Circular Error Research Articles

Optimizing IOL Calculators with Deep Learning Prediction of Total Corneal Astigmatism.

Background/Objectives: This study aims to identify the most accurate regression model for predicting total corneal astigmatism (TCA) from anterior corneal astigmatism (ACA) and to fine-tune the best model's architecture to further optimize predictive accuracy. Methods: A retrospective review of 19,468 eyes screened for refractive surgery was conducted using electronic medical records. Corneal topography data were acquired using the Pentacam HR. Various types (7) and subtypes (21) of regression learners were tested, with a deep neural network (DNN) emerging as the most suitable. The DNN was further refined, experimenting with 23 different architectures. Model performance was evaluated using root mean squared error (RMSE), R2, average residual error, and circular error. The final model only used age, ACA magnitude, and ACA axis to predict TCA magnitude and axis. Results were compared to predictions from one of the leading TCA prediction formulas. Results: Our model achieved higher performance for TCA magnitude prediction (R2 = 0.9740, RMSE = 0.0963 D, and average residual error = 0.0733 D) compared to the leading formula (R2 = 0.8590, RMSE = 0.2257 D, and average residual error = 0.1928 D). Axis prediction error also improved by an average of 8.1° (average axis prediction error = 4.74° versus 12.8°). The deep learning approach consistently demonstrated smaller errors and tighter clustering around actual values compared to the traditional formula. Conclusion: Deep learning techniques significantly outperformed traditional methods for TCA prediction accuracy using the Pentacam HR. This approach may lead to more precise TCA calculations and better IOL selection, potentially enhancing surgical outcomes.

Technical note: assessing GPS sensor accuracy using real-time kinematic device for livestock tracking.

The technical aspects of global positioning system (GPS) sensors have been improved substantially over the years, making them valuable and popular tools for livestock tracking. Using GPS sensors allows producers and researchers to locate grazing livestock, monitor their behavior and distribution, and gather referencing information about the health status of the animals and pastures. However, interpreting the behavior of grazing livestock, such as cattle, from GPS data can be difficult due to positioning inaccuracies. Without knowing the positioning accuracy range of GPS sensors, achieving high-level confidence in determining grazing densities and identifying abnormal livestock movement patterns is challenging. In this study, the positioning accuracy of 3 different types of commercial GPS sensors was assessed using a survey-grade real-time kinematics (RTK) device. We outlined the procedures and essential equations and compared the recorded locations from the GPS sensors with reference locations collected from the RTK device. The results demonstrated statistically significant differences (P < 0.05) in positioning accuracy between different types of GPS sensors. The circular error probable (CEP) at 95% probability levels (CEP95) of the 3 sensors ranged from 2.46 to 11.06 m. This accuracy varied among individual sensors within the same brand and across different brands, which underscores the importance of evaluating the positioning accuracy of GPS sensors in livestock tracking. This study provides significant insights for animal scientists, ecologists, and livestock producers engaged in GPS sensor-related research and practices.

Bio-inspired machine-learning aided geo-magnetic field based AUV navigation system

The navigational accuracy of sea animals and trans-ocean birds provides inspiration in using geo-magnetic field (GMF) for realizing strategic truly autonomous underwater vehicles (AUV) capable of determining their absolute position on earth, without the aid of ship-referenced acoustic baseline systems. Supervised Machine Learning algorithms are applied on the GMF intensity data obtained from NOAA World Magnetic Model for a 900 km2 within the Indian mineral exploratory area in the Central Indian Ocean, with a resolution of 50 m, considering the sensitivity of commercially available magnetometers. It is identified that, for AUVs equipped with magnetometers with a detection sensitivity of 0.1 nT, the supervisory random forest regression and decision tree algorithm trained with priori GMF data, could provide trajectory guidance to AUVs with an absolute mean position accuracy in 2D plane, with reference to the last known position from Integrated Navigation system aided initially with GPS and with acoustic positioning in underwater. Circular Error Probable (CEP 50) of 53 m and 56 m, respectively. The scalar GMF anomaly navigation demonstrated to be a viable GPS-alternative navigation system could be extended to larger areas with inclination and declination vectors, as unique identifiers.

High-Precision Time Difference of Arrival Estimation Method Based on Phase Measurement

In unmanned aerial vehicle (UAV)-based time difference of arrival (TDOA) positioning technique, baselines are limited due to communication constraints. In this case, the accuracy is highly sensitive to the TDOA measurements’ error. This article primarily addresses the problem of short-baseline high-precision time synchronization and TDOA measurement. We conducted a detailed analysis of error models in TDOA systems, considering both the time and phase measurement. We utilize the frequency division wireless phase synchronization technique in TDOA systems. Building upon this synchronization scheme, we propose a novel time delay estimation method that relies on phase measurements based on the integer least squares method. The performance of this method is demonstrated through Monte Carlo simulations and outdoor experiments. The standard deviations of synchronization and TDOA measurements in experiments are 1.12 ps and 1.66 ps, respectively. Furthermore, the circular error probable (CEP) accuracy is improved from 0.33%R to 0.02%R, offering support for the practical application of distributed short-baseline high-precision passive location techniques.

Hysteresis controller based on a circular error area table applied to a variable speed renewable energy system.

Nowadays the proliferation of renewable energies has the problem of the limited capacity of the grid to absorb these types of energies due to their low quality. In order to increase their penetration in the electrical system it is mandatory to improve the control of the power stages used to inject the generated power and, in many cases, to achieve variable speed operation. The paper proposes a new current control method based on a switching table that keeps the current error in a circular area and compares it with other table hysteresis control [1],[2]. As it is shown, both the THD and the frequency is better in the proposed method.

Development of a low-harmonic vector hysteresis current controller

The increasing interest in the use of renewable energy sources for the generation of electrical energy makes it necessary to ensure that these type of installations do not jeopardize the global operation of the electrical system to which they are connected. Up until now, this safety has been achieved by imposing very strict limits to the percentage of “non-controllable” renewable energy that can be connected to the grid. In order to increase these limits, new control schemes must be developed, focusing in power quality and, if possible, in trying to help grid stability. The paper proposes two new control methods for the current injected by a variable-speed generation system and compares them to a traditional hysteresis control. The first one obtains a table by using an algorithm that calculates the switching state that minimises switching frequency. The commutation is determined by a single comparator applied to the error vector, achieving a circular error area. The use of this table, along with the selection of a circular error area for the current vector makes that the current error remains always inside the specified error area. The second method is a predictive one, based on the previous one, that decides the optimum switching vector in the precise time when the commutation occurs, taking into account the present state of the system.

Co-registration accuracy between Landsat-8 and Sentinel-2 orthorectified products

Landsat orthorectified products use Ground Control Points (GCPs) and Digital Elevation Models (DEM) to improve the geolocation accuracy and temporal consistency, and to account for the relief displacements due to the sensor-target geometry. In Collection-2, to improve the geometric harmonization between Landsat and Sentinel-2 (S2) orthorectified products, the Landsat GCP's absolute and relative accuracies were improved using the S2 Global Reference Image (GRI) dataset through a continent-level bundle adjustment method. The GRI is a highly accurate global image dataset that was developed by the European Space Agency (ESA) to improve the S2 multi-temporal geolocation accuracy. Since late August 2021, ESA has been using the GRI dataset in the geometric refinement process to generate S2 terrain-corrected (L1C) products. This paper presents the co-registration accuracy between the Landsat-8 (L8) Collection-2 terrain-corrected products and the S2 L1C products that were processed with and without the use of the GRI dataset. The image-to-image registration (I2I) analysis performed between the L8 and S2 data products over a set of globally distributed tiles shows a significant improvement in their co-registration accuracy when GRI is used in the S2 L1C product generation. The co-registration error is estimated to be <6 m circular error at 90% probability (CE90) when GRI is used, and >12 m CE90 when GRI is not used in the S2 product generation process. A similar I2I analysis was conducted between S2 L1C products, L8 L1TP products, and L8 and Landsat 9 (L9) L1TP products. The analysis shows that the S2 L1C products are co-registered with each other temporally to better than 5.1 m CE90 when GRI is used. The L8 L1TP products and L8 versus L9 L1TP products are both co-registered temporally to better than 3 m CE90.

Adverse effects of receiver clock bias and drift on NavIC user position coordinates and their mitigation

We investigated the effects of receiver clock bias and drift on NavIC receiver position coordinates at a low latitude station and proposed a mitigation technique. For this, Five weeks data of Accord IRNSS-GPS-SPS (AIGS) receiver are considered. Error in each position coordinates (X, Y and Z) is estimated and observed that the maximum error occurred in user position Z-coordinate. CEP for 2D position is analyzed and observed that the Circular Error Probability (CEP) values are high in Z coordinate of YZ and ZX planes. Further, it is noticed that the timing of sudden enhancement of both clock bias and drift parameters coincides with the periodic anomaly of the X, Y and Z coordinates. The error in individual position coordinates is minimized by applying 6th order Butterworth low pass filter resulting in improved position accuracy. If such errors are not mitigated, the position estimation of the receiver becomes highly erroneous.

GPS technology as a tool to aid pasture management on dairy farms

This research determined the accuracy and precision of Global Positioning System (GPS) enabled devices as a potential tool to automate the recording of onfarm grazing events, which can be used to indicate productivity of paddocks (with number of grazings per year), or, when combined with other farm data, estimate nergy harvested. Static tests were initially conducted to determine the devices’ accuracy (location error) and precision (Circular Error Probability; CEP). Based on 11 Agtech and 22 mOOvement devices tested, the mean location error was 5.4 m and 34.2 m, respectively. The 95% CEP was 13.9 m and 77.6 m, respectively. In the subsequent on-farm study, 11 cows in a 400- cow milking herd were fitted with an Agtech and mOOvement ear tag and two with digitanimal collars. Data were analysed for the AM and PM grazing periods for four days. The digitanimal collars recorded 62.3% of total observations in the correct paddock, instead of adjacent paddocks or races, compared with 52.5% for the Agtech devices and 45.2% for the mOOvement ear tags. These results suggested that GPS technology isfeasible for the automated recording of grazing events. However, a longer-term study is required to demonstrate the value this technology could have for farmers.

Design and Parameter Optimization of Trajectory Correction Control Strategy for Air Duct Structure Projectile

In order to make the new air duct structure trajectory correction projectile have good dynamic correction control effect, the control strategy of the projectile’s correction mechanism is studied in this paper. A design method of trajectory correction control strategy based on particle swarm optimization-cuckoo search (PSO-CS) hybrid algorithm is proposed to obtain the optimal control parameters that can make the projectile flight stable and correct accurately. Firstly, the mathematical model of the air duct structure projectile is established. Secondly, the multiobjective optimization problem is analyzed. The projectile’s correction control strategy optimization model is established by taking the start control time, the number of corrections, the correction working time, and the interval time as the control variables. The optimization model innovatively considers the influence of the correction action on the flight stability of the projectile and the influence of the start control time on the correction range. Finally, the PSO-CS hybrid algorithm is used to design the calculation method of the optimization model and solve the optimal correction working parameters. The simulation results indicate that the control strategy optimization model can be solved by the proposed calculation method. Moreover, optimal correction working parameters of the correction mechanism in the current state can be obtained. Compared with the results of using single PSO algorithm and CS algorithm, the correction scheme calculated by PSO-CS hybrid optimization algorithm is better. This correction control scheme can effectively reduce the impact point deviation and make the projectile flight stable. At the same time, the circular error probable (CEP) of the projectile after correction is reduced from 42.3 m to 4.6 m while the impact point dispersion is lowered. The research results show that the design method of correction control strategy proposed in this paper is effective for trajectory correction of the new air duct structure projectile.

Short Landing for Flying-Wing Unmanned Aircraft with Thrust Vector

The task of achieving a safe and short landing for a flying-wing unmanned aircraft with a three-bearing-swivel thrust vector is highly challenging. The process is further complicated due to the need to switch between multiple control modes, while also ensuring the protection of the flight boundaries from environmental disturbances and model uncertainties to ensure flight safety. To address this challenge, this paper proposes a short-landing strategy that employs mixed control using lift fans, thrust vectors, and aerodynamic control surfaces. The extended state observer (ESO) is integrated into the inner angular rate control and outer sink rate control to account for environmental disturbances and model uncertainties. To ensure flight safety, the attainable linear and angular acceleration is calculated through a trim analysis to determine the command value of velocity and angle of attack during a short landing. Additionally, a flight boundary protection method is employed which includes an additional command value of the angle of attack, resulting in a higher probability of a successful landing. This paper provides a detailed description of the short-landing strategy, including the control objectives for each phase. Finally, a Monte Carlo simulation is conducted to evaluate the effectiveness and robustness of the short-landing strategy, and the landing accuracy is assessed using the circular error probability metric.

Improving the precision and accuracy of wildlife monitoring with multi‐constellation, multi‐frequency GNSS collars

AbstractThe use of global navigation satellite systems (GNSS) technology within the fields of ecology and biology has increased over recent years. With Global Positioning System, GLObalnaya NAvigatsionnaya Sputnikovaya Sistema, Galileo, and BeiDou systems fully deployed, &gt;140 navigation satellites are currently available for navigation and high precision positioning applications. The technological improvements in GNSS devices, mainly due to the multi‐frequency capability, reduce signal acquisition time and increase the reliability, the continuity, and the accuracy of the estimated position, especially in complex environments like forests or areas with a steep topography. This study aims to test experimentally the influence of multi‐constellation multi‐frequency modules on the performance of the GNSS collars used to monitor wildlife. We applied static and kinematic tests designed to assess and compare the performance of GNSS collars equipped with a single‐frequency versus a multi‐frequency chipset. We evaluated the availability and continuity of solutions, number of satellites used, dilution of precision, precision, accuracy, and repeatability of these quality parameters for GNSS devices in southeastern Spain from February 2021 to June 2022. The results confirmed that the multi‐constellation multi‐frequency GNSS collar showed a stable and good performance in terms of the number of satellites used (&gt;10), horizontal dilution of precision (&lt;1.3), fix success rate (100%), mean location error (&lt;1.5 m), and circular error probability (CEP), which was better by approximately one order of magnitude than the single‐frequency collar (1–10 m). The use of reliable and accurate GNSS devices will expand our knowledge of animal behavior and the interactions between species. Multi‐frequency GNSS collars allow collection of accurate locations, providing fine‐scale information about animal behavior (e.g., feeding strategies, competition for resources), whereas the single‐frequency GNSS collars can used for broad‐scale studies (e.g., home ranges, habitat use).

Improving the Position Accuracy of Rover Receiver using Differential Positioning in Indian Regional Navigation Satellite System

Navigation with Indian Constellation (NavIC) is the Indian Regional Navigation Satellite System (IRNSS) developed by Indian Space Research Organization (ISRO) to provide the position and navigation services for Indian region. NavIC or IRNSS is individual satellite constellation which has seven satellites covering the Indian subcontinent. Accuracy of NavIC standalone is insufficient in certain applications such as civil aviation. To improve the position accuracy performance of NavIC system, differential positioning technique is utilized. In this paper, differential positioning is carried out, considering two IGS (IRNSS-GPS-SBAS) receivers (one as reference station and the other as rover), which are capable of receiving IRNSS signals from 7 satellites, GPS signals from 12 satellites, SBAS signals from 2 satellites. Here, NavIC constellation alone is considered for the analysis. The differential positioning is carried out using the pseudorange measurements on L5 (1176.45 MHz), S1 (2492.028 MHz) and dual (L5 and S1 both) and accuracies are compared in terms of the statistical parameters Circular Error Probability (CEP), Distance Root Mean Square (DRMS), 2DRMS (twice the DRMS). The improvement in the horizontal accuracy (2DRMS) of the rover using pseudorange measurements on L5 is observed to be 78.81%, on S1 it is 69.14 % and using dual frequency (L5 and S1 both) it is 80.73% when compared to NavIC standalone.

Horizontal and Vertical Geometric Accuracy of Agisoft Photoscan and Pix4D Mapper Softwares at Kebun Raya Universitas Mulawarman in Samarinda, East Kalimantan, Indonesia

The advent of unmanned aerial vehicles has improved aerial photography, which is now aided by computer software for data acquisition and processing. These developments allow for accurate aerial photographs of Kebun Raya Universitas Mulamarwan Samarinda (KRUS) for managerial purposes. This study aims to compare the accuracy of horizontal and vertical geometry with Agisoft Photoscan (AP) and Pix4D Mapper (PM) software. The materials consisted of 150 aerial photographs of KRUS with eight ground control points (GCP) and one internal control point (ICP). Data were obtained from nine flight paths with AP and PM software linked to GCP and ICP. These data were processed and compared to manual measurements using linear error (LE) 90 and circular error (CE) 90 criteria. The commission omission equation was used for the object accuracy test on orthophoto. The vertical geometry accuracy test was carried out using the criteria of root mean square error (RMSE) and LE90 values on the digital elevation model. In comparison, the horizontal geometry accuracy test was performed by using the obtained orthophoto based on RMSE and CE90 criteria. The result demonstrated that the horizontal geometry accuracy for AP was higher than PM, indicated by lower RMSE and CE90 values, which were 0.091 versus 0.148 and 0.139 versus 0.224 for AP and PM, respectively. The vertical geometry accuracy was similar, with lower RMSE and LE90 values of 0.169 versus 0.309 and LE90 0.279 versus 0.224 for AP and PM, respectively. Furthermore, AP is a potential tool for KRUS spatial mapping.

Stance Phase Detection for ZUPT-Aided INS Using Knee-Mounted IMU in Crawling Scenarios

This letter presents a study on the navigational accuracy of crawling using heel and knee-mounted inertial measurement units (IMU). The navigation method is based on a stance phase detection in combination with the zero-velocity UPdaTe algorithm and strapdown inertial navigation systems (INS). A parameter search considering window size, detector type, and statistical threshold was performed to determine the parameters that minimized the circular error probable (CEP). Under the experimental conditions, the knee-mounted IMU position rendered improved navigation accuracy compared with the heel-mounted IMU. Based on the IMU used in this experiment, accelerometer-based zero-velocity detectors appeared to have improved performance for the knee-mounted IMU compared with the angular rate energy and stance phase hypothesis detectors. Under the optimal parameters, the CEP/corresponding root-mean-square error (RMSE) for heel-mounted and knee-mounted IMUs was 0.95/1.05 m and 0.22/0.43 m, respectively, for ten crawling trials over a 42.6 m straight trajectory marking a 77.3% CEP and 59.1% RMSE improvement when using a knee-mounted versus a heel-mounted IMU.

Study of Model Uncertainties Influence on the Impact Point Dispersion for a Gasodynamicaly Controlled Projectile.

The article presents the analysis of the impact point dispersion reduction using lateral correction thrusters. Two types of control algorithms are used and four sources of uncertainties are taken into account: aerodynamic parameters, thrust curve, initial conditions and IMU errors. The Monte Carlo approach was used for simulations and Circular Error Probable was used as a measure of dispersion. Generic rocket mathematical and simulation model was created in MATLAB/Simulink 2020b environment. Results show that the use of control algorithms greatly reduces the impact point dispersion.

Improved Position Estimation Algorithm of Agricultural Mobile Robots Based on Multisensor Fusion and Autoencoder Neural Network.

High-precision position estimations of agricultural mobile robots (AMRs) are crucial for implementing control instructions. Although the global navigation satellite system (GNSS) and real-time kinematic GNSS (RTK-GNSS) provide high-precision positioning, the AMR accuracy decreases when the signals interfere with buildings or trees. An improved position estimation algorithm based on multisensor fusion and autoencoder neural network is proposed. The multisensor, RTK-GNSS, inertial-measurement-unit, and dual-rotary-encoder data are fused with Extended Kalman filter (EKF). To optimize the EKF noise matrix, the autoencoder and radial basis function (ARBF) neural network was used for modeling the state equation noise and EKF measurement equation. A multisensor AMR test platform was constructed for static experiments to estimate the circular error probability and twice-the-distance root-mean-squared criteria. Dynamic experiments were conducted on road, grass, and field environments. To validate the robustness of the proposed algorithm, abnormal working conditions of the sensors were tested on the road. The results showed that the positioning estimation accuracy was improved compared to the RTK-GNSS in all three environments. When the RTK-GNSS signal experienced interference or rotary encoders failed, the system could still improve the position estimation accuracy. The proposed system and optimization algorithm are thus significant for improving AMR position prediction performance.

UWB Sensor Placement for Foot-to-Foot Ranging in Dual-Foot-Mounted ZUPT-Aided INS

This letter studies the impact of the ultra-wideband (UWB) sensor placement for a zero velocity update aided pedestrian inertial navigation solution that uses foot-to-foot ranging feedback to improve its localization accuracy. Several sensor configurations are investigated in both static and dynamic cases. The root mean square error is used as the performance metric for the static measurement accuracy, whereas the circular error probable is chosen to evaluate the sensor configurations in dynamic experiments.

Assessment of Android Network Positioning as an Alternative Source of Navigation for Drone Operations

Applications of drones have increased significantly in the past decade for both indoor and outdoor operations. In order to assist autonomous drone navigation, there are numerous sensors installed onboard the vehicles. These include Global Navigation Satellite Systems (GNSS) chipsets, inertial sensors, barometer, lidar, radar and vision sensors. The two sensors used most often by drone autopilot controllers for absolute positioning are the GNSS chipsets and barometer. Although, for most outdoor operations, these sensors provide accurate and reliable position information, their accuracy, availability, and integrity deteriorate for indoor applications and in the presence of radio frequency interference (RFI), such as GNSS spoofing and jamming. Therefore, it is possible to derive network-based locations from Wi-Fi and cellular transmission. Although there have been many theoretical studies on network positioning, limited resources are available for the expected quantitative performance of these positioning methodologies. In this paper, the authors investigate both the horizontal and vertical accuracy of the Android network location engines under rural, suburban, and urban environments. The paper determines the horizontal location accuracy to be approximately 1637 m, 38 m, and 32 m in terms of 68% circular error probable (CEP) for rural, suburban, and urban environments, respectively, and the vertical accuracy to be 1.2 m and 4.6 m in terms of 68% CEP for suburban and urban environments, respectively. In addition, the availability and latency of the location engines are explored. Furthermore, the paper assesses the accuracy of the Android network location accuracy indicator for various drone operation environments. The assessed accuracies of the network locations provide a deeper insight into their potential for drone navigation.

Evaluating Two Low-Cost GPS Receivers for Accuracy and Eventual Use in Pastured Cattle Research

HighlightsA stand-alone GPS receiver produced comparably lower location errors than a smartphone GPS.Low-cost GPS receivers are suitable for use in research on large-herd cattle behavioral response to UAVs.Different testing placements can influence the horizontal accuracy of low-cost GPS receivers and smartphones.Abstract. Using animal-borne global positioning system (GPS) collars, cattle behavioral response to anthropogenic disturbances can be accurately quantified at fine scale. However, the use of dedicated commercial GPS collars in large herd studies is cost-prohibitive. Therefore, low-cost GPS receiver alternatives were evaluated in static placements to determine how their accuracy compares to published data for commercial animal-borne GPS collars. The static accuracies of identical low-cost stand-alone GPS receivers and smartphones were evaluated in an open field without obstructions, under trees with and without canopy, and near an electric fence at 5 min and 1 s sample intervals. The mean circular error probable (CEP) value of the stand-alone GPS receiver was =2 m at 5 min and at 1 s in open field placement. The mean CEP value of the stand-alone GPS receiver was =3 m at 5 min and at 1 s when placed near the electric fence. The smartphone produced mean CEP values of =4 m at 5 min and =3 m at 1 s for the fence line and open field placements. Static testing under trees with canopy at the 5 min sample interval produced mean CEP values 100% greater than under trees without canopy at the 1 s sample interval. Low-cost commercial GPS receivers and smartphones with horizontal accuracy of =5 m at high sample resolution may offer accurate means of quantifying the behavioral response of cattle to UAVs in large herd studies. Keywords: Cattle behavior, Global positioning system, Horizontal accuracy, Smartphone GPS, Stand-alone GPS receiver, UAV, Unmanned aerial vehicle.