployment. Estimation stability and reliability were improved by using a Kalman Filter to cope with sensor uncertainties caused by the real-world flight environment. Consequently, we show that the average error in the lateral position estimation by the proposed method is comparable to the accuracy of a single GNSS and demonstrate successful autonomous landing of our test aircraft with a set of flight tests.

Real-time localization with probabilistic maps and unscented kalman filtering: a dynamic sensor fusion approach

This paper presents a robust position estimation technique for autonomous vehicles navigating urban and highway environments. It employs a probabilistic framework, integrating Monte Carlo simulation and Bayesian filtering via particle filters to represent position estimates beyond Gaussian distributions. To improve accuracy, Unscented Kalman Filtering (UKF) is used to fuse radar and lidar data, facilitating the detection of static, pole-like objects. These objects are matched with landmarks from a detailed reference map generated through 3D lidar scans. The proposed method addresses both lateral and longitudinal localisation challenges, ensuring precise vehicle positioning. Comprehensive simulation tests validate the system's effectiveness, demonstrating reliable performance across various driving conditions.

Extracting terrain elevation information in front of the vehicle based on vehicle-mounted LiDAR in dynamic environments

Abstract Point cloud maps constructed using 3D LiDAR, are widely used for robot navigation and localization. Few studies have utilized point cloud maps to extract terrain elevationinformation in front of a vehicle, which can be used as active suspension inputs to reduce vehicle bumps. In addition, the trajectories of dynamic objects in point cloud maps and global navigation satellite system (GNSS) data loss can affect the extraction of elevation information. To solve these problems, this paper proposes a framework for extracting terrain elevation information in front of the vehicle based on vehicle-mounted LiDAR in dynamic environments. The framework consists of two modules: point cloud map construction and vehicle front terrain elevation information extraction. In the point cloud map construction module, a system for simultaneous localization and mapping (SLAM) is proposed, which is capable of building point cloud maps without GNSS. Furthermore, a dynamic descriptor-based dynamic object filtering algorithm is proposed which is applied to SLAM. Therefore, the SLAM system overcomes the influence of dynamic objects on vehicle position and attitude estimation, and there are no trajectories of dynamic objects in the point cloud maps built by the system. In the vehicle front terrain elevation information extraction module, the unscented Kalman filter is utilized to predict the vehicle position at the next moment. Based on the geometric features of the tire-ground contact area, the terrain elevation information of the tire contact area at the predicted position on the point cloud map is extracted. Experiments show that the algorithm in this paper overcomes the effect of dynamic objects and builds a vehicle point cloud map without dynamic objects under GNSS data loss, which improves the accuracy of the extraction of terrain elevation information in front of the vehicle.

Spaceborne COTS-Capsule hodoscope: Detecting and characterizing particle radiation

The COTS-Capsule Spaceborne hodoscope was launched into low Earth orbit aboard the International Space Station and operated from 2021 to 2022. The primary objectives of the payload are measuring and characterizing the radiation environment within the space station, serving as a technology demonstrator for the COTS-Capsule radiation mitigation apparatus, and testing the interaction of high-energy cosmic particles on-orbit with our detectors. The payload features a particle hodoscope equipped with an array of novel detectors based on polyvinyl toluene scintillators and silicon photomultiplier sensors that are used for radiation detection and characterization employing 2D intensity-based triangulation. This paper provides a comprehensive account of the COTS-Capsule payload’s construction, preflight performance, testing, qualification, and on-orbit calibration. The hodoscope, sensitive to ionizing cosmic particles, facilitates impinging particle track reconstruction by multi-detector 2D position estimation, energy deposition estimation, and linear energy transfer estimation.

Robust Real-Time Cancer Tracking via Dual-Panel X-Ray Images for Precision Radiotherapy

Respiratory-induced tumor motion presents a critical challenge in lung cancer radiotherapy, potentially impacting treatment precision and efficacy. This study introduces an innovative, deep learning-based approach for real-time, markerless lung tumor tracking utilizing orthogonal X-ray projection images. It incorporates three key components: (1) a sophisticated data augmentation technique combining a hybrid deformable model with 3D thin-plate spline transformation, (2) a state-of-the-art Transformer-based segmentation network for precise tumor boundary delineation, and (3) a CNN regression network for accurate 3D tumor position estimation. We rigorously evaluated this approach using both patient data from The Cancer Imaging Archive and dynamic thorax phantom data, assessing performance across various noise levels and comparing it with current leading algorithms. For TCIA patient data, the average DSC and HD95 values were 0.9789 and 1.8423 mm, respectively, with an average centroid localization deviation of 0.5441 mm. On CIRS phantoms, DSCs were 0.9671 (large tumor) and 0.9438 (small tumor) with corresponding HD95 values of 1.8178 mm and 1.9679 mm. The 3D centroid localization accuracy was consistently below 0.33 mm. The processing time averaged 90 ms/frame. Even under high noise conditions (S2 = 25), errors for all data remained within 1 mm with tracking success rates mostly at 100%. In conclusion, the proposed markerless tracking method demonstrates superior accuracy, noise robustness, and real-time performance for lung tumor localization during radiotherapy. Its potential to enhance treatment precision, especially for small tumors, represents a significant step toward improving radiotherapy efficacy and personalizing cancer treatment.

Advancements in amphibious robot navigation through wheeled odometer uncertainty extension and distributed information fusion

The advancement and safeguarding of the water-land interface region is of paramount importance, and amphibious robots with the capacity for autonomous operation can play a pivotal role in this domain. However, the inability of the majority of reliable navigation sensors to adapt to the water-land interface environment presents a significant challenge for amphibious robots, as obtaining positional information is crucial for autonomous operation. To address this issue, we have proposed a positioning and navigation framework, designated as NAWR (Navigation Algorithm for Amphibious Wheeled Robots), with the objective of enhancing the navigation capabilities of amphibious robots. Firstly, a method for representing the odometer's confidence based on a simplified wheel-terrain interaction model has been developed. This method quantitatively assesses the reliability of each odometer by estimating the slip rate. Secondly, we have introduced an improved split covariance intersection filter (I-SCIF), which maximizes the utilization of navigation information sources to enhance the accuracy of positional estimation. Finally, we will integrate these two methods to form the NAWR framework and validate the effectiveness of the proposed methods through multiple robot field trials. The results from both field trials and ablation tests collectively demonstrate that the modules and overall approach within the NAWR framework effectively enhance the navigation capabilities of amphibious robots.