A The Linear Regression Kalman Filter

2005 ◽  
pp. 205-210 ◽  
Author(s):  
Tine Lefebvre ◽  
Herman Bruyninckx ◽  
Joris De Schutter
Keyword(s):  
Kalman Filter ◽  
Linear Regression

scholarly journals A New Linear Regression Kalman Filter with Symmetric Samples

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2139
Author(s):  
Xiuqiong Chen ◽  
Jiayi Kang ◽  
Mina Teicher ◽  
Stephen S.-T. Yau
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Particle Filter ◽  
Normal Distribution ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Unscented Kalman Filter ◽  
Standard Normal Distribution ◽  
Leibler Divergence ◽  
Standard Normal

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

scholarly journals Tracking—A

2021 ◽  
pp. 163-192
Author(s):  
Jean Walrand
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Least Squares ◽  
Recursive Algorithm ◽  
Nonlinear Function ◽  
Random Variables ◽  
Random Variable ◽  
Linear Least Squares ◽  
Least Squares Estimate ◽  
Related Notion

AbstractThis chapter explains how to estimate an unobserved random variable or vector from available observations. This problem arises in many examples, as illustrated in Sect. 9.1. The basic problem is defined in Sect. 9.2. One commonly used approach is the linear least squares estimate explained in Sect. 9.3. A related notion is the linear regression covered in Sect. 9.4. Section 9.5 comments on the problem of overfitting. Sections 9.6 and 9.7 explain the minimum means squares estimate that may be a nonlinear function of the observations and the remarkable fact that it is linear for jointly Gaussian random variables. Section 9.8 is devoted to the Kalman filter, which is a recursive algorithm for calculating the linear least squares estimate of the state of a system given previous observations.

Kalman Filter Algorithm for Adaptive Digital Predistortion

2013 ◽  
Vol 347-350 ◽  
pp. 2385-2389
Author(s):  
Xiao Wei Kong ◽  
Jin Zheng Li ◽  
Wei Xia ◽  
Zi Shu He
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
State Space ◽  
Recursive Algorithm ◽  
Digital Predistortion ◽  
Parameters Extraction ◽  
Kalman Filter Algorithm ◽  
Digital Predistorter ◽  
Space Equation ◽  
Accuracy And Stability

This paper introduces a recursive algorithm of Kalman filter for digital predistorter parameters extraction based on memory polynomials predistorter model. The predistorter model is firstly formulated as linear regression expression. Then we derive the state-space equation of the model and attain the steps of the algorithm. Finally, the accuracy and stability of the algorithm is proved by simulation.

scholarly journals Quadratic Polynomial Regression Using Serial Observation Processing: Implementation within DART

2017 ◽  
Vol 145 (11) ◽  
pp. 4467-4479 ◽  
Author(s):  
Daniel Hodyss ◽  
Jeffrey L. Anderson ◽  
Nancy Collins ◽  
William F. Campbell ◽  
Patrick A. Reinecke
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Data Assimilation ◽  
Polynomial Regression ◽  
Quadratic Polynomial ◽  
State Estimate ◽  
Serial Data ◽  
Serial Observation ◽  
Hierarchy Of Models

It is well known that the ensemble-based variants of the Kalman filter may be thought of as producing a state estimate that is consistent with linear regression. Here, it is shown how quadratic polynomial regression can be performed within a serial data assimilation framework. The addition of quadratic polynomial regression to the Data Assimilation Research Testbed (DART) is also discussed and its performance is illustrated using a hierarchy of models from simple scalar systems to a GCM.

scholarly journals Coupling the K-nearest neighbors and locally weighted linear regression with ensemble Kalman filter for data-driven data assimilation

2021 ◽  
Vol 13 (1) ◽  
pp. 1395-1413
Author(s):  
Manhong Fan ◽  
Yulong Bai ◽  
Lili Wang ◽  
Lihong Tang ◽  
Lin Ding
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Forecast Model ◽  
Data Driven ◽  
Sequential Data ◽  
Weighted Linear Regression

Abstract Machine learning-based data-driven methods are increasingly being used to extract structures and essences from the ever-increasing pool of geoscience-related big data, which are often used in relation to the atmosphere, oceans, and land surfaces. This study focuses on applying a data-driven forecast model to the classical ensemble Kalman filter process to reconstruct, analyze, and elucidate the model. In this study, a nonparametric sampler from a catalog of historical datasets, namely, a nearest neighbor or analog sampler, is given by numerical simulations. Based on this catalog (sampler), the dynamics physics model is reconstructed using the K-nearest neighbors algorithm. The optimal values of the surrogate model are found, and the forecast step is performed using locally weighted linear regression. Several numerical experiments carried out using the Lorenz-63 and Lorenz-96 models demonstrate that the proposed approach performs as good as the ensemble Kalman filter for larger catalog sizes. This approach is restricted to the ensemble Kalman filter form. However, the basic strategy is not restricted to any particular version of the Kalman filter. It is found that this combined approach can outperform the generally used sequential data assimilation approach when the size of the catalog is substantially large.

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