Optimal and Robust State Estimation

3State Estimation

Gauss's batch least squares is routinely used today, and it often gives accuracy that is superior to the best available EKF.

Fred Daum, [40], p. 65

Although SDEs provide accessible mathematical models and have become standard models in many areas of science and engineering, features extraction from high‐order processes is usually much more complex than from first‐order processes such as the Langevin equation. The state-space representation avoids many inconveniences by replacing high‐order SDEs with first‐order vector SDEs. Estimation performed using the state‐space model solves simultaneously two problems: 1) filtering measurement noise and, in some cases, process noise and thus filter, and 2) solving state‐space equations with respect to the process state and thus state estimator. For well‐defined linear models, state estimation is usually organized using optimal, optimal unbiased, and unbiased estimators. However, any uncertainty in the model, interference, and/or errors in the noise description may require a norm‐bounded state estimator to obtain better results. Methods of linear state estimation can be extended to nonlinear problems to obtain acceptable estimates in the case of smooth nonlinearities. Otherwise, special nonlinear estimators can be more successful in accuracy. In this chapter, we lay the foundations of state estimation and introduce the reader to the most widely used methods applied to linear and nonlinear stochastic systems and processes. ...