An Application of the Kalman Filter Recursive Algorithm to Estimate the Gaussian Errors by Minimizing the Symmetric Loss Function

Cristian Busu,Mihail Busu

doi:10.3390/sym13020240

Abstract

Kalman filtering is a linear quadratic estimation (LQE) algorithm that uses a time series of observed data to produce estimations of unknown variables. The Kalman filter (KF) concept is widely used in applied mathematics and signal processing. In this study, we developed a methodology for estimating Gaussian errors by minimizing the symmetric loss function. Relevant applications of the kinetic models are described at the end of the manuscript.

Highlights

Linear quadratic estimation (LQE) is a statistical method with many technological applications
Over the past few decades, generalizations of and extensions to the KF method have been established, such as the unscented Kalman filter (UKF) and the extended Kalman filter (EKF), which both work on nonlinear systems [5,6]
The KFThis are last in economics, biology, and the environmental and it is an important example shows another important utility sciences, of the estimation, i.e., a proper topic in control systems engineering andreveal controlthe theory

Summary

Introduction

Linear quadratic estimation (LQE) is a statistical method with many technological applications. Other applications [2,3] are based on the lag between the issuing signals and receiving a response, in which the Kalman filter (KF) makes assessments of the condition of the framework and issues directions. A KF assumes that the noise is normally (Gaussian) distributed and the observation models are linear [4]. The filter gives the posterior conditional probability estimate in the case when the errors follow a Gaussian distribution. Over the past few decades, generalizations of and extensions to the KF method have been established, such as the unscented Kalman filter (UKF) and the extended Kalman filter (EKF), which both work on nonlinear systems [5,6]. EKF is probably the most widely used estimation algorithm for nonlinear systems [7]

Objectives

Methods

Conclusion