Linear and nonlinear estimation with uncertain observations

The state estimation problems with observations which may or may not contain a signal at any sample time is considered from a covariance assignment viewpoint. The closed form solution for directly assigning steady state estimation error covariances and their assignability conditions are derived for the linear case. For the nonlinear case, upper bounds on the estimation error covariance are assigned. An example is given for illustration in which the robustness of the proposed scheme is assessed.