History and Applications of Kalman Filter: A Review - Aiswarya Nair P.; Resmi R. (International Journal of Electrical Power and Machine Systems, 2024)
The Kalman filter is a powerful algorithm that is used to estimate the dynamic system states with noisy measurements and uncertain behaviors. It is an optimal estimator that minimizes the average squared error between the estimated states and the true states, given the noisy data and a model of the system. The recursive algorithm is highly effective in tracking and predicting the state of complex systems over time. Kalman filters have been a very crucial part of estimation theory since their development in 1960. Originally used in missile tracking and aerospace engineering for specific purposes such as tracking and optometric estimations, they have come a long way and proved to be useful in the modern scenario in a plethora of engineering applications. Various modifications have already been brought to this recursive algorithm for state estimation, so that they can be used for a wide variety of applications in engineering such as object tracking, state of charge estimation, and localization to name a few. The main types of Kalman filters discussed in this paper are the traditional Kalman filter, the extended Kalman filter, the unscented Kalman filter, the cubature Kalman filter, and the ensemble Kalman filter. Each of these variations of the algorithm adopt unique mathematical approaches which are different from each other to solve the problem at hand. In presented paper a review of the history of Kalman filter and some of its applications is presented.
Keywords: Estimation theory; Kalman filter; cubature; ensemble Kalman filter; extended Kalman filter; unscented Kalman filter