A resettable Kalman filter based on numerical differentiation

The extended Kalman filter is known to have excellent filtering characteristics, but its convergence is guaranteed only if it is initialized close enough to the true state value. Numerical differentiation based observers, on the other hand, may be designed to be globally convergent to a neighborhood of the true state value, but when the measurements are corrupted by uncertain signals their state estimates are delayed. We propose, in this Communication, an observer design scheme for nonlinear systems which combines these two techniques to yield a globally exponentially converging observer.