scholarly journals A Robust Extended Kalman Filter Applied to Ultrawideband Positioning

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Chuanyang Wang ◽  
Houzeng Han ◽  
Jian Wang ◽  
Hang Yu ◽  
Deng Yang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Robust Estimation ◽  
Hypothesis Test ◽  
Systematic Errors ◽  
Random Errors ◽  
Model Errors ◽  
Global Test ◽  
Practical Applications ◽  
The Individual

Ultrawideband (UWB) is well-suited for indoor positioning due to its high resolution and good penetration through objects. The observation model of UWB positioning is nonlinear. As one of nonlinear filter algorithms, extended Kalman filter (EKF) is widely used to estimate the position. In practical applications, the dynamic estimation is subject to the outliers caused by gross errors. However, the EKF cannot resist the effect of gross errors. The innovation will become abnormally large and the performance and the reliability of the filter algorithm are inevitably influenced. In this study, a robust EKF (REKF) method accompanied by hypothesis test and robust estimation is proposed. To judge the validity of model, the global test based on Mahalanobis distance is implemented to assess whether the test statistical term exceeds the threshold for outlier detection. To reduce and eliminate the effects of the individual outlier, the robust estimation using scheme III of the Institute of Geodesy and Geophysics of China (IGGIII) based on local test of the normalized residual is performed. Meanwhile, three kinds of stochastic models for outliers are expressed by modeling the contaminated distributions. Furthermore, the simulation and measurement experiments are performed to verify the effectiveness and feasibility of the proposed REKF for resisting the outliers. Simulation experiment results are given to demonstrate that the outliers following all the three kinds of contaminated distributions can be detected. The proposed REKF can effectively control the influences of the outliers being treated as systematic errors and large variance random errors. When the outliers come from the thick-tailed distribution, the robust estimation does not play a role, and the REKF are equivalent to the EKF method. The measured experiment results show that the outliers will be generated in the nonline-of-sight environment whose impact is abnormally serious. The robust estimation can provide relatively reliable optimized residuals and control the influences of the outliers caused by gross errors. We can believe that the proposed REKF is effective to resist the effects of outliers and improves the positioning accuracy compared with least-squares (LS) and EKF method. Moreover, the adaptive filter and ranging error model should be considered to compensate the state model errors and ranging systematic errors respectively. Then, the measurement outliers will be detected more correctly, and the robust estimation will be used effectively.

Robust estimation of traffic density with missing data using an adaptive-R extended Kalman filter

2022 ◽  
Vol 421 ◽  
pp. 126915
Author(s):  
A.S.M. Bakibillah ◽  
Yong Hwa Tan ◽  
Junn Yong Loo ◽  
Chee Pin Tan ◽  
M.A.S. Kamal ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Missing Data ◽  
Extended Kalman Filter ◽  
Robust Estimation ◽  
Traffic Density

scholarly journals A Modified Extended Kalman Filter for a Two-Antenna GPS/INS Vehicular Navigation System

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3809 ◽  
Author(s):  
Yushi Hao ◽  
Aigong Xu ◽  
Xin Sui ◽  
Yulei Wang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Navigation System ◽  
Adaptive Estimation ◽  
Estimation Method ◽  
Measurement Noise ◽  
Model Errors ◽  
State Process ◽  
Stability And Accuracy ◽  
The Impact

Recently, the integration of an inertial navigation system (INS) and the Global Positioning System (GPS) with a two-antenna GPS receiver has been suggested to improve the stability and accuracy in harsh environments. As is well known, the statistics of state process noise and measurement noise are critical factors to avoid numerical problems and obtain stable and accurate estimates. In this paper, a modified extended Kalman filter (EKF) is proposed by properly adapting the statistics of state process and observation noises through the innovation-based adaptive estimation (IAE) method. The impact of innovation perturbation produced by measurement outliers is found to account for positive feedback and numerical issues. Measurement noise covariance is updated based on a remodification algorithm according to measurement reliability specifications. An experimental field test was performed to demonstrate the robustness of the proposed state estimation method against dynamic model errors and measurement outliers.

scholarly journals Calibration of Photometry from the Gemini Multi-Object Spectrograph on Gemini North

2009 ◽  
Vol 26 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Inger Jørgensen
Keyword(s):  
Systematic Errors ◽  
Random Errors ◽  
Standard Star ◽  
Primary Mirror ◽  
Color Terms ◽  
User Community ◽  
Color Term ◽  
The Individual ◽  
Zero Points

AbstractAll available observations of photometric standard stars obtained with the Gemini Multi-Object Spectrograph at Gemini North in the period from August 2001 to December 2003 have been used to establish the calibrations for photometry obtained with the instrument. The calibrations presented in this paper are based on significantly more photometric standard star observations than usually used by the individual users. Nightly photometric zero points as well as color terms are determined. The color terms are expected to be valid for all observations taken prior to UT 2004 November 21 at which time the Gemini North primary mirror was coated with silver instead of aluminium. While the nightly zero points are accurate to 0.02 mag or better (random errors), the accuracy of the calibrations is limited by systematic errors from so-called ‘sky concentration’, an effect seen in all focal reducer instruments. We conclude that an accuracy of 0.035 to 0.05 mag can be achieved by using calibrations derived in this paper. The color terms are strongest for very red objects, e.g. for objects with (r′ – z′) = 3.0 the resulting z′ magnitudes will be ≈0.35 mag too bright if the color term is ignored. The calibrations are of importance to the large Gemini user community with data obtained prior to UT 2004 November 21, as well as future users of achive data from this period in time.

SET UP ERRORS AND RECOMMENDED SAFETY MARGINS IN THE PELVIC RADIOTHERAPY FIELDS OF CANCER CERVIX PATIENTS: AN INSTITUTIONAL EXPERIENCE

2016 ◽  
Vol 1 (2) ◽  
Author(s):  
Jitendra Nigam ◽  
Piyush Kumar ◽  
Uthya Balan
Keyword(s):  
Safety Margin ◽  
Conformal Radiotherapy ◽  
Systematic Errors ◽  
Random Errors ◽  
Cancer Cervix ◽  
Lateral Field ◽  
Bony Landmarks ◽  
Safety Margins ◽  
Set Up ◽  
The Individual

INTRODUCTION: Uncertainty exists in radiotherapy delivery due to daily patients set up errors resulting in a difference between planned and delivered dose. The conformal radiotherapy requires reduced margins around the clinical target volume (CTV) with respect to traditional radiotherapy technique and hence these positioning errors are accounted in CTV-PTV margin calculations. The primary aim of this study is to evaluate the set up errors and find out the optimum safety margins for the anterior and lateral fields of pelvis in the patients of cancer cervix treated with 3DCRT by four field box technique. The secondary objective was to study the adequacy of safety margin using the dosimetric and volumetric DVH data. METHODS AND MATERIALS: Study was conducted on twenty one patients of cancer cervix. All patients were immobilsed by full body Vaclok cushions. The radiotherapy to whole pelvis was planned by four field (Anterio-posterior, Posterio-anterior and two laterals) box technique with shielding of corners using multieaf collimators in Varian CLINAC 2300C/D. Weekly EPID images were acquired with Varian aS500 for each patient and were compared with the DRR images using the Portal Vision (Version 7.3.10). The displacement of EPID image from the DRR image was measured by defining reproducible bony landmarks in directions- X (Left to right (LR)), Z (Superior to inferior (SI)) in Anterio-posterior field, and Y (Anterior to posterior (AP)) in lateral field. The systematic and random set up errors for individual and population were calculated. Then the adequate safety margins were calculated by Stroom’s formula. RESULTS: A total of 242 images (42 DRR images and 200 portal images) and 363 match points were evaluated. Set up errors were -7.9 to 8.1mm (LR), -7.3 to 7.3mm (AP) and -9.9 to 8.2mm (SI). The individual systematic errors ranged from -6.6 to 4.9mm (LR), -4.9 to 3.5mm (AP) and -6.3 to 6.5mm (SI) while the individual random errors ranged from 0.5 to 8.3mm (LR), 0.7 to 5.2mm (AP) and 1.1 to 4.6mm (SI). The adequate safety margins which ensures at least 95% of prescribed dose to 99% of the CTV calculated by using Stroom’s formula were 7.9mm (LR), 7.0mm (AP) and 9.1mm (SI). The effect of dose was calculated by simulating a plan by shifting the isocenter along the three axes, where each shift corresponds to the displacement. Dose received by 99% of CTV volume for treatment plans with and without shifts was 99.51±0.81 and 98.63±1.46 respectively. CONCLUSION: In this study, the effect of the systematic errors and the random errors on dose distribution shows that the safety margin of 1 cm appears to be adequate for all the patients.

scholarly journals Integrated Approach Based on Dual Extended Kalman Filter and Multivariate Autoregressive Model for Predicting Battery Capacity Using Health Indicator and SOC/SOH

Energies ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2138 ◽  
Author(s):  
Jinhyeong Park ◽  
Munsu Lee ◽  
Gunwoo Kim ◽  
Seongyun Park ◽  
Jonghoon Kim
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Storage System ◽  
Integrated Approach ◽  
Energy Storage System ◽  
Measured Data ◽  
Ar Model ◽  
Health Indicator ◽  
Practical Applications ◽  
Battery Capacity

To enhance the efficiency of an energy storage system, it is important to predict and estimate the battery state, including the state of charge (SOC) and state of health (SOH). In general, the statistical approaches for predicting the battery state depend on historical data measured via experiments. The statistical methods based on experimental data may not be suitable for practical applications. After reviewing the various methodologies for predicting the battery capacity without measured data, it is found that a joint estimator that estimates the SOC and SOH is needed to compensate for the data shortage. Therefore, this study proposes an integrated model in which the dual extended Kalman filter (DEKF) and autoregressive (AR) model are combined for predicting the SOH via a statistical model in cases where the amount of measured data is insufficient. The DEKF is advantageous for estimating the battery state in real-time and the AR model performs better for predicting the battery state using previous data. Because the DEKF has limited performance for capacity estimation, the multivariate AR model is employed and a health indicator is used to enhance the performance of the prediction model. The results of the multivariate AR model are significantly better than those obtained using a single variable. The mean absolute percentage errors are 1.45% and 0.5183%, respectively.

Accounting for Model Errors in Ensemble Data Assimilation

2009 ◽  
Vol 137 (10) ◽  
pp. 3407-3419 ◽  
Author(s):  
Hong Li ◽  
Eugenia Kalnay ◽  
Takemasa Miyoshi ◽  
Christopher M. Danforth
Keyword(s):  
Kalman Filter ◽  
Forecast Errors ◽  
Random Errors ◽  
Model Errors ◽  
State Dependent ◽  
Constant Bias ◽  
Perfect Model ◽  
Ensemble Transform Kalman Filter ◽  
Low Dimensional ◽  
Bias Removal

Abstract This study addresses the issue of model errors with the ensemble Kalman filter. Observations generated from the NCEP–NCAR reanalysis fields are assimilated into a low-resolution AGCM. Without an effort to account for model errors, the performance of the local ensemble transform Kalman filter (LETKF) is seriously degraded when compared with the perfect-model scenario. Several methods to account for model errors, including model bias and system noise, are investigated. The results suggest that the two pure bias removal methods considered [Dee and Da Silva (DdSM) and low dimensional (LDM)] are not able to beat the multiplicative or additive inflation schemes used to account for the effects of total model errors. In contrast, when the bias removal methods are augmented by additive noise representing random errors (DdSM+ and LDM+), they outperform the pure inflation schemes. Of these augmented methods, the LDM+, where the constant bias, diurnal bias, and state-dependent errors are estimated from a large sample of 6-h forecast errors, gives the best results. The advantage of the LDM+ over other methods is larger in data-sparse regions than in data-dense regions.

scholarly journals MIPAS level 2 operational analysis

2006 ◽  
Vol 6 (4) ◽  
pp. 6525-6585 ◽  
Author(s):  
P. Raspollini ◽  
C. Belotti ◽  
A. Burgess ◽  
B. Carli ◽  
M. Carlotti ◽  
...  
Keyword(s):  
Total Error ◽  
Michelson Interferometer ◽  
A Priori Estimate ◽  
Infrared Region ◽  
Forward Model ◽  
Random Errors ◽  
Model Errors ◽  
Convergence Criteria ◽  
Practical Applications ◽  
Level 2

Abstract. The MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument has been operating on-board the ENVISAT satellite since March 2002. In the first two years, it acquired in a nearly continuous manner high resolution (0.025 cm−1 unapodised) emission spectra of the Earth's atmosphere at limb in the middle infrared region. This paper describes the level 2 near real-time (NRT) and off-line (OL) ESA processors that have been used to derive level 2 geophysical products from the calibrated and geolocated level 1b spectra. The design of the code and the analysis methodology have been driven by the requirements for NRT processing. This paper reviews the performance of the optimised retrieval strategy that has been implemented to achieve these requirements and provides estimated error budgets for the target products: pressure/temperature, O3, H2O, CH4, HNO3, N2O and NO2, in the altitude measurement range from 6 to 68 km. From application to real MIPAS data, it was found that no change was needed in the developed code although an external algorithm was introduced to identify clouds with high opacity and to exclude affected spectra from the analysis. In addition, a number of updates were made to the set-up parameters and to auxiliary data. In particular, a new version of the MIPAS dedicated spectroscopic database was used and, in the OL analysis, the retrieval range was extended to reduce errors due to uncertainties in extrapolation of the profile outside the retrieval range and more stringent convergence criteria were implemented. A statistical analysis on the χ2 values obtained in one year of measurements shows good agreement with the a priori estimate of the forward model errors. On the basis of the first two years of MIPAS measurements the estimates of the forward model and instrument errors are in general found to be conservative with excellent performance demonstrated for frequency calibration. It is noted that the total retrieval error is limited by forward model errors which make useless a further reduction of random errors. However, such a reduction is within the capabilities of MIPAS measurements, which contain many more spectral signatures of the target species than what currently used. Further work is needed to reduce the amplitude of the forward model errors, so that the random error and the total error budget can be reduced accordingly. The importance of the Averaging kernels for a full characterisation of the target products is underlined and the equations are provided for their practical applications.

scholarly journals MIPAS level 2 operational analysis

2006 ◽  
Vol 6 (12) ◽  
pp. 5605-5630 ◽  
Author(s):  
P. Raspollini ◽  
C. Belotti ◽  
A. Burgess ◽  
B. Carli ◽  
M. Carlotti ◽  
...  
Keyword(s):  
Total Error ◽  
Michelson Interferometer ◽  
A Priori Estimate ◽  
Infrared Region ◽  
Forward Model ◽  
Random Errors ◽  
Model Errors ◽  
Convergence Criteria ◽  
Practical Applications ◽  
Level 2

Abstract. The MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument has been operating on-board the ENVISAT satellite since March 2002. In the first two years, it acquired in a nearly continuous manner high resolution (0.025 cm−1 unapodized) emission spectra of the Earth's atmosphere at limb in the middle infrared region. This paper describes the level 2 near real-time (NRT) and off-line (OL) ESA processors that have been used to derive level 2 geophysical products from the calibrated and geolocated level 1b spectra. The design of the code and the analysis methodology have been driven by the requirements for NRT processing. This paper reviews the performance of the optimized retrieval strategy that has been implemented to achieve these requirements and provides estimated error budgets for the target products: pressure, temperature, O3, H2O, CH4, HNO3, N2O and NO2, in the altitude measurement range from 6 to 68 km. From application to real MIPAS data, it was found that no change was needed in the developed code although an external algorithm was introduced to identify clouds with high opacity and to exclude affected spectra from the analysis. In addition, a number of updates were made to the set-up parameters and to auxiliary data. In particular, a new version of the MIPAS dedicated spectroscopic database was used and, in the OL analysis, the retrieval range was extended to reduce errors due to uncertainties in extrapolation of the profile outside the retrieval range and more stringent convergence criteria were implemented. A statistical analysis on the χ2 values obtained in one year of measurements shows good agreement with the a priori estimate of the forward model errors. On the basis of the first two years of MIPAS measurements the estimates of the forward model and instrument errors are in general found to be conservative with excellent performance demonstrated for frequency calibration. It is noted that the total retrieval error is limited by forward model errors which make effectless a further reduction of random errors. However, such a reduction is within the capabilities of MIPAS measurements, which contain many more spectral signatures of the target species than what has currently been used. Further work is needed to reduce the amplitude of the forward model errors, so that the random error and the total error budget can be reduced accordingly. The importance of the Averaging kernels for a full characterization of the target products is underlined and the equations are provided for their practical applications.

Velocity Estimation for Quadrupeds Based on Extended Kalman Filter

2014 ◽  
Vol 621 ◽  
pp. 525-532 ◽  
Author(s):  
Man Tian Li ◽  
Cong Wei Wang ◽  
Peng Fei Wang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Random Error ◽  
Inertial Measurement Unit ◽  
Quadruped Robot ◽  
Velocity Estimation ◽  
Measurement Unit ◽  
Forward Kinematics ◽  
Random Errors ◽  
Inertial Measurement

Measuring robots’ real-time velocity correctly is important for locomotion control. Inertial Measurement Unit (IMU) is widely used for velocity measurement. Limited by the bias and random error, IMU alone often can’t meet the requirement. This paper makes use of Extended Kalman Filter (EKF) to fuse kinematics and IMU, and inhibits the drift successfully. We calibrate the bias and recognize the random errors of IMU. Then the forward kinematics of legs is established and the EKF algorithm for velocity estimation is designed based on IMU and kinematics. Finally, the presented algorithm is validated in simulation and on a quadruped robot based on hydraulic driver in trotting gait.

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