scholarly journals Kalman filter with a non-linear non-Gaussian observation relation

1991 ◽  
Vol 6 (2) ◽  
pp. 111-119 ◽  
Author(s):  
T. Cipra ◽  
A. Rubio
Keyword(s):  
Kalman Filter ◽  
Non Linear ◽  
Non Gaussian

Non Linear and Non Gaussian States and Parameters Estimation using Bayesian Methods-Comparatives Studies

2014 ◽  
pp. 711-748 ◽  
Author(s):  
Majdi Mansouri ◽  
Moustafa Mohamed-Seghir ◽  
Hazem Nounou ◽  
Mohamed Nounou ◽  
Haitham A. Abu-Rub
Keyword(s):  
Kalman Filter ◽  
Bayesian Methods ◽  
Process Model ◽  
Unscented Kalman Filter ◽  
Nonlinear Process ◽  
Parameters Estimation ◽  
Gaussian States ◽  
Estimation Algorithms ◽  
Non Linear ◽  
Non Gaussian

This chapter deals with the problem of non-linear and non-Gaussian states and parameters estimation using Bayesian methods. The performances of various conventional and state-of-the-art state estimation techniques are compared when they are utilized to achieve this objective. These techniques include the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF). In the current work, the authors consider two systems (biological model and power system) to perform evaluation of estimation algorithms. The results of the comparative studies show that the UKF provides a higher accuracy than the EKF due to the limited ability of EKF to accurately estimate the mean and covariance matrix of the estimated states through lineralization of the nonlinear process model. The results also show that the PF provides a significant improvement over the UKF because, unlike UKF, PF is not restricted by linear-Gaussian assumptions which greatly extends the range of problems that can be tackled.

Centered error entropy Kalman filter with application to satellite attitude determination

2021 ◽  
pp. 014233122110198
Author(s):  
Baojian Yang ◽  
Lu Cao ◽  
Dechao Ran ◽  
Bing Xiao
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Attitude Determination ◽  
Complexity Analysis ◽  
Iteration Algorithm ◽  
Robust Algorithms ◽  
Convergence Conditions ◽  
Satellite Attitude ◽  
Heavy Tailed ◽  
Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

Dynamic Target Tracking Based on Particle Filter in Actual Environment

2013 ◽  
Vol 683 ◽  
pp. 824-827
Author(s):  
Tian Ding Chen ◽  
Chao Lu ◽  
Jian Hu
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Target Tracking ◽  
Monitoring System ◽  
Filter Method ◽  
Complex Scene ◽  
Actual Environment ◽  
Dynamic Target ◽  
Gaussian System ◽  
Non Gaussian

With the development of science and technology, target tracking was applied to many aspects of people's life, such as missile navigation, tanks localization, the plot monitoring system, robot field operation. Particle filter method dealing with the nonlinear and non-Gaussian system was widely used due to the complexity of the actual environment. This paper uses the resampling technology to reduce the particle degradation appeared in our test. Meanwhile, it compared particle filter with Kalman filter to observe their accuracy .The experiment results show that particle filter is more suitable for complex scene, so particle filter is more practical and feasible on target tracking.

scholarly journals Non-linear wave data assimilation with an ANN-type wind-wave model and Ensemble Kalman Filter (EnKF)

2010 ◽  
Vol 34 (8) ◽  
pp. 1984-1999 ◽  
Author(s):  
Ahmadreza Zamani ◽  
Ahmadreza Azimian ◽  
Arnold Heemink ◽  
Dimitri Solomatine
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Wind Wave ◽  
Wave Model ◽  
Linear Wave ◽  
Wave Data ◽  
Non Linear

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.

Score matching filters

2021 ◽  
Author(s):  
Marie Turčičová ◽  
Jan Mandel ◽  
Kryštof Eben
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Markov Random Fields ◽  
Computational Cost ◽  
Time Step ◽  
Sample Covariance ◽  
Monte Carlo Approximation ◽  
Gauss Markov Random Fields ◽  
Ensemble Filtering ◽  
Non Gaussian

<p>A widely popular group of data assimilation methods in meteorological and geophysical sciences is formed by filters based on Monte-Carlo approximation of the traditional Kalman filter, e.g. <span>E</span><span>nsemble Kalman filter </span><span>(EnKF)</span><span>, </span><span>E</span><span>nsemble </span><span>s</span><span>quare-root filter and others. Due to the computational cost, ensemble </span><span>size </span><span>is </span><span>usually </span><span>small </span><span>compar</span><span>ed</span><span> to the dimension of the </span><span>s</span><span>tate </span><span>vector. </span><span>Traditional </span> <span>EnKF implicitly uses the sample covariance which is</span><span> a poor estimate of the </span><span>background covariance matrix - singular and </span><span>contaminated by </span><span>spurious correlations. </span></p><p><span>W</span><span>e focus on modelling the </span><span>background </span><span>covariance matrix by means of </span><span>a linear model for its inverse. This is </span><span>particularly </span><span>useful</span> <span>in</span><span> Gauss-Markov random fields (GMRF), </span><span>where</span> <span>the inverse covariance matrix has </span><span>a banded </span><span>structure</span><span>. </span><span>The parameters of the model are estimated by the</span><span> score matching </span><span>method which </span><span>provides</span><span> estimators in a closed form</span><span>, cheap to compute</span><span>. The resulting estimate</span><span> is a key component of the </span><span>proposed </span><span>ensemble filtering algorithms. </span><span>Under the assumption that the state vector is a GMRF in every time-step, t</span><span>he Score matching filter with Gaussian resamplin</span><span>g (SMF-GR) </span><span>gives</span><span> in every time-step a consistent (in the large ensemble limit) estimator of mean and covariance matrix </span><span>of the forecast and analysis distribution</span><span>. Further, we propose a filtering method called Score matching ensemble filter (SMEF), based on regularization of the EnK</span><span>F</span><span>. Th</span><span>is</span><span> filter performs well even for non-Gaussian systems with non-linear dynamic</span><span>s</span><span>. </span><span>The performance of both filters is illustrated on a simple linear convection model and Lorenz-96.</span></p>

Adaptive and augmented nonlinear filters : theory and applications

2018 ◽  
Author(s):  
◽  
Tao Sun
Keyword(s):  
Kalman Filter ◽  
Mean Square Error ◽  
Gaussian Approximation ◽  
Adaptive Strategy ◽  
Nonlinear Filters ◽  
Nonlinear Transformation ◽  
Mean Square ◽  
Gaussian Filters ◽  
Non Gaussian ◽  
Gaussian Estimation

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Nonlinear estimation and filtering have been intensively studied for decades since it has been widely used in engineering and science such as navigation, radar signal processing and target tracking systems. Because the posterior density function is not a Gaussian distribution, then the optimal solution is intractable. The nonlinear/non-Gaussian estimation problem is more challenging than the linear/Gaussian case, which has an optimal closed form solution, i.e. the celebrated Kalman filter. Many nonlinear filters including the extended Kalman filter, the unscented Kalman filter and the Gaussian-approximation filters, have been proposed to address nonlinear/non-Gaussian estimation problems in the past decades. Although the estimate yield by Gaussian-approximation filters such as cubature Kalman filters and Gaussian-Hermite quadrature filters is satisfied in many applications, there are two obvious drawbacks embedded in the use of Gaussian filters. On the one hand, with the increase of the quadrature points, much computational effort is devoted to approximate Gaussian integrals, which is not worthy sometimes. On the other hand, by the use of the update rule, the estimate constrains to be a linear function of the observation. In this dissertation, we aim to address this two shortcoming associated with the conventional nonlinear filters. We propose two nonlinear filters in the dissertation. Based on an adaptive strategy, the first one tries to reduce the computation cost during filtering without sacrificing much accuracy, because when the system is close to be linear, the lower level Gaussian quadrature filter is sufficient to provide accurate estimate. The adaptive strategy is used to evaluate the nonlinearity of the system at current time first and then utilize different quadrature rule for filtering. Another filter aims to modify the conventional update rule, i.e. the linear minimum mean square error (LMMSE) rule, to involve a nonlinear transformation of the observation, which is proven to be an efficient way to exploit more information from the original observation. According to the orthogonal property, we propose a novel approach to construct the nonlinear transformation systematically. The augmented nonlinear filter outperforms Gaussian filters and other conventional augmented filters in terms of the root mean square error and onsistency. Furthermore, we also extend the work to the more general case. The higher order moments can be utilized to construct the nonlinear transformation and in turn, the measurement space can be expand efficiently. Without the Gaussian assumption, the construction of the nonlinear transformation only demand the existence of a finite number of moments. Finally, the simulation results validate and demonstrate the superiority of the adaptive and augmented nonlinear filters.

scholarly journals Non-Gaussian inference from non-linear and non-Poisson biased distributed data

2014 ◽  
Vol 10 (S306) ◽  
pp. 258-261
Author(s):  
Metin Ata ◽  
Francisco-Shu Kitaura ◽  
Volker Müller
Keyword(s):  
Dark Matter ◽  
Statistical Inference ◽  
Computer Code ◽  
Matter Density ◽  
Density Field ◽  
Distributed Data ◽  
Dark Matter Density ◽  
Posterior Sampling ◽  
Non Linear ◽  
Non Gaussian

AbstractWe study the statistical inference of the cosmological dark matter density field from non-Gaussian, non-linear and non-Poisson biased distributed tracers. We have implemented a Bayesian posterior sampling computer-code solving this problem and tested it with mock data based onN-body simulations.

Sign in / Sign up

Export Citation Format

Share Document