The second order Central Divided-difference Kalman Filter

2011 ◽  
Author(s):  
Dongming Zhao ◽  
Qingbin Wang ◽  
Huan Bao ◽  
Zhan Gao
Keyword(s):  
Kalman Filter ◽  
Divided Difference ◽  
Second Order

scholarly journals Real-Time Freeway Traffic State Estimation Based on the Second-Order Divided Difference Kalman Filter

2019 ◽  
Vol 20 (2) ◽  
pp. 114-122 ◽  
Author(s):  
Asmâa Ouessai ◽  
Mokhtar Keche
Keyword(s):  
Kalman Filter ◽  
Real World ◽  
Road Traffic ◽  
Divided Difference ◽  
Estimation Error ◽  
Second Order ◽  
Parameters Estimation ◽  
Highway Traffic ◽  
Traffic State ◽  
State Identification

Abstract Reliable road traffic state identification systems should be designed to provide accurate traffic state information anywhere and anytime. In this paper we propose a road traffic classification system, based on traffic variables estimated using the second order Divided Difference Kalman Filter (DDKF2). This filter is compared with the Extended Kalman Filter (EKF) using both simulated and real-world dataset of highway traffic. Monte-Carlo simulations indicate that the DDKF2 outperforms the EKF filter in terms of parameters estimation error. The real-word evaluation of the DDKF2 filter in terms of classification rate confirms that this filter is promising for real-world traffic state identification systems.

scholarly journals Second order Kalman filtering channel estimation and machine learning methods for spectrum sensing in cognitive radio networks

2021 ◽  
Author(s):  
Olusegun Peter Awe ◽  
Daniel Adebowale Babatunde ◽  
Sangarapillai Lambotharan ◽  
Basil AsSadhan
Keyword(s):  
Machine Learning ◽  
Kalman Filter ◽  
Cognitive Radio ◽  
Spectrum Sensing ◽  
Cognitive Radio Networks ◽  
Clustering Algorithm ◽  
Polynomial Regression ◽  
Primary User ◽  
Radio Networks ◽  
Second Order

AbstractWe address the problem of spectrum sensing in decentralized cognitive radio networks using a parametric machine learning method. In particular, to mitigate sensing performance degradation due to the mobility of the secondary users (SUs) in the presence of scatterers, we propose and investigate a classifier that uses a pilot based second order Kalman filter tracker for estimating the slowly varying channel gain between the primary user (PU) transmitter and the mobile SUs. Using the energy measurements at SU terminals as feature vectors, the algorithm is initialized by a K-means clustering algorithm with two centroids corresponding to the active and inactive status of PU transmitter. Under mobility, the centroid corresponding to the active PU status is adapted according to the estimates of the channels given by the Kalman filter and an adaptive K-means clustering technique is used to make classification decisions on the PU activity. Furthermore, to address the possibility that the SU receiver might experience location dependent co-channel interference, we have proposed a quadratic polynomial regression algorithm for estimating the noise plus interference power in the presence of mobility which can be used for adapting the centroid corresponding to inactive PU status. Simulation results demonstrate the efficacy of the proposed algorithm.

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.

scholarly journals Leakage Detection in Pipeline Based on Second Order Extended Kalman Filter Observer

2019 ◽  
Vol 52 (29) ◽  
pp. 116-121 ◽  
Author(s):  
S. Razvarz ◽  
R. Jafari ◽  
C. Vargas-Jarillo ◽  
A. Gegov ◽  
M. Forooshani
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Second Order ◽  
Leakage Detection

scholarly journals On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 47 ◽  
Author(s):  
Mama Foupouagnigni ◽  
Salifou Mboutngam
Keyword(s):  
Difference Equation ◽  
Divided Difference ◽  
Polynomial Solution ◽  
Formal Proof ◽  
Second Order ◽  
Fixed Degree ◽  
Hypergeometric Type ◽  
The Mean ◽  
The Right

In this paper, we provide a formal proof of the existence of a polynomial solution of fixed degree for a second-order divided-difference equation of the hypergeometric type on non-uniform lattices, generalizing therefore previous work proving existence of the polynomial solution for second-order differential, difference or q-difference equation of hypergeometric type. This is achieved by studying the properties of the mean operator and the divided-difference operator as well as by defining explicitly, the right and the “left” inverse for the second operator. The method constructed to provide this formal proof is likely to play an important role in the characterization of orthogonal polynomials on non-uniform lattices and might also be used to provide hypergeometric representation (when it does exist) of the second solution—non polynomial solution—of a second-order divided-difference equation of hypergeometric type.

scholarly journals Soc Estimation of the Lithium-Ion Battery Pack using a Sigma Point Kalman Filter Based on a Cell’s Second Order Dynamic Model

2020 ◽  
Vol 10 (5) ◽  
pp. 1896 ◽  
Author(s):  
Chi Nguyen Van ◽  
Thuy Nguyen Vinh
Keyword(s):  
Kalman Filter ◽  
Lithium Ion Battery ◽  
Dynamic Model ◽  
Dynamic Models ◽  
Lithium Ion ◽  
Second Order ◽  
Battery Pack ◽  
Sigma Point ◽  
Soc Estimation ◽  
Cell Modules

This paper deals with the state of charge (SoC) estimation of a lithium-ion battery pack (LiBP) connected by some cells in series and parallel. The voltage noise, noise and current bias of current through the LiBP are taken into account in the SoC estimation problem. In order to describe the cell dynamic more accurately, especially for practical applications with charge and discharge amplitude varying suddenly, in this paper we use the second dynamic order model of the cell to estimate the SoC of the LiBP. By applying the sigma point Kalman filter (SPKF), the average SoC of the pack and bias current of current measurement are estimated by first estimator; the second estimator estimates the SoC differences of the cell modules from average SoC of the pack. The SoC of the cell modules are the sum of average SoCs of the pack and the SoC differences. By only using two estimators, the calculation complexity for SoC estimation is more reduced; this is very useful for the LiBP, which has the number of cells connected in a large series. This method was applied for the pack of SAMSUNG ICR18650-22P connected by seven cell modules; the cell modules were connected by nine cells in parallel; the LiBP was charged and discharged with amplitude varying suddenly. The estimated SoC of seven cell modules is smaller than 2% for a temperature operating range typically −5 °C to 45 °C. The comparison of the accuracy of SoC estimation based on the first and the second order dynamic models is made; the result shows that the SoC estimation used the second order dynamic model is more exact.

scholarly journals A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation

2015 ◽  
Vol 143 (4) ◽  
pp. 1347-1367 ◽  
Author(s):  
Julian Tödter ◽  
Bodo Ahrens
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Second Order ◽  
Square Root ◽  
Computationally Efficient ◽  
Research Activities ◽  
Wide Range ◽  
Matrix Square Root ◽  
Non Gaussian ◽  
Ensemble Transform

Abstract The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational data assimilation schemes and are applied in a wide range of operational and research activities. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the analysis mean and covariance are biased, and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) only relies on Bayes’s theorem, which guarantees an exact asymptotic behavior, but because of the so-called curse of dimensionality it is exposed to weight collapse. Here, it is shown how to obtain a new analysis ensemble whose mean and covariance exactly match the Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The properties and performance of the proposed algorithm are further investigated via a set of experiments. They indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. Localization enhances the potential applicability of this PF-inspired scheme in larger-dimensional systems. The proposed algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF).

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