Nonlinear Smoothing Theory

Differential equations are developed for the smoothing density function and for the smoothed expectation of an arbitrary function of the state. The exact equations developed herein are difficult to solve except in trivially simple cases. Approximations to these equations are developed for the smoothed expectation of the state and the smoothing covariance matrix. For linear systems these equations are shown to reduce to previously derived results. An iterative technique is suggested for even greater accuracy in approximations for severely nonlinear systems.