scholarly journals The Kalman Filter for Complex Fibonacci Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
John Donoghue
Keyword(s):  
Kalman Filter ◽  
Broad Class ◽  
Golden Ratio ◽  
Measurement Equation ◽  
Output Measurement ◽  
The Real ◽  
Error Covariance ◽  
Analytic Expressions ◽  
Noisy Output ◽  
Complex Coefficients

This paper investigates the characteristics of the Kalman filter for a broad class of complex Fibonacci systems and represents an extension to the complex domain of the state estimation problem for the real-valued Fibonacci system. Complex Fibonacci systems are obtained by modifying the real-valued Fibonacci recurrence relation to include complex coefficients, control and noise inputs, and a noisy output-measurement equation. Analytic expressions for the Kalman filter’s steady-state gain and error covariance matrices are obtained, and it is found that for a broad subclass of these complex systems the elements of the matrices are functions of the golden ratio.

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 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.

scholarly journals Two-Sample Kalman Filter for Steady-State Data Assimilation

2008 ◽  
Vol 136 (11) ◽  
pp. 4503-4516 ◽  
Author(s):  
Julius H. Sumihar ◽  
Martin Verlaan ◽  
Arnold W. Heemink
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Data Assimilation ◽  
Simple Wave ◽  
Wave Model ◽  
State Data ◽  
Error Covariance ◽  
Observation Network ◽  
Kalman Gain ◽  
Potential Applicability

Abstract In this paper, a new iterative algorithm for computing a steady-state Kalman gain is proposed. This algorithm utilizes two model forecasts with statistically independent random perturbations to determine the error covariance used to define a Kalman gain matrix for steady-state data assimilation. It is based on the assumption that the error process is weakly stationary and ergodic. The algorithm consists of an iterative procedure for improving the covariance estimate, which requires a fixed observation network. Two twin experiments using a simple wave model and an operational storm surge prediction model are performed to demonstrate the performance of the proposed algorithm. The experiments show that the results obtained by using the proposed algorithm converge to the ones produced by the classic Kalman filter algorithm. An additional experiment using the three-variable Lorenz model is also performed to demonstrate its potential applicability in unstable dynamical systems.

Road Adhesion Coefficient Estimation

2011 ◽  
Vol 52-54 ◽  
pp. 1503-1508
Author(s):  
Yan An Sun ◽  
Lu Xiong ◽  
Zhuo Ping Yu ◽  
Yuan Feng ◽  
Long Jie Ren
Keyword(s):  
Kalman Filter ◽  
Electric Vehicle ◽  
Slip Rate ◽  
Research Subject ◽  
Adhesion Coefficient ◽  
The Real ◽  
Coefficient Estimation ◽  
Improved Algorithm

Taking four in-wheel-motor electric vehicle as research subject, the paper focuses on the estimation of road adhesion coefficient based on curve. Through adding a forget factor, an improved algorithm on the basis of Forget Kalman Filter is proposed to estimate the slope of the curve at low slip rate. This new algorithm is proved effective through the real car test.

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