Properties of a physical system are measured and used to update estimated states of the system in an iterative manner. At each iteration, a state update weight is assigned for each state and the states are predicted from previous estimated states. System states are predicted from prior estimates and then updated dependent upon the measurements and the state update weights to provide updated estimated states. In addition, a prior covariance matrix of state errors is updated dependent upon the state update weights to provide an estimation error covariance matrix that is consistent with the updated estimated states. The updated state may be equivalent to a weighted sum of a prior estimated state and an initial updated estimated state. The approach provides improvements to a variety of estimators, including least squares estimators and estimators such as the Extended, Schmidt and Unscented Kalman Filters and the Rao-Blackwellized Particle Filter.