Localization Error Research Articles

An Enhanced Collaborative Localization Method Based on Belief Propagation Aided by 3D Terrain Modelling

Navigation system performance degrades significantly in complex environments. It is important to analyze satellite visibility through 3D terrain modelling and separate the satellite signals propagated by NLOS to suppress the NLOS error. However, the traditional 3D terrain modelling visibility analysis method based on the pure terrain cover angle is only suitable for determining the visibility of GNSS satellites and may incorrectly separate LOS propagate measurement signals from members with low relative ranges and elevation angles under air–ground swarm conditions. To this end, this paper proposes a belief-propagating cooperative navigation method based on air–ground visibility analysis, which avoids mistakenly separating close-range LOS cooperative navigation signals by simultaneously considering the distances, elevation angles, and azimuths of the signal sources relative to the air–ground swarm members. The simulation shows that the cooperative navigation NLOS identification method based on air–ground visibility analysis proposed in this paper can more accurately realize the separation of NLOS signals under cooperative conditions than the traditional pure angular 3D terrain modelling visibility analysis method can, and the localization error of the members to be assisted is significantly reduced.

Enhancing User Localization with an Integrated Sensing and Communication (ISAC) System: An Experimental UAV Search-and-Rescue Use Case

This paper explores the potential of an Integrated Sensing and Communication (ISAC) system to enhance search-and-rescue operations. While prior research has explored ISAC capabilities in Unmanned Aerial Vehicles (UAVs), our study focuses on addressing the specific challenges posed by modern communication standards (e.g., power, frequency, and bandwidth limitations) in the context of search-and-rescue missions. The paper details effective methods for processing echoed signals generated by downlink transmissions and evaluates key performance indicators, including Noise Equivalent Sigma Zero (NESZ) and channel capacity. Additionally, we utilize synchronization uplink signals transmitted by User Equipment (UE) to improve target detection and classification of possible victims by fusing SAR imagery with triangulation results from uplink signals. An experimental campaign validates the proposed setup by integrating SAR images of the environment with active localization results, both produced by a UAV equipped with a Software Defined Radio (SDR) payload. Our results demonstrate the system’s capability to detect and localize buried targets in avalanche scenarios, with localization errors ranging from centimeters to 10 m depending on environmental conditions. This successful integration highlights the practical applicability of our approach in challenging search-and-rescue missions.

A comparative study of range based and range free algorithms for node localization in underwater

The exploration of underwater surfaces and their monitoring has become an emerging field of interest for many researchers. Localization is a crucial task in the Underwater Wireless Sensor Network (UWSN). In comparison to terrestrial sensor nodes, localizing underwater sensor nodes is more difficult. In UWSN, the communication of signals between the nodes is a challenging task due to acoustic communication and the position of the node tends to move due to a strong water current in the deep sea whereas in terrestrial the nodes are static and the localization of the node is comparatively easier. Strategic surveillance relies on accurate localization in UWSN to follow underwater assets and activities. Addressing localization issues improves situational awareness, disaster response, and mitigation in crucial areas. We reviewed Range-Based and Range-Free UWSN localization algorithms from numerous research articles and discussed trade-offs and improvement opportunities. The comparative analysis was made based on various parameters like coverage area, density of node in the network, energy consumption, localization error and computational complexity. The performance comparison helps the researchers to decide the best localization algorithm or to improve the available algorithm for UWSN.

Semi-automated minimization of brick-mortar segmentation errors in 3D historical wall reconstruction

In current practices of geometric modeling and building information modeling (BIM) of architectural heritage, point cloud data acquired from site surveys is segmented into parts that correspond to actual building elements. Deep learning methods are used to automate the segmentation processes; however, each historical building presents unique challenges due to distinct construction techniques, irregular applications, deformations, and wear on the surveyed surfaces, and due to these peculiarities, segmented point cloud data may display local errors in the detection of individual architectural elements. This paper presents a method for post-processing segmented point cloud data to semi-automatically detect building elements such as bricks in historical walls. Results show that this approach, which involves testing neighborhoods of points and classified areas to identify and correct misclassified points, diminishes segmentation errors and reconstructs bricks close to their original form.

Leak detection and localization of fluid-filled pipeline using accelerometer pairs and mode separation method

Acoustic methods are commonly used to detect and locate leaks in pipelines, but they often overlook important multimodal characteristics of acoustic waves, limiting their applicability. Based on propagation theories regarding F(1,1) mode signal extraction, a new and easy-to-use method for leak detection and localization in pressurized pipelines is proposed. The F(1,1) mode signals are obtained using accelerometer pairs and mode separation method, which are then used to train detection models and to estimate the time difference of arrival (TDOA) for leak localization. Mode separation empowers the data-driven models with physically meaningful samples, aiming to broaden their applicability. The mode consistency between TDOA and velocity is achieved to ensure accurate leak localization. Experiments in buried water-filled ductile iron pipe (experiment A) and in fuel-filled iron pipe (experiment B) are conducted and the longest test distance reaches 72 m. The results validate that the employment of mode separation notably improves current leak detection and localization methods which primarily rely on original signals. The recognition rates rise about 3 %∼11 %, and the false alarm rates reduce about 1 %∼2 %, even when confronted with pipe junction interferences. Also, the leak localization errors are overall lower, with absolute errors below 2 m and relative errors less than 5 % of the test segment length for most cases.

Three-dimensional trans-rectal and trans-abdominal ultrasound image fusion for the guidance of gynecologic brachytherapy procedures: a proof of concept study

High dose-rate brachytherapy is a treatment technique for gynecologic cancers where intracavitary applicators are placed within the patient’s pelvic cavity. To ensure accurate radiation delivery, localization of the applicator at the time of insertion is vital. This study proposes a novel method for acquiring, registering, and fusing three-dimensional (3D) trans-abdominal and 3D trans-rectal ultrasound (US) images for visualization of the pelvic anatomy and applicators during gynecologic brachytherapy. The workflow was validated using custom multi-modal pelvic phantoms and demonstrated during two patient procedures. Experiments were performed for three types of intracavitary applicators: ring-and-tandem, ring-and-tandem with interstitial needles, and tandem-and-ovoids. Fused 3D US images were registered to magnetic resonance (MR) and computed tomography (CT) images for validation. The target registration error (TRE) and fiducial localization error (FLE) were calculated to quantify the accuracy of our fusion technique. For both phantom and patient images, TRE and FLE across all modality registrations (3D US versus MR or CT) resulted in mean ± standard deviation of 4.01 ± 1.01 mm and 0.43 ± 0.24 mm, respectively. This work indicates proof of concept for conducting further clinical studies leveraging 3D US imaging as an accurate, accessible alternative to advanced modalities for localizing brachytherapy applicators.

Spatially Resolved Uncertainties for Machine Learning Potentials.

Machine learning potentials have become an essential tool for atomistic simulations, yielding results close to ab initio simulations at a fraction of computational cost. With recent improvements on the achievable accuracies, the focus has now shifted on the data set composition itself. The reliable identification of erroneously predicted configurations to extend a given data set is therefore of high priority. Yet, uncertainty estimation techniques have achieved mixed results for machine learning potentials. Consequently, a general and versatile method to correlate energy or atomic force uncertainties with the model error has remained elusive to date. In the current work, we show that epistemic uncertainty cannot correlate with model error by definition but can be aggregated over groups of atoms to yield a strong correlation. We demonstrate that our method correctly estimates prediction errors both globally per structure and locally resolved per atom. The direct correlation of local uncertainty and local error is used to design an active learning framework based on identifying local subregions of a large simulation cell and performing ab initio calculations only for the subregion subsequently. We successfully utilized this method to perform active learning in the low-data regime for liquid water.

Attitude collaborative control strategy for space gravitational wave detection

This paper proposes a high-precision attitude cooperative control strategy for three spacecraft in space gravitational wave detection. Firstly, based on the layout of optical components on the spacecraft and factors such as external interference and model uncertainty, a relative attitude model based on the Euler angle is constructed for the characteristics of small angle motion in differential wavefront sensing mode. Secondly, aiming at the cooperative control problem of multi drag-free attitude control system after the laser link capture between two spacecraft is completed, an attitude control method based on consensus mode cooperative control strategy is proposed. It combines local neighbourhood error from star sensing and differential wavefront sensing with an adaptive controller for equilateral triangle configuration control. Additionally, a cooperative control strategy based on laser measurement information is established to improve control accuracy by avoiding star sensors with low accuracy. Simulation results indicate that the control accuracy of the consistency mode and its sub-mode laser measurement mode is superior to the master-slave and cyclic modes, achieving better than 5×10−6 rad. The laser measurement mode demonstrates the highest accuracy, with relative attitude control accuracy reaching 1.5×10−7 rad, meeting the requirements for space gravitational wave detection.

Unfolding coil localized errors from an imperfect slice profile using a structured autocalibration matrix: An application to reduce outflow effects in cine bSSFP imaging.

Balanced steady-state free precession (bSSFP) imaging is susceptible to outflow effects where excited spins leaving the slice as part of the blood stream are misprojected back onto the imaging plane. Previous work proposed using slice-encoding steps to localize these outflow effects from corrupting the target slice, at the expense of prolonged scan time. This present study extends this idea by proposing a means of significantly reducing most of the outflowing signal from the imaged slice using a coil localization method that acquires a slice-encoded calibration scan in addition to the 2D data, without being nearly as time-demanding as our previous method. This coil localization method is titled UNfolding Coil Localized Errors from an imperfect slice profile using a Structured Autocalibration Matrix (UNCLE SAM). Retrospective and prospective evaluations were carried out. Both featured a 2D acquisition and a separate slice-encoded calibration of the center in-plane -space lines across all desired slice-encoding steps. Retrospective results featured a slice-by-slice comparison of the slice-encoded images with UNCLE SAM. UNCLE SAM's subtraction from the slice-encoded image was compared with a subtraction from the flow-corrupted 2D image, to demonstrate UNCLE SAM's capability to unfold outflowing spins. UNCLE SAM's comparison with slice encoding showed that UNCLE SAM was able to unfold up to 74% of what slice encoding achieved. Prospective results showed significant reduction in outflow effects with only a marginal increase in scan time from the 2D acquisition. We developed a method that effectively unfolds most outflowing spins from corrupting the target slice and does not require the explicit use of slice-encoding gradients. This development offers a method to reduce most outflow effects from the target slice within a clinically feasible scan duration compared with the fully sampled slice-encoding technique.

An Efficient Modified Black Widow Optimized Node Localization in Wireless Sensor Network

Wireless Sensor Network (WSN) is an encouraging technology in various applications like atmosphere monitoring, vehicular systems, and targeting devices. Localization in WSN is performed to identify the current position or coordinates of sensor nodes. The crucial task of localization is to find coordinates without manual configuration and expensive hardware like GPS. This work proposes a new localization algorithm using Modified Black Widow Optimization (MBWO). The proposed method involves an optimal selection of anchor nodes to reduce localization errors. Black Widow Optimization (BWO) is a naturally inspired optimization algorithm encouraged by the unique coupling behaviour of black widow spiders. The performance of black widow optimization is improved by levy flight distribution to escape from local minima. Experimental results show that the proposed MBWO-optimized localization achieves a higher localized node count with minimized localized error compared to other optimization algorithms.

Adaptive conservative time integration for unsteady compressible flow

Unsteady flow computations typically rely on time integration schemes which employ the same step size everywhere. However, in cases with strong variations of wave speed and/or spatial resolution, local stability criteria and truncation errors would allow for much larger time steps in parts of the domain. To exploit this potential of improving the computational efficiency, adaptive time-stepping methods have been developed. Recently, an adaptive conservative time integration (ACTI) scheme for explicit finite volume methods was devised. Opposed to previous methods, ACTI guarantees exact conservation and periodic synchronization. Both are achieved by splitting a global time step into 2L (L≥0 is a cell dependent level) sub-steps, whereas the order of cell updates is critical. It has been demonstrated for flows in fractured porous media and for the Euler equations that ACTI can reduce the computational cost dramatically while preserving second order accuracy in space and time. In this paper, the ACTI scheme is extended to the compressible Navier-Stokes-Fourier system, and special attention is required for the spatio-temporal discretization of the convective and viscous fluxes. Numerical studies of unsteady flows involving shock boundary layer interaction demonstrate that the same accuracy is achieved with the new compressible ACTI flow solver as with classical time integration, but at much lower cost. Moreover, since the method is explicit, it has the potential for efficient computations on multiple CPUs and GPUs.

Triangular finite differences using bivariate Lagrange polynomials with applications to elliptic equations

This paper proposes finite-difference schemes based on triangular stencils to approximate partial derivatives using bivariate Lagrange polynomials. We use first-order partial derivative approximations on triangles to introduce a novel hexagonal scheme for the second-order partial derivative on any rotated parallelogram grid. Numerical analysis of the local truncation errors shows that first-order partial derivative approximations depend strongly on the triangle vertices getting at least a first-order method. On the other hand, we prove that the proposed hexagonal scheme is always second-order accurate. Simulations performed at different triangular configurations reveal that numerical errors agree with our theoretical results. Results demonstrate that the proposed method is second-order accurate for the Poisson and Helmholtz equation. Furthermore, this paper shows that the hexagonal scheme with equilateral triangles results in a fourth-order accurate method to the Laplace equation. Finally, we study two-dimensional elliptic differential equations on different triangular grids and domains.

Fast model calibration for predicting the response of breast cancer to chemotherapy using proper orthogonal decomposition

Constructing digital twins for predictive tumor treatment response models can have a high computational demand that presents a practical barrier for their clinical adoption. In this work, we demonstrate that proper orthogonal decomposition, by which a low-dimensional representation of the full model is constructed, can be used to dramatically reduce the computational time required to calibrate a partial differential equation model to magnetic resonance imaging (MRI) data for rapid predictions of tumor growth and response to chemotherapy. In the proposed formulation, the reduction basis is based on each patient’s own MRI data and controls the overall size of the “reduced order model”. Using the full model as the reference, we validate that the reduced order mathematical model can accurately predict response in 50 triple negative breast cancer patients receiving standard of care neoadjuvant chemotherapy. The concordance correlation coefficient between the full and reduced order models was 0.986 ± 0.012 (mean ± standard deviation) for predicting changes in both tumor volume and cellularity across the entire model family, with a corresponding median local error (inter-quartile range) of 4.36 % (1.22 %, 15.04 %). The total time to estimate parameters and to predict response dramatically improves with the reduced framework. Specifically, the reduced order model accelerates our calibration by a factor of (mean ± standard deviation) 378.4 ± 279.8 when compared to the full order model for a non-mechanically coupled model. This enormous reduction in computational time can directly help realize the practical construction of digital twins when the access to computational resources is limited.

Localization and detection of underwater acoustic communication signals using convolutional recursive neural networks

Abstract This paper employs a multi-task neural network (UWAELD) to simultaneously perform the Underwater Acoustic Communication Event Detection (UACED) and direction-of-arrival (DOA) mission. Typically, the UACED and DOA tasks are executed separately, as the UACED task is identified through time-frequency analysis, while the DOA task is identified through the amplitude and phase differences of the signal, making it very difficult to jointly perform both tasks. To overcome this, we utilize a logarithmic spectrogram for time-frequency analysis and stack the normalized eigenvectors obtained by processing the signal covariance matrix. We ultimately evaluate the network’s feasibility using simulation data and lake test data, utilizing acoustical signals measured in actual experiments. Finally, for the UADCED task, the error rate is only 6%, with an F1 score of 0.83; for the DOA task, the localization error is only 1.72°, with a localization recall score of 0.87. Additionally, for the DOA task, we employ the classical MUSIC algorithm to demonstrate the network’s superiority.

Krylov-based adaptive-rank implicit time integrators for stiff problems with application to nonlinear Fokker-Planck kinetic models

We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of solutions with significantly reduced computational costs. We further introduce an efficient mechanism for residual evaluation and an adaptive rank-seeking strategy that optimizes low-rank settings based on a comparison between the residual size and the local truncation errors of the time-stepping discretization. We demonstrate our approach with the challenging Lenard-Bernstein Fokker-Planck (LBFP) nonlinear equation, which describes collisional processes in a fully ionized plasma. The preservation of the equilibrium state is achieved through the Chang-Cooper discretization, and strict conservation of mass, momentum and energy via a Locally Macroscopic Conservative (LoMaC) procedure. The development of implicit adaptive-rank integrators, demonstrated here up to third-order temporal accuracy via diagonally implicit Runge-Kutta schemes, showcases superior performance in terms of accuracy, computational efficiency, equilibrium preservation, and conservation of macroscopic moments. This study offers a starting point for developing scalable, efficient, and accurate methods for high-dimensional time-dependent problems.

Asynchronous iterative Q-learning based tracking control for nonlinear discrete-time multi-agent systems

This paper addresses the tracking control problem of nonlinear discrete-time multi-agent systems (MASs). First, a local neighborhood error system (LNES) is constructed. Then, a novel tracking algorithm based on asynchronous iterative Q-learning (AIQL) is developed, which can transform the tracking problem into the optimal regulation of LNES. The AIQL-based algorithm has two Q values QiA and QiB for each agent i, where QiA is used for improving the control policy and QiB is used for evaluating the value of the control policy. Moreover, the convergence of LNES is given. It is shown that the LNES converges to 0 and the tracking problem is solved. A neural network-based actor-critic framework is used to implement AIQL. The critic network of AIQL is composed of two neural networks, which are used for approximating QiA and QiB respectively. Finally, simulation results are given to verify the performance of the developed algorithm. It is shown that the AIQL-based tracking algorithm has a lower cost value and faster convergence speed than the IQL-based tracking algorithm.

The maximum norm error estimate and Richardson extrapolation methods of a second-order box scheme for a hyperbolic-difference equation with shifts

The study aims at the development and theoretical analyses of a box method used to solve a kind of hyperbolic equations with shifts. By using the discrete energy method, it is shown that numerical solutions converge to exact solutions with an order of O(τ 2 + h 2) in L ∞-norm as τ = O(h). Here, τ and h are temporal and spatial meshsizes, respectively. According to local truncation error, the asymptotic expansion formula of the numerical solutions is derived by introducing two auxiliary problems. By applying this asymptotic expansion formula, a class of Richardson extrapolations methods have been derived to achieve extrapolation solutions with an order of O(τ 4 + h 4) in L ∞-norm. Numerical results show the high performance of the proposed methods and the exactness of theoretical findings.

Deep learning‐based location prediction in VANET

AbstractIn recent years, Vehicular Ad‐hoc Network (VANET) has become an essential component of intelligent transportation systems that, along with the previous systems such as traffic condition, accident alert, automatic parking, and cruise control, use the communication of vehicle to vehicle and vehicle to the roadside unit to facilitate road transportation. Several challenges hinder efforts to improve traffic conditions and reduce traffic fatalities through VANET. A critical challenge is achieving highly accurate and reliable vehicle localization within the VANET. Additionally, the frequent unavailability of Global Positioning System (GPS), particularly in tunnels and parking lots, presents another significant obstacle. Traditional methods like Dead Reckoning offer low accuracy and reliability due to accumulating errors. Similarly, GPS positioning, map matching with mobile phone location services, and other existing solutions struggle with accuracy and economic feasibility. In this article, two Kalman filter approaches are used based on signal statistical information and the other learning‐based networks, including traditional neural network, deep neural network and LSTM (long short‐term memory) to locate the car. The prediction error of car position with root mean square measures. The squared error and distance prediction error are evaluated. It is shown that in terms of prediction time and processing time of vehicle localization, all the vehicle localization methods are efficient in terms of response time for localization, and Kalman filter methods, traditional neural network and deep neural network are faster than LSTM method. Also, in terms of localization error, Kalman filter works better than learning‐based methods, and in learning‐based methods, both deep neural network and LSTM methods perform better than traditional neural network in terms of localization error.

Enhanced river suspended sediment concentration identification via multimodal video image, optical flow, and water temperature data fusion

Monitoring suspended sediment concentration (SSC) in rivers is pivotal for water quality management and sustainable river ecosystem development. However, achieving continuous and precise SSC monitoring is fraught with challenges, including low automation, lengthy measurement processes, and high cost. This study proposes an innovative approach for SSC identification in rivers using multimodal data fusion. We developed a robust model by harnessing colour features from video images, motion characteristics from the Lucas–Kanade (LK) optical flow method, and temperature data. By integrating ResNet with a mixed density network (MDN), our method fused the image and optical flow fields, and temperature data to enhance accuracy and reliability. Validated at a hydropower station in the Xinjiang Uygur Autonomous Region, China, the results demonstrated that while the image field alone offers a baseline level of SSC identification, it experiences local errors under specific conditions. The incorporation of optical flow and water temperature information enhanced model robustness, particularly when coupling the image and optical flow fields, yielding a Nash–Sutcliffe efficiency (NSE) of 0.91. Further enhancement was observed with the combined use of all three data types, attaining an NSE of 0.93. This integrated approach offers a more accurate SSC identification solution, enabling non-contact, low-cost measurements, facilitating remote online monitoring, and supporting water resource management and river water–sediment element monitoring.

System error analysis and target localization of distributed pulse radars

AbstractTarget localization for distributed radars requires precise knowledge of the calibration errors in time, frequency, and space. Previous studies focus on the sensor location error and sensor directional error in space. This paper concentrates on the system errors in time and frequency which directly affect the targets estimation of range and velocity. Based on linear frequency modulation waveform, the impact of the system errors including sample interval, pulse repetition interval, and centre frequency are analysed. An alternating optimization algorithm is proposed to achieve the target localization, velocity estimation and system errors estimation simultaneously. Simulation shows the effectiveness of the algorithm and the influence on localization due to varying number of targets and radars.