Open AccessThe Composite Covariance of a Kalman Filter Estimation
Author(s) -
Winston C. Chow
Publication year - 2021
Publication title -
international journal of georesources and environment
Language(s) - English
Resource type - Journals
ISSN - 2371-9508
DOI - 10.15273/ijge.2021.06.083
Subject(s) - covariance intersection , covariance , kalman filter , extended kalman filter , ensemble kalman filter , fast kalman filter , mathematics , gaussian , multivariate normal distribution , covariance function , univariate , invariant extended kalman filter , state vector , statistics , computer science , multivariate statistics , physics , classical mechanics , quantum mechanics
A Kalman filter estimation of the state of a system is merely a random vector that has a normal, also called Gaussian, distribution. Elementary statistics teaches any Gaussian distribution is completely and uniquely characterized by its mean and covariance (variance if univariate). Such characterization is required for statistical inference problems on a Gaussian random vector. This mean and composite covariance of a Kalman filter estimate of a system state will be derived here. The derived covariance is in recursive form. One must not confuse it with the “error covariance” output of a Kalman filter. Potential applications, including geological ones, of the derivation are described and illustrated with a simple example.