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

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.

Keywords

• unscented Kalman filter (UKF)
• extended Kalman filter (EKF)
• recursive algorithm
• Gaussian errors
• linear quadratic estimation (LQE)
• contraction property