Minimizing forecast error requires accurately specifying the initial state from which the forecast is made by optimally using available observing resources to obtain the most accurate possible analysis. The Kalman filter accomplishes this for linear systems and experience shows that the extended Kalman filter also performs well in nonlinear systems. Unfortunately, the Kalman filter and the exte...

Precise state estimation is crucial for any autonomous system as it enables the system to provide appropriate control inputs to its actuators. However, estimation is challenging as it must be able to handle imprecise system models (often described by complex non-linear functions) as well as noisy sensor measurements in order to compute the system’s state. In this work, we explore three approach...

The concept of complementarity (or quasi-orthogonality) is extended to POVM's. It is shown in the setting of unconstrained state estimation that the determinant of the mean quadratic error matrix is minimal if the POVM's are complementary (and informationally complete). Several examples of the scheme are given.

In a post m o r t e m (after the fact) analysis, it is possible to wait for more observations to accumulate. In that case, the estimate can be improved by smoothing.-Andrew Jazwinski jJaz70, p. 1431 In previous chapters, we discussed how to obtain the optimal a priori and a posteriori state estimates. The a priori state estimate at time k, 2;, is the state estimate at time k based on all the me...

Steady state simulation is used to study long-run behavior. Usually only the expected value of the steady state probability distribution function is estimated. In many cases quantiles of this distribution are of higher interest. In this paper a new usage of quantile estimators is proposed, which is derived from mean value analysis and is based on multiple independent replications. The advantage...