Kalman Filter and Its Application in Data Assimilation
11
Citation
47
Reference
10
Related Paper
Citation Trend
Abstract:
In 1960, R.E. Kalman published his famous paper describing a recursive solution, the Kalman filter, to the discrete-data linear filtering problem. In the following decades, thanks to the continuous progress of numerical computing, as well as the increasing demand for weather prediction, target tracking, and many other problems, the Kalman filter has gradually become one of the most important tools in science and engineering. With the continuous improvement of its theory, the Kalman filter and its derivative algorithms have become one of the core algorithms in optimal estimation. This paper attempts to systematically collect and sort out the basic principles of the Kalman filter and some of its important derivative algorithms (mainly including the Extended Kalman filter (EKF), the Unscented Kalman filter (UKF), the Ensemble Kalman filter (EnKF)), as well as the scope of their application, and also to compare their advantages and limitations. In addition, because there are a large number of applications based on the Kalman filter in data assimilation, this paper also provides examples and classifies the applications of both the Kalman filter and its derivative algorithms in the field of data assimilation.Keywords:
Alpha beta filter
Unscented transform
The objective of this paper is to explore the standard Kalman filter and two non-linear variations. Additionally, we will discuss the derivation of the Kalman filter using Newton’s method. Next we will consider the implementation of both the Extended Kalman filter and the Unscented Kalman filter, paying special attention to the cases where the Unscented Kalman filter performs better than the Extended Kalman filter. Finally, we will make a comparison between these two Kalman filter variations and consider a few other modifications to the standard Kalman filter. iii تیاس ب لتم Matlab Site.com MatlabSite.com تیاس بلتم
Alpha beta filter
Unscented transform
Cite
Citations (2)
Unscented transform
Alpha beta filter
Cite
Citations (0)
This chapter covers the Kalman filter and its variants. Kalman filter is the optimal Bayesian filter in the sense of minimizing the mean-square estimation error for linear systems with Gaussian noise. Algorithms that extend the applicability of the Kalman filter to nonlinear systems either use power series to approximate the nonlinear functions in the state-space model or use numerical methods to approximate the corresponding probability distributions. While the extended Kalman filter and the divided-difference filter belong to the former category of algorithms, the unscented Kalman filter and the cubature Kalman filter belong to the latter. Information filter and extended information filter provide alternative formulations of the Kalman filter and the extended Kalman filter by recursively updating the inverse of the estimation error covariance matrix. Using a mixture of Gaussians to approximate the posterior, the Gaussian-sum filter extends the applicability of the Kalman filter to non-Gaussian systems. In the Kalman filter algorithm, the corrective term is reminiscent of the proportional controller. The generalized proportional-integral-derivative (PID) filter uses a more sophisticated corrective term inspired by the PID controller. Finally, a number of applications of Kalman filtering algorithms are reviewed including information fusion, augmented reality, urban traffic network, cybersecurity of power systems, incidence of influenza, and COVID-19 pandemic.
Alpha beta filter
Unscented transform
Filtering problem
Cite
Citations (3)
In order to obtain the optimal minimum variance state estimation for electro-optical tracking,a nonlinear Kalman filter algorithm is provided by combining reduced state Kalman filter and first-order linear in nonlinear system,and the algorithm structure is summarized in detail. Then,it is applied in nonlinear measurement electro-optical tracking system and compared the performances of reduced state Kalman filter with extended Kalman filter and unscented Kalman filter. The Matlab simulation results show that combining reduced state Kalman filter and first-order linear in nonlinear system is valid,and the performance outperforms the extended Kalman filter and unscented Kalman filter.
Alpha beta filter
Unscented transform
Nonlinear filter
Cite
Citations (0)
Статья посвящена сравнению трех методов усвоения данных наблюденй: фильтр Калмана (Kalman Filter, KF), ансамблевый фильтр Калмана (Ensemble Kalman Filter, EnKF) и локальный фильтр Калмана (Local Kalman Filter, LKF). Выполнены численные эксперименты по усвоению синтетических данных этими методами в двух разных моделях, описываемых системами дифференциальных уравнений. Первая описывается одномерным линейным уравнением адвекции, а вторая - системой Лоренца. Проведено сравнение средних ошибок и времени исполнения этих методов при различных размерах модели, которые согласуются с теоретическим оценками. Показано, что вычислительная сложность ансамблевого и локального фильтров Калмана растет линейно с увеличением размера модели, в то время как у первого метода эта сложность растет со скоростью куба. Рассмотрена эффективность одной из возможных параллельных реализаций локального фильтра Калмана. The paper is devoted to the comparison of three data assimilation methods: the Kalman Filter (Kalman Filter, KF), the ensemble Kalman Filter (EnKF), and the local Kalman Filter (LKF). A number of numerical experiments on data assimilation by these methods are performed on two different models described by systems of differential equations. The first one is a simple one-dimensional linear equation of advection and the second one is the Lorenz system. The mean errors and the execution time of these assimilation methods are compared for different model sizes. The numerical results are consistent with the theoretical estimates. It is shown that the computational complexity of local and ensemble Kalman filters grows linearly with the size of the model, whereas in the classical Kalman Filter this complexity increases according to the cubic law. The efficiency of parallel implementation of the local Kalman filter is considered.
Alpha beta filter
Cite
Citations (1)
Abstract This paper mainly describes the basic principles of extended Kalman filter and unscented Kalman filter and the application of them in target tracking based on observation distance At last the two algorithms are compared by Matlab software The simulation results show that unscented Kalman filter has better matching effect than extended Kalman filter and the former has smaller error variation and better convergence than the latter
Unscented transform
Alpha beta filter
Tracking (education)
Cite
Citations (2)
This correspondence presents the results of the application of the matrix inversion lemma to the Kalman filter equation. This operation eliminates the inversion process in the Kalman filter and enables one to sequentially compute the optimum estimate of the state without the use of the inversion process.
Alpha beta filter
Lemma (botany)
Cite
Citations (3)
The relative effects of initialization error on the Extended and Unscented Kalman filters were investigated for an example scalar system. Analytical methods were applied in order to derive the conditions under which one filter outperformed the other in response to initial error. Some simulation results were presented to support the analytically derived results. For the considered example, the Extended Kalman filter was able to outperform the Unscented Kalman filter when the assumed initial state was greater in magnitude than the actual initial state, and vice versa. Additionally, cases with larger measurement noise demonstrated further performance advantage of the Extended Kalman Filter.
Unscented transform
Alpha beta filter
Initialization
Cite
Citations (5)
Abstract Estimation distribution of air pollution is necessary to determine the level of pollution in a location so it can be used to recommend emission minimization. This research use some modification of Kalman Filter method for estimation distribution of air pollution. Three estimation methods namely Fractional Kalman Filter (FKF), Ensemble Kalman Filter (EnKF), Unscented Kalman Filter (UKF). The simulation result of three methods will be compared. Distribution of carbon monoxide and nitrogen dioxide in Surabaya was estimated using three methods. This reserach showed that Fractional Kalman Filter method is the best estimator among the others because error value is the smallest.
Alpha beta filter
Unscented transform
Cite
Citations (1)
In any linear system the Kalman Filter is highly used to tracking and estimation. Extended Kalman Filter is deal nonlinear system better than Kalman Filter. But the framework of Extended Kalman Filter is not easy to draw they requires some highly numerical terms in nature. So, there using a new method called Unscented Kalman Filter to provide an easy task to user with use of sigma focus points. Nonlinear approach is used to estimate the state of the System.
Unscented transform
Alpha beta filter
Nonlinear filter
Cite
Citations (50)