Broyden’s update based extended Kalman Filter for nonlinear state estimation

Abstract

State estimation is a pre-requisite for advanced control applications such as optimization based nonlinear model predictive control since the latter needs to know the current state vector. Thus, any decrease in computation time for the state estimation module can lead to significant benefits in the overall closed loop implementation by reducing the overall computational delay in implementing the control move. The current work contributes to this area by proposing a novel variant of the widely used Extended Kalman Filter (EKF) for nonlinear state estimation. The proposed variant has significantly reduced computation time requirement compared to its traditional implementation. This reduction is obtained by using Broyden’s rank-one update procedure for approximating the time varying process and measurement Jacobian matrices which are needed in EKF at each time instant. Broyden’s update of Jacobian matrix is widely used in numerical techniques literature but its use in estimation literature has hitherto not been reported. In the current work, we map the iterative procedure of Broyden’s update to the time and measurement update steps of EKF to approximate the process and measurement Jacobian matrices needed in EKF using rank-one updates. The proposed approach neither requires any analytical derivative nor additional evaluation of the process and measurement functions. It only utilizes the predicted and filtered states, and predicted measurements as available in EKF. It thus leads to significant reduction in computation time. Comparison of the theoretical Floating Point Operations (FLOPs) requirements, actual computation times, and the estimation performances of the proposed approach with traditional EKF on two case studies including the Tennessee Eastman challenge problem demonstrates the efficacy of the proposed approach.