Nonlinear descriptor system Kalman estimator with colored noise

Aiming at linear and nonlinear descriptor systems with colored noise, a Kalman state estimator is presented. Firstly, the nonlinear system is transformed into linear system with Taylor formula. For linear descriptor system, the singular value decomposition is used to transform the filter problems of original descriptor systems into the filter problems of two normal subsystems. The measurement transformation method is applied to change the colored observation noise to white noise. So the problems are transformed to the Kalman state estimator problems of normal systems with correlated white noise. In the end, the descriptor Kalman estimator with colored noise is derived on the basis of Kalman filter, and then, the original descriptor system filter with colored noise is obtained. Two Monte-Carlo simulation examples show the effectiveness of the two algorithms.