State estimation theory is one of the best mathematical approaches to analyze variants in the states of the system or process. The state of the system is defined by a set of variables that provide a complete representation of the internal condition at any given instant of time. Filtering of Random processes is referred to as Estimation, and is a well-defined statistical technique. There are two types of state estimation processes, Linear and Nonlinear. Linear estimation of a system can easily be analyzed by using Kalman Filter (KF) and is used to compute the target state parameters with a priori information under noisy environment. But the traditional KF is optimal only when the model is linear and its performance is well defined under the assumptions that the system model and noise statistics are well known. Most of the state estimation problems are nonlinear, thereby limiting the practical applications of the KF. The modified KF, aka EKF, Unscented Kalman filter and Particle filter are best known for nonlinear estimates. Extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about the current mean and covariance. The estimation can be linearised around the current estimate using the partial derivatives to compute estimates even in the face of nonlinear relationships.. The EKF has been considered the standard in the theory of nonlinear state estimation. This paper deals with how to estimate a nonlinear model with Extended Kalman filter (EKF). The approach in this paper is to analyze Extended Kalman filter where EKF provides better probability of state estimation for a free falling body towards earth.
Kumari., L., Raju., P., .V.Y.V, C., Krishna., S., & Rao, V. M. J. (2011). Application Of Extended Kalman Filter For A Free Falling Body Towards Earth. International Journal of Advanced Computer Science and Applications, 2(4). https://doi.org/10.14569/ijacsa.2011.020420