A derivative-free implementation of the extended Kalman filter

A nonlinear estimation paradigm is developed to estimate the mean and covariance of a time-evolving state distribution. The approach represents uncertainty by an ensemble set of state vectors rather than by the traditional mean and covariance measures, avoiding the need for the calculation of matrix partial derivatives (Jacobian matrices). The paradigm is shown to be equivalent to the extended Kalman filter in a limiting case. Implementation of the new filtering approach is illustrated with a simple example and a step-by-step description. The paradigm is not significantly more computationally intensive than traditional filters and proves ideal for the rapid implementation of complex nonlinear system and observation models.