scholarly journals Multiple Adaptive Fading Schmidt-Kalman Filter for Unknown Bias

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Tai-Shan Lou ◽  
Zhi-Hua Wang ◽  
Meng-Li Xiao ◽  
Hui-Min Fu
Keyword(s):  
Kalman Filter ◽  
Dynamic Systems ◽  
Measurement Model ◽  
Covariance Matrices ◽  
The State ◽  
Negative Effects ◽  
Measurement Models ◽  
Initial Values ◽  
Kalman Filter Algorithm ◽  
Unknown Bias

Unknown biases in dynamic and measurement models of the dynamic systems can bring greatly negative effects to the state estimates when using a conventional Kalman filter algorithm. Schmidt introduces the “consider” analysis to account for errors in both the dynamic and measurement models due to the unknown biases. Although the Schmidt-Kalman filter “considers” the biases, the uncertain initial values and incorrect covariance matrices of the unknown biases still are not considered. To solve this problem, a multiple adaptive fading Schmidt-Kalman filter (MAFSKF) is designed by using the proposed multiple adaptive fading Kalman filter to mitigate the negative effects of the unknown biases in dynamic or measurement model. The performance of the MAFSKF algorithm is verified by simulation.

An Advanced Formulation of Kalman Filter Time Series Reference Frame Realization for Geophysical Applications

2020 ◽  
Author(s):  
Xiaoping Wu ◽  
Bruce Haines ◽  
Michael Heflin ◽  
Felix Landerer
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
Reference Frame ◽  
State Vector ◽  
Terrestrial Reference Frame ◽  
Covariance Matrices ◽  
Time Variable ◽  
The State ◽  
Geocenter Motion ◽  
Over Time

<p>A Kalman filter and time series approach to the International Terrestrial Reference Frame (ITRF) realization (KALREF) has been developed and used in JPL. KALREF combines weekly or daily SLR, VLBI, GNSS and DORIS data and realizes a terrestrial reference frame in the form of time-variable geocentric station coordinate time series. The origin is defined at nearly instantaneous Center-of-Mass of the Earth system (CM) sensed by weekly SLR data and the scale is implicitly defined by the weighted averages of those of weekly SLR and daily VLBI data. The standard KALREF formulation describes the state vector in terms of time variable station coordinates and other constant parameters. Such a formulation is fine for station positions and their uncertainties or covariance matrices at individual epochs. However, coordinate errors are strongly correlated over time given KALREF’s unique nature of combining different technique data with various frame strengths through local tie measurements and co-motion constraints and its use of random walk processes. For long time series and large space geodetic networks in the ITRF, KALREF cannot keep track of such correlations over time. If they are ignored when forming geocentric displacements for geophysical inverse or network shift geocenter motion studies, the covariance matrices of coordinate differences cannot adequately represent those of displacements. Consequently, significant non-uniqueness and inaccuracies would occur in the results of studies using such matrices. To overcome this difficulty, an advanced KALREF formulation is implemented that features explicit displacement parameters in the state vector that would allow the Kalman filter and smoother to compute and return covariance matrices of displacements. The use of displacement covariance matrices reduces the impact of time correlated errors and completely solves the non-uniqueness problem. However, errors in the displacements are still correlated in time. Further calibrations are needed to accurately assess covariance matrices of derivative quantities such as averages, velocities and accelerations during various time periods. We will present KALREF results of the new formulation and their use along with newly reprocessed RL06 GRACE gravity data in a new unified inversion for geocenter motion.</p>

A novel cubature statistically linearized Kalman filter for fractional-order nonlinear discrete-time stochastic systems

2017 ◽  
Vol 24 (24) ◽  
pp. 5880-5897 ◽  
Author(s):  
Hamed Torabi ◽  
Naser Pariz ◽  
Ali Karimpour
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Fractional Order ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Taylor Series Expansion ◽  
The State ◽  
Nonlinear Functions ◽  
Measurement Models

In this paper, the state estimation problem for fractional-order nonlinear discrete-time stochastic systems is considered. A new method for the state estimation of fractional nonlinear systems using the statistically linearized method and cubature transform is presented. The fractional extended Kalman filter suffers from two problems. Firstly, the dynamic and measurement models must be differentiable and, secondly, nonlinearity is approximated by neglecting the higher order terms in the Taylor series expansion; by the proposed method in this paper, these problems can be solved using a statistically linearized algorithm for the linearization of fractional nonlinear dynamics and cubature transform for calculating the expected values of the nonlinear functions. The effectiveness of this proposed method is demonstrated through simulation results and its superiority is shown by comparing our method with some other present methods, such as the fractional extended Kalman filter.

scholarly journals Two-Step Adaptive Augmented Unscented Kalman Filter for Roll Angles of Spinning Missiles Based on Magnetometer Measurements

2018 ◽  
Vol 51 (3-4) ◽  
pp. 73-82 ◽  
Author(s):  
Xiaolong Yan ◽  
Guoguang Chen ◽  
Xiaoli Tian
Keyword(s):  
Kalman Filter ◽  
State Vector ◽  
Unscented Kalman Filter ◽  
Sampling Rate ◽  
The State ◽  
Roll Angle ◽  
Estimation Accuracy ◽  
Measurement Circuit ◽  
Kalman Filter Algorithm ◽  
Stop Rule

It is critical to measure the roll angle of a spinning missile quickly and accurately. Magnetometers are commonly used to implement these measurements. At present, the estimation of roll angle parameters is usually performed with the unscented Kalman filter algorithm. In this paper, the two-step adaptive augmented unscented Kalman filter algorithm is proposed to calibrate the biaxial magnetometer and circuit measurements quickly, which allows accurate estimates of the missile roll angle. Unlike the existing algorithms, the state vector of the algorithm is based on the missile roll angle parameters and the error factors caused by the magnetometer and the measurement circuit errors. Next, a two-step fast fitting algorithm is used to fit the initial value. After satisfying the stop rule, the state vector of the filter is configured to estimate the roll angle parameters and the calibration parameters. This method is evaluated by running numerous simulations. In the experiment, the algorithm completes the calibration of the magnetometer and the measurement circuit 1 s after the missile launches, with a sampling rate of 1 ms and an output roll attitude angle with a 0.0015 rad precision. The conventional unscented Kalman filter algorithm requires more time to achieve such a high accuracy. The simulation results demonstrate that the proposed two-step augmented unscented Kalman filter outperforms the conventional unscented Kalman filter in its estimation accuracy and convergence characteristics.

Navigation Kalman Filter Design for Pipeline Pigging

2005 ◽  
Vol 58 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Eun-Hwan Shin ◽  
Naser El-Sheimy
Keyword(s):  
Kalman Filter ◽  
Natural Gas ◽  
Filter Design ◽  
Measurement Model ◽  
Velocity Measurements ◽  
Adaptive Kalman Filter ◽  
Holonomic Constraints ◽  
Measurement Models ◽  
The Past ◽  
Natural Gas Pipeline

The paper discusses the development of an adaptive Kalman filter for pipeline surveying applications. Various measurement models are developed and numerically tested using a real natural gas pipeline dataset. Since, for tactical-grade IMUs, odometer-derived velocity measurements alone cannot yield good results, two non-holonomic constraints are augmented to make the three-direction measurement model. Smoothing computation is also applied to yield the best trajectory using all the information contained in the past, current and future measurements. The trajectory errors are within 10–20 m for extreme cases, and within 10 m for most cases. RMS of the trajectory errors is expected to be about 2·5 m.

State of Energy Estimation Based on AUKF for Lithium Battery Used on Pure Electric Vehicle

2012 ◽  
Vol 608-609 ◽  
pp. 1627-1630
Author(s):  
Hong Wei Liu ◽  
Hai Feng Wang ◽  
Chong Guo
Keyword(s):  
Kalman Filter ◽  
Electric Vehicle ◽  
Unscented Kalman Filter ◽  
The State ◽  
Estimation Accuracy ◽  
Battery Management System ◽  
Battery Management ◽  
Process Noise ◽  
Energy Estimation ◽  
Kalman Filter Algorithm

State of Energy can be used to predict the driving mileage of electric vehicles, design the control strategy of vehicle energy distribution, and improve the safety of electric vehicle. Accurate estimaion of state of energy is one of the key technologies in the study on battery management system of electric vehicle. In this paper, the State of Energy is estimated by using Unscented Kalman Filter, while the process noise and measurement noise is adjusted by using the Sage-Husa adaptive algorithm, as a result the estimation accuracy is improved. The result shows that the State of Energy estimation by using Adaptive Unscented Kalman Filter algorithm is satisfactory to electric vehicle.

Combined estimation of the state of charge of a lithium battery based on a back-propagation– adaptive Kalman filter algorithm

2017 ◽  
Vol 232 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Wanzhong Zhao ◽  
Xiangchuang Kong ◽  
Chunyan Wang
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
The State ◽  
State Of Charge ◽  
Recursive Least Squares ◽  
Adaptive Kalman Filter ◽  
Precise Estimation ◽  
Kalman Filter Algorithm

The precise estimation of the battery’s state of charge is one of the most significant and difficult techniques for battery management systems. In order to improve the accuracy of estimation of the state of charge, the forgetting-factor recursive least-squares method is used to achieve online identification of the model parameters based on the first-order RC battery model, and a back-propagation neural-network-assisted adaptive Kalman filter algorithm is proposed. A back-propagation neural network is established by using the MATLAB neural network toolbox and is trained offline on the basis of the battery test data; then the trained back-propagation neural network is used to realize the online optimized results of an adaptive Kalman filter algorithm for estimation of the state of charge. The proposed methodology for estimation of the state of charge is demonstrated using experimental lithium-ion battery module data in dynamic stress tests. The results indicate that, in comparison with the common adaptive Kalman filter algorithm, the back-propagation–adaptive Kalman filter algorithm significantly improved precise estimation of the state of charge.

scholarly journals A Kalman filter application for rainfall estimation using radar reflectivity measurements

2019 ◽  
pp. 1198-1212
Author(s):  
ENGİN MAŞAZADE ◽  
ALİ KEMAL BAKIR ◽  
PINAR KIRCI
Keyword(s):  
Kalman Filter ◽  
Process Model ◽  
Measurement Model ◽  
Rainfall Amount ◽  
Radar Reflectivity ◽  
Measurement Models ◽  
Weather Radars ◽  
Filter Process ◽  
The Mean ◽  
Weather Observation

The rainfall amount observed at a given location mostly depend on the cloud density, which can be quantified with the reflectivity values observed by meteorology weather radars. In this study, we aim to estimate the rainfall amount using a Kalman filter with radar reflectivity measurements. We first assume that the amount of rainfall observed at automatic weather observation stations (AWOSs) are elements of an unknown state vector and consider the Kalman filter process model as the true rainfall amounts observed at these AWOSs over time. For the measurement model of the Kalman filter, we use the radar reflectivity values observed at each AWOS location. For the execution of the Kalman filter, a number of rainfall amount and radar reflectivity value pairs are first required to learn the process and measurement models of the Kalman filter. The estimation performance of the proposed Kalman filter is then compared with empirical reflectivity (Z) - rainfall (R) relationships. Numerical results show that when the Kalman filter is executed with radar reflectivity measurements observed around a large number of AWOS locations, the mean squared errors of the Kalman filter rainfall estimates are smaller than the ones obtained with empirical ZR relationships.

scholarly journals Autonomous Positioning of Satellite Constellations via X-ray Pulsar Measurements

2013 ◽  
Vol 66 (5) ◽  
pp. 671-682 ◽  
Author(s):  
Li Liu ◽  
Wei Zheng ◽  
Guojian Tang
Keyword(s):  
Numerical Simulation ◽  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Measurement Model ◽  
Orbital Dynamics ◽  
Satellite Constellations ◽  
X Ray ◽  
Measurement Models ◽  
Measurement Scheme ◽  
Dynamics Models

A novel autonomous positioning approach based on X-ray pulsars is proposed in this paper. First, the principles of the pulsar–based measurement model and the inter-satellite range model in the autonomous positioning of satellite constellations are presented. The observability of the pulsar-based measurement model is then shown. Second, the autonomous positioning algorithms, including measurement models and orbital dynamics models, are formulated using an unscented Kalman filter to estimate the position vectors of satellites. Finally, the feasibility of the proposed measurement scheme compared with an inter-satellite range scheme is illustrated by numerical simulation. The results show that the proposed approach can keep the satellite state convergent, and achieve position accuracies of 2 m. The proposed scheme provides a promising approach for autonomous absolute positioning of constellation systems by using X-ray pulsars.

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