Nonlinear state-space modeling and filtering using extended state vectors

A self-consistent approach to nonlinear state-space filtering, based on power series and extended state vectors, is developed and compared with extended Kalman filtering. Using a numerical example, the new filter is demonstrated to be more accurate than the extended Kalman filter when measurements are infrequent. For an n-state nonlinear system expanded to the pth order, the proposed filtering algorithm uses an extended state vector of dimension np to compute state estimates of the original system. This extended state filter employs the minimum-variance linear estimator to update the state estimate with linear measurements.<>