Identification of moderately nonlinear flight mechanics systems withadditive process and measurement noise

Abstract

The parameter estimation problem for dynamic systems with both process and measurement noise from nonlinear model postulates is addressed in this paper. A two-step estimation procedure explicitly computes the covariance matrix of residuals and updates the system parameters, the initial conditions, and the state noise matrix using the Gauss-Newton optimization method. For the purpose of state estimation in nonlinear systems with process noise, an approximate steady-state filter is used. In each iteration, the filter-gain matrix is obtained from the postulated system model linearized at the updated initial conditions. The gradients of the output variables and of the system functions are approximated by finite differences. The proposed approach for nonlinear systems with unknown process and measurement noise covariances is first validated on simulated aircraft response data. It is then applied to estimate the aircraft longitudinal derivatives from flight test data using two models with different degrees of nonlinearities. Advantages and possible limitations of the method are discussed.