ELEC-E8107 - Stochastic models, estimation and control D, Lecture, 6.9.2022-7.12.2022
Kurssiasetusten perusteella kurssi on päättynyt 07.12.2022 Etsi kursseja: ELEC-E8107
Lecture 5, Oct 11: STATE ESTIMATION FOR NONLINEAR DYNAMIC SYSTEMS, THE EXTENDED KALMAN FILTER
STATE ESTIMATION FOR NONLINEAR DYNAMIC SYSTEMS
• Present the optimal discrete-time estimator.
• Discuss the difficulty in implementing it in practice due to memory requirements and computational requirements.
• Discuss numerical implementation of the optimal discrete-time estimator.
• Derive the suboptimal filter known as the extended Kalman Filter
THE EXTENDED KALMAN FILTER
• Very limited feasibility of the implementation of the optimal filter, the functional recursion, suboptimal algorithms are of interest.
• The recursive calculation of the sufficient statistic consisting of the conditional mean and variance in the linear-Gaussian case is the simplest possible state estimation filter.
• As indicated earlier, in the case of a linear system with non-Gaussian random variables the same simple recursion yields an approximate mean and variance.
• A framework similar is desirable for a nonlinear system. Such an estimator, called the extended Kalman filter (EKF), can be obtained by a series expansion of the nonlinear dynamics and of the measurement equations.