Chapter 7
The Analytical Linearization Class of Kalman Filters: The Extended Kalman Filter
For mildly nonlinear and smooth (differentiable) functions, analytical methods can be used to linearize the nonlinear equations, making the linear Kalman filter structure available for use with nonlinear dynamic and/or observation equations. To accomplish this linearization, the nonlinear function 
in (5.51)–(5.57) can be expanded in a multidimensional Taylor polynomial about the mean value 
leading to the extended Kalman filter [1,2]. To make understanding of the method easier, and for future reference, we will develop the scalar extended Kalman filter (EKF) first and then move to the multidimensional case.
