Vehicle state and parameter estimation based on improved extend Kalman filter

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

DNA methylation markers in combination with skeletal and dental ages to improve age estimation in children

Rapid and accurate estimation of leaf area index (LAI) is of great significance for the precision agriculture because LAI is an important parameter to evaluate crop canopy structure and growth status. In this study, 20 vegetation indices were constructed by using cotton canopy spectra. Then, cotton LAI estimation models were constructed based on multiple machine learning (ML) methods extreme learning machine (ELM), random forest (RF), back propagation (BP), multivariable linear regression (MLR), support vector machine (SVM)], and the optimal modeling strategy (RF) was selected. Finally, the vegetation indices with a high correlation with LAI were fused to construct the VI-fusion RF model, to explore the potential of multi-vegetation index fusion in the estimation of cotton LAI. The RF model had the highest estimation accuracy among the LAI estimation models, and the estimation accuracy of models constructed by fusing multiple VIs was higher than that of models constructed based on single VIs. Among the multi-VI fusion models, the RF model constructed based on the fusion of seven vegetation indices (MNDSI, SRI, GRVI, REP, CIred-edge, MSR, and NVI) had the highest estimation accuracy, with coefficient of determination (R2), rootmean square error (RMSE), normalized rootmean square error (NRMSE), and mean absolute error (MAE) of 0.90, 0.50, 0.14, and 0.26, respectively. Appropriate fusion of vegetation indices can include more spectral features in modeling and significantly improve the cotton LAI estimation accuracy. This study will provide a technical reference for improving the cotton LAI estimation accuracy, and the proposed method has great potential for crop growth monitoring applications.

Globally, wind energy if properly harnessed, could serve as a source of energy generation in Africa. This study compared the performance of two Machine Learning (ML) algorithms (Linear regression and Random Forest) in predicting wind speed in five major cities in Africa (Yaoundé, Pretoria, Nairobi, Cairo and Abuja). Wind data were collected between January 1, 2000, and December 31, 2022, using the Solar Radiation Data Archive. The data preprocessing was carried out with 80% of the data used for training and 20% for validation. The performance of these ML algorithms was evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and coefficient of determination (R2). The result shows that Nairobi (3.814795 m/s) closely followed by Cairo (3.606453 m/s) has the highest mean wind speed while Yaoundé (1.090512 m/s) has the lowest. Based on the performance metrics used, the two Machine Learning algorithms were competitive. Still, the Linear Regression (LR) algorithm outperformed the Random Forest Algorithm in predicting wind speed in all the selected major African cities. In Yaoundé (RMSE = 0.3892, MAE= 0.3001, MAPE =0.5030), Pretoria (RMSE=1.2339, MAE=0.9480, MAPE=0.7450) Nairobi (RMSE= 0.4223, MAE =0.6499, MAPE =0.1872), Nairobi (RMSE=0.6499, MAE=0.5171, MAPE =0.1872), Cairo (RMSE =1.0909, MAE =0.8544, MAPE =0.3541) and Abuja (RMSE = 0.70245, MAE =0.5441, MAPE= 0.4515) the Linear regression algorithms was found to outperformed Random Forest Regression. Therefore, the Linear regression algorithm is more reliable in predicting wind speed compared with the Random Forest regression.

Accurate forest biomass estimation serves as the foundation of forest management and holds critical significance for a comprehensive understanding of forest carbon storage and balance. This study aimed to integrate Landsat 8 OLI and Sentinel-1A SAR satellite image data and selected a portion of the Shanxia Experimental Forest in Jiangxi Province as the study area to establish a biomass estimation model by screening influencing factors. Firstly, we extracted spectral information, vegetation indices, principal component features, and texture features within 3 × 3-pixel neighborhoods from Landsat 8 OLI. Moreover, we incorporated Sentinel-1’s VV (vertical transmit–vertical receive) and VH (vertical transmit–horizontal receive) polarizations. We proposed an ensemble AGB (aboveground biomass) model based on a neural network. In addition to the neural network model, namely the tent mapping atom search optimized BP neural network (Tent_ASO_BP) model, partial least squares regression (PLSR), support vector machine (SVR), and random forest (RF) regression prediction techniques were also employed to establish the relationship between multisource remote sensing data and forest biomass. Optical variables (Landsat 8 OLI), SAR variables (Sentinel-1A), and their combinations were input into the four prediction models. The results indicate that Tent_ ASO_ BP model can better estimate forest biomass. Compared to pure optical or single microwave data, the Tent_ASO_BP model with the optimal combination of optical and microwave input features achieved the highest accuracy. Its R2 was 0.74, root mean square error (RMSE) was 11.54 Mg/ha, and mean absolute error (MAE) was 9.06 Mg/ha. Following this, the RF model (R2 = 0.54, RMSE = 21.33 Mg/ha, MAE = 17.35 Mg/ha), SVR (R2 = 0.52, RMSE = 17.66 Mg/ha, MAE = 15.11 Mg/ha), and PLSR (R2 = 0.50, RMSE = 16.52 Mg/ha, MAE = 12.15 Mg/ha) models were employed. In conclusion, the BP neural network model improved by tent mapping atom search optimization algorithm significantly enhanced the accuracy of AGB estimation in biomass studies. This will provide a new avenue for large-scale forest resource surveys.

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.

Full text Figures and data Side by side Abstract Editor's evaluation Introduction Materials and methods Results Discussion Data availability References Decision letter Author response Article and author information Metrics Abstract Background: Oxygen uptake (VO2) is one of the most important measures of fitness and critical vital sign. Cardiopulmonary exercise testing (CPET) is a valuable method of assessing fitness in sport and clinical settings. There is a lack of large studies on athletic populations to predict VO2max using somatic or submaximal CPET variables. Thus, this study aimed to: (1) derive prediction models for maximal VO2 (VO2max) based on submaximal exercise variables at anaerobic threshold (AT) or respiratory compensation point (RCP) or only somatic and (2) internally validate provided equations. Methods: Four thousand four hundred twenty-four male endurance athletes (EA) underwent maximal symptom-limited CPET on a treadmill (n=3330) or cycle ergometer (n=1094). The cohort was randomly divided between: variables selection (nrunners = 1998; ncyclist = 656), model building (nrunners = 666; ncyclist = 219), and validation (nrunners = 666; ncyclist = 219). Random forest was used to select the most significant variables. Models were derived and internally validated with multiple linear regression. Results: Runners were 36.24±8.45 years; BMI = 23.94 ± 2.43 kg·m−2; VO2max=53.81±6.67 mL·min−1·kg−1. Cyclists were 37.33±9.13 years; BMI = 24.34 ± 2.63 kg·m−2; VO2max=51.74±7.99 mL·min−1·kg−1. VO2 at AT and RCP were the most contributing variables to exercise equations. Body mass and body fat had the highest impact on the somatic equation. Model performance for VO2max based on variables at AT was R2=0.81, at RCP was R2=0.91, at AT and RCP was R2=0.91 and for somatic-only was R2=0.43. Conclusions: Derived prediction models were highly accurate and fairly replicable. Formulae allow for precise estimation of VO2max based on submaximal exercise performance or somatic variables. Presented models are applicable for sport and clinical settling. They are a valuable supplementary method for fitness practitioners to adjust individualised training recommendations. Funding: No external funding was received for this work. Editor's evaluation The authors have established new formulas to predict maximum oxygen uptake for cyclists and runners based on submaximal exercise testing and anthropometric characteristics. This is an important study with a large and comprehensive dataset, which may be helpful for many exercise labs. The work is convincing, using appropriate and validated methodology in line with the current state-of-the-art, as shown by references to common exercise books. https://doi.org/10.7554/eLife.86291.sa0 Decision letter Reviews on Sciety eLife's review process Introduction The oxygen uptake (VO2) is considered an important metric in assessing cardiorespiratory fitness, health status, or endurance performance potential (Guazzi et al., 2012). With the application of standardised procedures and interpretation protocols, during graded exercise tests (GXT), the (maximal oxygen uptake) VO2max can be established (Bentley et al., 2007). GXT is the most widely used assessment to examine the dynamic relationship between exercise and integrated physiological systems (Albouaini et al., 2007; Bentley et al., 2007). The information from GXT during cardiopulmonary exercise testing (CPET) can be applied across the spectrum of sport performance, occupational safety screening, research, and clinical diagnostics (Guazzi et al., 2017). VO2 max is often used as a boundary between severe and extreme intensity domains and by definition requires maximal effort from the tested subject (Gaesser and Poole, 1996). However, it is not always recommended or possible to undertake a test to exhaustion (Guazzi et al., 2012). For the athletes, the proximity of competition or injury history can allow submaximal testing, but not testing to exhaustion (Sassi et al., 2006). Testing that requires maximal effort may be disruptive to the training process or interfere with race performance (Coutts et al., 2007; Lamberts et al., 2011). Due to practical constraints, tests to exhaustion or peak-power-output tests are often performed only two or three times a year (Coutts et al., 2007). However, VO2 values are widely used in sport science and the decision-making process (Mann et al., 2013). VO2 is widely considered one of the major endurance performance determinants (Joyner and Coyle, 2008). Using VO2max to guide the selection process, prescribing training intensity, assessing training adaptations, or predicting race times is a common practice in high-performance sports (Bassett and Howley, 2000; Bentley et al., 2007; Hawley and Noakes, 1992; Noakes et al., 1990). VO2max is also one of the critical vital signs coordinating the function of the cardiovascular, respiratory, and muscular systems, it is an indicator of overall body health status (Kaminsky et al., 2017). Quantifying VO2max provides additional input regarding clinical decision-making, risk stratification, evaluation of therapy, and physical activity guidelines (Guazzi et al., 2012). For patients undertaking a test to exhaustion is rarely needed or possible due to health restraints or cardiac risk (Guazzi et al., 2016). For many years researchers have studied indirect methods of estimating VO2max(Sartor et al., 2013). Protocols such as the Astrand-Ryhming Test, Six-Minute Walk Test, or YMCA Step Test have been established and validated (Astrand and Ryhming, 1954; Beutner et al., 2015; Carey, 2022; Jalili et al., 2018). Moreover, estimation of the VO2 and heart rate (HR) values below the ventilatory threshold can be based on cardiorespiratory kinetics assessment using randomised changes in the work rate known as a pseudo-random binary sequences testing (Hoffmann et al., 2022). However, with the development of technology, the accessibility of laboratory testing and mobile testing improved (Montoye et al., 2020; Pritchard et al., 2021). Therefore, new opportunities to develop more precise yet simple and accessible methods and models to assess VO2max occur (Jurov et al., 2023). This appears to be especially important considering the low prediction accuracy of most of the VO2max formulae that were validated in our previous study (Wiecha et al., 2023). Recently, we have been observing the development of prediction methods with the usage of machine learning (ML) and artificial intelligence (AI) (Ashfaq et al., 2022). Both ML and AI are used in sport science as forecasting and decision-making support tools (Abut and Akay, 2015; Bobowik and Wiszomirska, 2022; Chmait and Westerbeek, 2021; Hammes et al., 2022; Rossi et al., 2021). There is growing evidence that VO2max prediction based on ML models, especially support vector ML and artificial neural network models, exhibits more robust and accurate results compared to MLR only (Abut and Akay, 2015; Ashfaq et al., 2022). Therefore, in this research, with the support of ML, we look for algorithms and prediction patterns that allow us to use values obtained during submaximal CPET and somatic measurements to estimate maximal VO2max values in male runners and cyclists. We stipulate that prediction models allow for accurate calculation of VO2max based on somatic or submaximal CPET variables. Materials and methods We have applied the development and validation of the prediction TRIPOD guidelines to conduct the study (see Supplementary Material 1TRIPOD Checklist for Prediction Model Development and Validation) (Collins et al., 2015). The study is based on retrospective data analysis from the CPET registry collected from 2013 to 2021 at the medical clinic (Sportslab, Warsaw, Poland). All CPET have been performed at the individual request of participants, as a part of regular training monitoring or performance assessment. Ethical approval Request a detailed protocol The Institutional Review Board of the Bioethical Committee at the Medical University of Warsaw (AKBE/32/2021) has approved the study protocol. The regulations of the Declaration of Helsinki were met during all parts of the study. Each study participant delivered written consent to undergo CPET and participate in the study. Derivation cohort Request a detailed protocol We selected the cohort with the use of rigorous exclusion/inclusion criteria. Due to the insufficient number of women in our database and the number of potential variables in the regression models for adequate power, we had to limit ourselves to conduct analysis in the male population only (Martens and Logan, 2021). Out of 6439 healthy, adult male cyclists and long-distance runners that undergone CPET, 4423 met the criteria as further: (1) age ≥18 years, (2) declared regular cycling or running training for ≥3 months, (3) had no extreme outliers ≤ or ≥±3 standard deviations (SD) from mean for all of the testing variables (beyond ≥±3 SD in VO2max), (4) lack of any injury, medical condition, or addiction in medical history that may affect exercise capacity, (5) not taking any medications with a modifying effect on exercise capacity, (6) maximum exertion achieved during CPET. We defined the maximum exertion in CPET as the fulfilment of the minimum six of the following criteria: (1) respiratory exchange ratio (RER) ≥1.10, (2) present VO2 plateau (growth <100 mL·min–1 in VO2 despite increased running speed or cycling power), (3) respiratory frequency (fR) ≥45 breaths·min–1, (4) declared subjective exertion intensity during CPET ≥18 in the Borg scale (Borg, 1970), (5) blood lactate concentration [La-]b ≥8 mmol·L–1, (6) growth in speed/power ≥10% of respiratory compensation point (RCP) values after exceeding the RCP, (7) peak heart rate (HRpeak) ≥15 beats·min–1 below predicted maximal heart rate (HRmax) (Lach et al., 2021). Participants’ selection procedure has been shown in Figure 1. Figure 1 Download asset Open asset Flowchart of the preliminary inclusion and exclusion process. Abbreviations: EA, endurance athlete; CPET, cardiopulmonary exercise testing; SD, standard deviation; TE, treadmill; RER, respiratory exchange ratio; VO2, oxygen uptake (mL·min−1·kg−1); [La−]b, lactate concentration (mmol·L−1); fR, breathing frequency (breaths·min−1); RCP, respiratory compensation point; HRpeak, peak heart rate (beats·min−1); HRmax, maximal heart rate (bpm). At both stages of the selection, some participants met several (>1) exclusion criteria. Somatic measurements and CPET protocols Request a detailed protocol Body mass was measured with a body composition (BC) analyser (Tanita, MC 718, Japan) with the multifrequency of 5 kHz/50 kHz/250 kHz via the bioimpedance analysis and normal testing mode. The participants’ skin was cleaned with alcohol before placing the electrodes on the skin. Prior to the test, the participants received instructions to refrain from exercising for 2 hr, consume a light meal rich in carbohydrates 2–3 hr beforehand, and maintain hydration by drinking isotonic beverages. Additionally, they were advised to abstain from medications, caffeine, and cigarettes on the day of the test. Running CPET (TE) was performed on a mechanical treadmill (h/p/Cosmos Quasar, Germany). Cycling CPET (CE) was performed on Cyclus-2 (RBM elektronik-automation GmbH, Leipzig, Germany). Hans Rudolph V2 mask (Hans Rudolph, Inc, Shawnee, KS, USA), breath-by-breath method with Cosmed Quark CPET gas exchange analysing device (Cosmed Srl, Rome, Italy), and Quark PFT Suite to Omnia 1.6 software were utilised. The gas analyser device was regularly calibrated with the reference gas (16% O2; 5% CO2) in accordance with the manufacturer’s instructions (Airgas USA, LLC, Plumsteadville, PA, USA). From 2013 to 2021, three Cosmed Quark CPET units were used. HR was measured with the Cosmed torso belt (Cosmed srl, Rome, Italy). [La-]b was measured via enzymatic-amperometric electrochemical technique with Super GL2 analyser (Müller Gerätebau GmbH, Freital, Germany). The [La-]b analyser was regularly calibrated before each measurement series. The 40 m2 indoor, air-conditioned laboratory with 20–22°C temperature and 40–60% humidity, and 100 m ASL provided the same conditions for all BC and CPET. Each CPET began with a 5 min personalised warm-up (walk or easy jog with ‘conversational’ intensity for running, easy pedalling with ‘conversational’ intensity for cycling). Then after the preparation (about 5 min), the continuous progressive step test was conducted. Due to the population diversity (training status), the running test speed started from 7 to 12 km·hr–1 with a 1% treadmill incline. The choice of initial starting speed was determined by the interview and sports results achieved. For example, those running less than 60 min at a distance of 10 km started the test at 7 km/hr, while those running 10 km for less than 35 min started the test at an initial speed of 12 km/hr. The pace increased by 1 km·hr–1 every 2 min with no change in incline. The cycling test began at 60–150 W, depending on the athletes training status. The power increased by 20–30 W every 2 min. It was recommended to maintain a constant cadence of 80–90 (repetition·min–1) during the test. The tests were terminated due to exhaustion: volitional inability to continue the activity or/and VO2 and HR plateau with increasing load or/and observed disturbance of coordination in running or/and inability to maintain the set cadence. Due to the graded protocol used, the cycling power and running speed values have been calculated as a function of time to better reflect the actual level for the test moment being determined (Kuipers et al., 1985). Before the test, after every step, and 3 min after the termination of the effort technician took a 20 µL blood sample from a fingertip. Samples were collected during the test without interrupting the effort. The samples were taken from the initial puncture. The first blood drop was collected into the swab and the second blood drop was drawn for further analysis into the capillary. VO2max was recorded as the highest value (15 s intervals) before the termination of the test. HRmax was recorded as the highest value obtained at the end of the test, without averaging. The anaerobic threshold (AT) was established with the following criteria: (1) common start of VE/VO2 and VE/VCO2 curves, (2) end-tidal partial pressure of oxygen raised constantly with the end-tidal partial pressure of carbon dioxide (Beaver et al., 1986). The was established with the following criteria: (1) PetCO2 must decrease after reaching maximal amount, (2) the presence of fast nonlinear growth in VE (second deflection), (3) the VE/VCO2 ratio achieved minimum and started to rise, and (4) a nonlinear increase in VCO2 versus VO2 (lack of linearity) (Beaver et al., 1986). The [La-]b was estimated for AT and RCP in relation to power or speed (Wiecha et al., 2022). Data analysis Request a detailed protocol Our comprehensive ML approach enables the evaluation of each formula by preliminary variables precision (at the stage of selection), then accuracy (during the model’s building) and recall (in internal validation). Individual CPET results were saved into the Excel file (Microsoft Corporation, Redmond, WA, USA) and a custom-made script was used to generate the database in Excel (Python programming). Further, mean, SD, and 95% confidence intervals (CI) were calculated. The normality of the distribution of the data was examined using the Shapiro-Wilk test and intergroup differences were calculated using the Student’s t-test for independent variables. Three-step variable selection procedures based on random forests were applied using the R package VSURF in RStudio software (R Core Team, Vienna, Austria; version 3.6.4) (Genuer et al., 2016). For each level of measurement (AT, RCP) and their combination (AT+RCP), significant variables were identified separately. The first step was dedicated to eliminate irrelevant variables from the dataset. Second step aimed to select all variables related to the response for interpretation purposes. The third step refined the selection by eliminating redundancy in the set of variables selected by the second step, for prediction purposes (Genuer et al., 2017). Each time for variables selection, the anthropometric variables as in Tables 1–2 and the CPET parameters given in Tables 3–4 from a specific level of measurement (AT; RCP) and their combinations were visible. Table 1 Basic anthropometric characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDAge (years)36.235.6–36.98.4535.935.5–36.38.0535.534.9–36.28.14Height (cm)180.0179.6–180.56.04179.4179.1–179.76.13179.7179.2–180.26.61BM (kg)77.777.0–78.49.3577.777.3–78.19.2977.977.1–78.610.1BMI (kg·m–2)23.923.8–24.12.4324.124.0–24.22.4124.123.9–24.32.56BF (%)15.415.1–15.74.5515.515.3–15.74.5215.415.1–15.84.55FM (kg)12.211.9–12.64.6812.312.1–12.54.6512.311.9–12.74.92FFM (kg)65.565.0–66.06.4365.465.1–65.76.3165.665.1–66.16.86 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 2 Basic anthropometric characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDAge (years)37.336.6–38.09.1337.135.9–38.49.5037.636.5–38.88.46Height (cm)179.9179.4–180.46.27180.1179.2–181.06.96180.2179.4–181.06.13BM (kg)78.878.1–79.69.8079.177.7–80.510.479.878.4–81.310.9BMI (kg·m–2)24.324.1–24.62.6324.424.0–24.72.8024.624.2–25.02.96BF (%)16.415.7–17.14.9916.115.7–16.54.8116.215.5–16.84.87FM (kg)13.312.6–14.15.6613.012.6–13.45.2713.312.5–14.05.85FFM (kg)65.864.9–66.66.2565.865.4–66.36.0666.665.7–67.46.58 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 3 Cardiopulmonary exercise testing (CPET) characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)38.438.1–38.85.0138.538.3–38.74.8838.137.7–38.55.16RERAT0.870.86–0.870.040.870.86–0.870.040.870.86–0.870.04HRAT (beats·min–1)151.5150.8–152.310.3151.0150.6–151.510.8152.0151.2–152.810.8VEAT (L·min–1)79.178.1–80.012.278.377.8–78.912.077.276.3–78.212.0SPEEDAT (km·h–1)11.010.9–11.11.4511.011.0–11.11.3610.910.8–11.01.42LAAT (mmol·L–1)2.082.02–2.140.631.801.76–1.830.622.352.27–2.420.72rVO2RCP (mL·min–1·kg–1)47.547.0–48.05.8847.747.4–48.06.1547.346.8–47.86.16RERRCP1.001.00–1.000.041.001.00–1.000.041.001.00–1.000.03HRRCP (beats·min–1)173.4172.7–174.19.21173.2172.8–173.69.30174.3173.5–175.09.50VERCP (L·min–1)114.7113.5–116.015.9113.9113.1–114.616.7112.7111.4–114.016.2SPEEDRCP (km·h–1)14.013.9–14.11.7714.114.0–14.11.7013.913.8–14.11.75LARCP (mmol·L–1)4.724.63–4.821.044.404.34–4.451.044.814.69–4.931.14rVO2max (mL·min–1·kg–1)53.853.3–54.36.6754.354.0–54.66.9553.853.3–54.37.09 CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; SPEEDAT, velocity at anaerobic threshold; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; SPEEDRCP, velocity at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; rVO2max, maximal oxygen uptake relative to body mass. Table 4 Cardiopulmonary exercise testing (CPET) characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)33.032.5–33.45.8433.232.4–33.95.6833.732.9–34.55.89RERAT0.870.87–0.870.040.870.87–0.880.040.870.87–0.880.04HRAT CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; power at anaerobic threshold relative to body mass; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; power at respiratory compensation point relative to body mass; rVO2max, maximal oxygen uptake relative to body mass. selection variables were in the further only selected parameters were into multiple linear regression The data for MLR model building were randomly into that is testing, validation and of the a only significant were in the Derived are by the of mean and mean analysis was used to the model’s precision and accuracy during validation and tests to the fulfilment of MLR test the of in MLR test assessment between and test of Each model was examined the and any have not been 2 package in RStudio (R Core Team, Vienna, Austria; version version for and software version were used in was considered as the Results Somatic measurements and CPET results data of the runners models for testing, and validation are in Table while cyclists are in Table The runners of and for testing, and validation the cyclists and differences between of runners and cyclists were in BMI and between testing in all between validation only in CPET results for runners models are in Table 3 and for cyclists in Table Runners in the cohort achieved relative to body mass VO2max of in testing group and in validation group cyclists mean was and for testing, and validation to body mass oxygen uptake at anaerobic threshold in runners for ± ± and ± of in testing, and validation it was ± ± and ± of rVO2max, relative to body mass oxygen uptake at respiratory compensation point in runners for ± ± and ± of for testing, and validation while in cyclists for ± ± and ± of rVO2max, There were no significant differences in values between testing, and validation the runners and cyclists between runners and cyclists results were all significant Prediction models based on AT and RCP Full of MLR prediction models for cyclists are in Table for runners in Table The models prediction performance is as with and for cyclists from for somatic parameters to for RCP equations. For runners from for to for AT and equations. for cyclists models was the for RCP and the highest for For from for AT and to for equation. observed for cyclists was the for RCP in the validation group and the highest for while in runners the for AT and and the highest for The performance of prediction is in Figure Figure 2 Download asset Open asset of prediction for Abbreviations: maximal oxygen anaerobic threshold; RCP, respiratory compensation point; All values are in performance for running while the performance for cycling equations. performance of the prediction model for for for AT and for somatic-only equation. Table 5 VO2max prediction for cyclists. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass power at anaerobic threshold relative to body mass rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass VERCP, pulmonary ventilation at respiratory compensation point BF, body fat BM, body mass Table VO2max prediction for runners. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass SPEEDAT, velocity at anaerobic threshold FFM, fat mass VEAT, pulmonary ventilation at anaerobic threshold HRAT, heart rate at anaerobic threshold BF, body fat rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass SPEEDRCP, velocity at respiratory compensation point Models validation of each model for cyclists is in Table while for runners in Table the performance of our prediction was to that observed in the

Nowadays , nonlinear time series and artificial neural networks (ANN) models are used for forecasting in the field of business, agriculture and soon. Recent studies have shown, ANN have been successfully used for forecasting of financial and agriculture data series The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. ANN have more advantages that can approximate to model both linear and nonlinear structures in time series, they are not able to handling both structures equally well. The autoregressive integrated moving average (ARIMA) model and two ANN models namely, Radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) methods were applied to Hyderabad airport traffic data. The data obtained for 15 years from 2002–2003 to 2016–2017 about domestic and international passenger of International Airport of Hyderabad, India. In this research paper, we compared the performances of ARIMA, RBFNN and ERNN were based on three measures: mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results showed that RBFNN obtained the smallest MAE, MAPE and RMSE in both the modeling and forecasting processes. The performances of the three models ranked in ascending order were: ARIMA, ERNN and the RBFNN model. Keywords: T ime series, forecasting, artificial neural networks, ARIMA models, radial basis function neural networks, and Elman recurrent neural networks Cite this Article R. Ramakrishna, Berhe Aregay, Tewodros Gebregergs. The Comparison in Time Series Forecasting of Air Traffic Data by Autoregressive Integrated Moving Average Model, Radial Basis Function and Elman Recurrent Neural Networks. Research & Reviews: Journal of Statistics . 2018; 7(3): 75–90p.

Research on the theoretical prediction method for surface movement duration considering the spatio-temporal subsidence characteristics

This article uses machine learning techniques as fuzzy and neuro-fuzzy ANFISs, to develop and compare prediction models capable of relating pregnant women’s exposure to air pollutants, such as Nitrogen Dioxide and Particulate Matter, the mother’s age, and the number of prenatal consultations to the incidence of premature birth. In the current literature, studies can be found that relate prematurity to the exposure of pregnant women to NO2, O3, and PM10; to Toluene and benzene, mainly in the window 5 to 10 days before birth; and to PM10 in the week before birth. Both models used logistic regression to quantify the effects of pollutants as a result of premature birth. Datasets from Brazil—Departamento de Informatica do Sistema Único de Saúde (DATASUS) and Companhia Ambiental do Estado de São Paulo (CETESB)—were used, covering the period from 2016 to 2018 and comprising women living in the city of São José dos Campos (SP), Brazil. In order to evaluate and compare the different techniques used, evaluation metrics were calculated, such as correlation (r), coefficient of determination (R2), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Square Error (MSE), and Mean Absolute Error (MAE). These metrics are widely used in the literature due to their ability to evaluate the robustness and efficiency of prediction models. For the RMSE, MAPE, MSE, and MAE metrics, lower values indicate that prediction errors are smaller, demonstrating better model accuracy and confidence. In the case of (r) and R2, a positive and strong result indicates alignment and better performance between the real and predicted data. The neuro-fuzzy ANFIS model showed superior performance, with a correlation (r) of 0.59, R2 = 0.35, RMSE = 2.83, MAPE = 5.35%, MSE = 8.00, and MAE = 1.70, while the fuzzy model returned results of r = 0.20, R2 = 0.04, RMSE = 3.29, MSE = 10.81, MAPE = 6.67%, and MAE = 2.01. Therefore, the results from the ANFIS neuro-fuzzy system indicate greater prediction capacity and precision in relation to the fuzzy system. This superiority can be explained by integration with neural networks, allowing data learning and, consequently, more efficient modeling. In addition, the findings obtained in this study have potential for the formulation of public health policies aimed at reducing the number of premature births and promoting improvements in maternal and neonatal health.

Drought is a complex and frequently occurring natural hazard in many parts of the world. Therefore, accurate drought forecasting is essential to mitigate its adverse impacts. This research has inferred the implication and the appropriateness of the extreme learning machine (ELM) algorithm for drought forecasting. For numerical evaluation, time series data of the Standardized Precipitating Temperature Index (SPTI) are used for nine meteorological stations located in various climatological zones of Pakistan. To assess the performance of ELM, this research includes parallel inferences of multilayer perceptron (MLP) and autoregressive integrated moving average (ARIMA) models. The performance of each model is assessed using root mean square error (RMSE), mean absolute error (MAE), mean absolute percent error (MAPE), Kling‐Gupta efficiency (KGE), Willmott index (WI), and Karl Pearson’s correlation coefficient. Generally, graphical results illustrated an excellent performance of the ELM algorithm over MLP and ARIMA models. For training data of SPTI‐1, ELM’s best performance has observed at Chitral station (RMSE = 0.374, KGE = 0.838, WI = 0.960, MAE = 0.272, MAPE = 259.59, R = 0.93). For SPTI‐1 at Astore station, the numerical results are (RMSE = 0.688, KGE = 0.988, WI = 0.997, MAE = 0.798, MAPE = 247.35). The overall results indicate that the ELM outperformed by producing the smallest RMSE, MAE, and MAPE values and maximum values for KGE, WI, and correlation coefficient values at almost all the selected meteorological stations for (1, 3, 6, 9, and 12) month time scales. In summary, this research endorses the use of ELM for accurate drought forecasting.

The rapid, accurate estimation of leaf nitrogen content (LNC) and plant nitrogen content (PNC) in cotton in a non-destructive way is of great significance to the nutrient management of cotton fields. The RGB images of cotton fields in Shihezi (China) were obtained by using a low-cost unmanned aerial vehicle (UAV) with a visible-light digital camera. Combined with the data of LNC and PNC in different growth stages, the correlation between N content and visible light vegetation indices (VIs) was analyzed, and then the Random Forest (RF), Support Vector Machine (SVM), Back Propagation Neural Network (BP), and stepwise multiple linear regression (SMLR) were used to develop N content estimation models at different growth stages. The accuracy of the estimation model was assessed by coefficient of determination (R2), root mean squared error (RMSE), and relative root mean square error (rRMSE), so as to determine the optimal estimated growth stage and the best model. The results showed that the correlation between VIs and LNC was stronger than that between PNC, and the estimation accuracy of different models decreased continuously with the development of growth stages, with higher estimation accuracy in the peak squaring stage. Among the four algorithms, the best accuracy (R2 = 0.9001, RMSE = 1.2309, rRMSE = 2.46% for model establishment, and R2 = 0.8782, RMSE = 1.3877, rRMSE = 2.82% for model validation) was obtained when applying RF at the peak squaring stage. The LNC model for whole growth stages could be used in the later growth stage due to its higher accuracy. The results of this study showed that there is a potential for using an affordable and non-destructive UAV-based digital system to produce predicted LNC content maps that are representative of the current field nitrogen status.

Purpose of reseach. The article deals with the study of the operation of the extended Kalman filter (EKF), supplemented with an adaptive digital filter in order to compensate for the error in the operation of the EKF when performing data integration of the mobile robot control system.Methods. The adaptive digital filter (ADF) is a self-tuning filter that iteratively changes its variable parameters to achieve the optimal desired values of the output data. The EKF supplemented with the ADF with the NLMS adaptation algorithm will be called the EKF–ADF system or the EKF+NLMS digital filter. An important task is the selection of the number of frames and ADF weighting coefficients at which the optimum quality of noise suppression and the convergence rate of the adaptation algorithm are achieved.Results. With various options of organizing the operation of the ADF buffer memory, the adjusted values for assessing the state of the ‘mobile robot–environment’ system may differ. When the number of input data frames and ADF weighting coefficients are small, low quality noise suppression will be observed. With an increase in the number of frames and weighting coefficients, the quality of noise suppression is improved, and the convergence rate of the adaptation algorithm decreases.Conclusion. The EKF+NLMS digital filter algorithm takes an intermediate place between the EKF algorithm and the serial filtering of the EKF and ADF signals with the NLMS algorithm according to the criteria for estimating the mean square error, mean absolute error, signal-to-noise ratio, and convergence rate.

Background and Objectives: Teak (Tectona grandis) is one of Thailand's most valuable economic tree species, prized for its exceptional qualities such as durability, aesthetic appeal, and resistance to pests and diseases. Its popularity spans both domestic and international markets, making accurate estimation of merchantable teak volume essential for forest management and the timber industry. Precise volume estimation facilitates accurate economic valuation and minimizes resource losses associated with traditional destructive tree-felling methods. Recent advancements in technology, light detection and ranging or LiDAR, have provided opportunities to enhance the accuracy and efficiency of forest resource data collection. Among these tools, the Terrestrial Laser Scanner (TLS) stands out for its ability to generate high-resolution three-dimensional (3D) models of individual trees and forest stands in a non-destructive method. Unlike traditional methods, TLS enables data collection without damaging trees, offering a sustainable and efficient alternative for forestry applications. This study aimed to develop a methodology for utilizing TLS to construct 3D models of teak trees to estimate merchantable wood volume. The results were compared with the traditional felling method, which is considered the most accurate but destructive. In addition, the study attempts to establish predictive equations and volume tables for estimating merchantable teak volume. These outputs aimed to support sustainable forest management practices, reduce resource wastes, and facilitate the economic valuations of teak for the timber industry. Methods: The study was conducted in the Mae Chang forest plantation, located in Mae Mo district, Lampang province, Thailand. The stratified random sampling was employed to establish 12 sample plots, each sizing 40 m × 40 m. The plots were divided into two age groups based on plantation year: 18 years old (planted in 2006) and 39 years old (planted in 1985), with six plots in each group. Data collection involved using a Faro Focus S150 TLS to scan individual trees in each plot. The TLS data were processed to create detailed 3D tree models for further analysis. Merchantable timber volume was calculated using two methods: the stem curve method and quantitative structure models (QSM), both implemented through the 3D forest software. The TLS-derived volume estimates were validated by felling selected sample trees. The diameters and merchantable lengths of these felled trees were measured, and their volumes were calculated using Huber’s formula. Statistical analysis was performed to compare TLS-derived volumes with traditional felling-based volumes using paired t-tests. The accuracy of TLS-derived estimates was evaluated using root mean square error (RMSE). Additionally, predictive equations for merchantable volume estimation were developed using regression analysis. Two types of equations were created: one using diameter at breast height (DBH) as the sole variable and the other incorporating both DBH and merchantable height (HM). A volume table was constructed based on these equations, enabling non-destructive volume estimation for teak trees of varying DBH and HM ranges. Results: The 3D models generated using TLS provided merchantable volume estimates that closely aligned with volumes derived from felled trees. Statistical analysis revealed no significant differences between TLS-derived volumes and traditional felling-based volumes (p &gt; 0.05). The RMSE values for TLS-derived estimates were 0.02 and 0.03 cubic meters when using the stem curve and QSM methods, respectively, indicating high accuracy. Two predictive equations for merchantable volume estimation were developed. The first equation utilized DBH as a single predictor variable and demonstrated a coefficient of determination (R²) of 0.966. The second equation incorporated both DBH and HM, achieving a higher R² value of 0.988. Validation of these equations using data from felled trees showed mean absolute percentage errors (MAPE) of 17.81% and 11.01%, respectively, confirming their suitability for practical applications. The most accurate equation was subsequently used to construct a merchantable volume table, which estimating based on DBH and HM ranges without requiring tree felling. This table provides a practical tool for forest managers and timber industry stakeholders to assess teak volume efficiently and sustainably. Conclusion: The results of this study demonstrate that TLS is a reliable and effective tool for non-destructive estimation of merchantable teak volume. The 3D models generated using TLS data enable precise volume estimation through methods such as stem curve and QSM, producing results that are statistically comparable to traditional destructive felling methods. The acceptable error margins and high accuracy of TLS-derived estimates highlight its potential as a sustainable alternative to conventional volume estimation techniques. By minimizing the need for destructive sampling, TLS-based methods contribute to sustainable forest management practices, preserving valuable tree resources while maintaining economic productivity. Furthermore, the development of predictive equations and merchantable volume tables offers practical solutions for forest managers and timber industry professionals, streamlining the assessment of merchantable volume and economic valuation. Overall, this study underscores the importance of integrating advanced technologies such as TLS into forestry practices. By improving the accuracy and sustainability of resource assessments, these innovations can support long-term forest conservation and enhance the economic potential of Thailand's teak plantations.

Kalman filter based on a fractional discrete-time stochastic augmented CoVid-19 model