A Review on Kalman Filter Models

• Published in: Archives of computational methods in engineering Vol. 30; no. 1; pp. 727 - 747
• Main Authors: Khodarahmi, Masoud, Maihami, Vafa
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2023; Springer Nature B.V
• Subjects: Algorithms; Engineering; Estimation; Kalman filters; Mathematical and Computational Engineering; Nonlinear systems; Review Article
• ISSN: 1134-3060; 1886-1784
• DOI: 10.1007/s11831-022-09815-7

Kalman Filter (KF) that is also known as linear quadratic estimation filter estimates current states of a system through time as recursive using input measurements in mathematical process model. Thus algorithm is implemented in two steps: in the prediction step an estimation of current state of variables in uncertainty conditions is presented. In the next step, after obtaining the measurement, previous estimation is updated by weighted arithmetic mean. Accordingly, using KF in non-linear systems can be difficult. For nonlinear systems Extended KF (EKF) and Unscented KF (UKF) represent the first-order and higher order linear approximations. KF cannot predict appropriate values for modeling system behavior in more complicated systems. In the current study, in addition to referring to basic methods, a review on recent researches on Multiple Model (MM) filters has been done. More reliable estimations obtain by using two or more filters with different models in parallel, by allocating an estimation to each filter, outputs of each filter are calculated. MM Adaptive Estimation (MMAE) and Interacting MM (IMM) are the most used methods for estimating MMs.