Evaluation of Derivative Free Kalman Filter for Non-linear State-Parameter Estimation and Fusion

Abstract

The estimation of the states-parameters of non-linear system is often carried out using Extended Kalman Filter (EKF). The EKF is only reliable for systems that are almost linear on the time scale of the updates (i.e. sampling interval). The limitation of EKF can be overcome by use of another class of recursive estimator named derivative free Kalman filter (DFKF) or more popularly known as Unscented Kalman filter, a method that propagates mean and covariance using non-linear transformation. In this paper two methods: i) factorized version of EKF (UD Extended Kalman Filter or UDEKF) and ii) DFKF are studied and evaluated using various sets of simulated data of the non-linear systems as well as one real data set. Sensitivity study of DFKF with respect to tuning parameters such as α, β, and κ (used in creation of sigma points and their associated weights) is also carried out using one set of simulated data. DFKF as compared to EKF is more accurate, easier to implement and has same order of calculations. The concept of DFKF is extended to data fusion (DF) for similar sensors and algorithm is named DF-DFKF. Application of DFKF is demonstrated in parameter estimation problem.