Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition

Lesson 24 Iterated Least Squares and Extended Kalman Filtering

Summary

This lesson is devoted primarily to the extended Kalman filter (EKF), which is a form of the Kalman filter “extended” to nonlinear dynamical systems of the form described in Lessons 23. We show that the EKF is related to the method of iterated least squares (ILS), the major difference being that the EKF is for dynamical systems, whereas ILS is not.

We explain ILS for the model z(k) = f(θ, k) + v(k), k = 1, 2,…, N, where the objective is to estimate θ from the measurements. A four-step procedure is given for ILS, from which we observe that in each complete cycle of this procedure we use both the nonlinear and linearized models and that ILS uses the estimate obtained from ...