scholarly journals The Composite Covariance of a Kalman Filter Estimation

2021 ◽  
Vol 6 ◽  
Author(s):  
Winston C Chow
Keyword(s):  
Kalman Filter ◽  
Statistical Inference ◽  
Random Vector ◽  
Gaussian Distribution ◽  
System State ◽  
Gaussian Random Vector ◽  
Inference Problems ◽  
Error Covariance ◽  
Potential Applications ◽  
Elementary Statistics

A Kalman filter estimation of the state of a system is merely a random vector that has a normal, also called Gaussian, distribution. Elementary statistics teaches any Gaussian distribution is completely and uniquely characterized by its mean and covariance (variance if univariate). Such characterization is required for statistical inference problems on a Gaussian random vector. This mean and composite covariance of a Kalman filter estimate of a system state will be derived here. The derived covariance is in recursive form. One must not confuse it with the “error covariance” output of a Kalman filter. Potential applications, including geological ones, of the derivation are described and illustrated with a simple example.

Maximum Correntropy Criterion Constrained Kalman Filter

2017 ◽  
Author(s):  
Seyed Fakoorian ◽  
Mahmoud Moosavi ◽  
Reza Izanloo ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Constraints ◽  
Statistical Information ◽  
Second Order ◽  
System Model ◽  
Error Covariance ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

scholarly journals A data augmentation approach for a class of statistical inference problems

PLoS ONE ◽  
2018 ◽  
Vol 13 (12) ◽  
pp. e0208499 ◽  
Author(s):  
Rodrigo Carvajal ◽  
Rafael Orellana ◽  
Dimitrios Katselis ◽  
Pedro Escárate ◽  
Juan Carlos Agüero
Keyword(s):  
Statistical Inference ◽  
Data Augmentation ◽  
Inference Problems

scholarly journals A Robust and Adaptive Complementary Kalman Filter Based on Mahalanobis Distance for Ultra Wideband/Inertial Measurement Unit Fusion Positioning

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3435 ◽  
Author(s):  
Xin Li ◽  
Yan Wang ◽  
Kourosh Khoshelham
Keyword(s):  
Kalman Filter ◽  
Mahalanobis Distance ◽  
Inertial Measurement Unit ◽  
Least Squares Method ◽  
Ultra Wideband ◽  
Measurement Unit ◽  
Observation Error ◽  
System State ◽  
Inertial Measurement ◽  
The Impact

Ultra wideband (UWB) has been a popular technology for indoor positioning due to its high accuracy. However, in many indoor application scenarios UWB measurements are influenced by outliers under non-line of sight (NLOS) conditions. To detect and eliminate outlying UWB observations, we propose a UWB/Inertial Measurement Unit (UWB/IMU) fusion filter based on a Complementary Kalman Filter to track the errors of position, velocity and direction. By using the least squares method, the positioning residual of the UWB observation is calculated, the robustness factor of the observation is determined, and an observation weight is dynamically set. When the robustness factor does not exceed a pre-defined threshold, the observed value is considered trusted, and adaptive filtering is used to track the system state, while the abnormity of system state, which might be caused by IMU data exceptions or unreasonable noise settings, is detected by using Mahalanobis distance from the observation to the prior distribution. When the robustness factor exceeds the threshold, the observed value is considered abnormal, and robust filtering is used, whereby the impact of UWB data exceptions on the positioning results is reduced by exploiting Mahalanobis distance. Experimental results show that the observation error can be effectively estimated, and the proposed algorithm can achieve an improved positioning accuracy when affected by outlying system states of different quantity as well as outlying observations of different proportion.

scholarly journals Adaptive fading factor unscented Kalman filter with application to target tracking

2020 ◽  
Author(s):  
Peng Gu ◽  
Zhongliang Jing ◽  
Liangbin Wu
Keyword(s):  
Kalman Filter ◽  
Target Tracking ◽  
Unscented Kalman Filter ◽  
System Model ◽  
Mismatch Error ◽  
Tracking Accuracy ◽  
Model Mismatch ◽  
Error Covariance ◽  
Nonlinear Tracking ◽  
Fading Factor

AbstractOne purpose of target tracking is to estimate the states of targets, and unscented Kalman filter is one of the effective algorithms for estimating in the nonlinear tracking problem. Considering the characteristics of complex maneuverability, it is easy to reduce the tracking accuracy and cause divergence due to the mismatch between the system model and the practical target motion model. Adaptive fading factor is an effective counter to this problem, having been instrumental in solving accuracy and divergence problems. Fading factor can adaptively adjust covariance matrix online to compensate model mismatch error. Moreover, fading factor not only improves the filtering accuracy, but also automatically adjusts the error covariance in response to the different situation. The simulation results show that the adaptive fading factor unscented Kalman filter has more advantages in target tracking and it can be better applied to nonlinear target tracking.

Theoretical Application of Ensemble Kalman Filter to Adsorptive Solute Cr(VI) Transfer from Soil into Surface Runoff

2014 ◽  
Vol 919-921 ◽  
pp. 1257-1261
Author(s):  
Chao Qun Tan ◽  
Ju Xiu Tong ◽  
Bill X. Hu ◽  
Jin Zhong Yang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Surface Runoff ◽  
Amplification Factor ◽  
Forecast Error ◽  
Assimilation Effect ◽  
Solute Transfer ◽  
Error Covariance ◽  
Theoretical Application

This paper mainly discusses some details when applying data assimilation method via an ensemble Kalman filter (EnKF) to improve prediction of adsorptive solute Cr(VI) transfer from soil into runoff. Based on this work, we could make better use of our theoretical model to predict adsorptive solute transfer from soil into surface runoff in practice. The results show that the ensemble number of 100 is reasonable, considering assimilation effect and efficiency after selecting its number from 25 to 225 at an interval of 25. While the initial ensemble value makes little difference to data assimilation (DA) results. Besides, DA results could be improved by multiplying an amplification factor to forecast error covariance matrix due to underestimation of forecast error.

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