History
The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The primary drawback of the Kalman Filter is that it is the optimal estimate for linear system models with additive independent white noise in both the transition and the measurement systems. Unfortunately in engineering most systems are nonlinear, so some attempt was immediately made to apply this filtering method to nonlinear systems. Most of this work was done at NASA Ames. The EKF which adapted techniques, namely multivariate Taylor Series expansions, from calculus to linearize about a working point became the working solution. If the system model (as described below) is not well known or is inaccurate, then Monte Carlo methods, especially particle filters are employed for estimation. Monte Carlo techniques predate the existence of the EKF but are more computationally expensive for any moderately dimensioned state-space.
Read more about this topic: Extended Kalman Filter
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