IOSR Journal of Computer Engineering (IOSR-JCE) e-ISSN: 2278-0661,p-ISSN: 2278-8727, Volume 18, Issue 5, Ver. IV (Sep. - Oct. 2016), PP 14-19 www.iosrjournals.org DOI: 10.9790/0661-1805041419 www.iosrjournals.org 14 | Page Tuning of Extended Kalman Filter for nonlinear State Estimation Navreet Kaur 1 , Amanpreet Kaur 2 1, 2 (Information Technology Department, Chandigarh Engineering college, Landran, India) Abstract: Kalman Filter is the most popular method for state estimation when the system is linear. State estimation is the typical issue in every part of engineering and science. But, for non linear systems, different extensions of Kalman Filter are used. Extended Kalman Filter is famous to discard the non linearity which uses First order Taylor series expansion. But for these estimation techniques, the tuning of process noise covariance and measurement noise covariance matrices is required. There are different optimization techniques used to tune the parameters of Extended Kalman Filter. In this paper, Particle Swarm Optimization has been proposed to tune the EKF parameters and then the simulations are implemented for permanent magnet synchronous motor. Keywords: Extended Kalman Filter, Particle Swarm Optimization, non-linear, state estimation, tuning of EKF. I. Introduction For a Dynamic system, it is mandatory to estimate the state using a sequence of noisy measurements. Somewhat there is need of two models to analyze and make presumption about a dynamic system: First is, a system model, which express the evolution of the state with time and the second is the measurement model, which is related to the noisy measurements of the state [1]. There are various filters used to solve the issue of state estimation. These filters include the Kalman filter, Particle filter, Unscented Kalman Filter, Extended Kalman filter and also a Fokker-Planck equation based constant rate filter [2]. Kalman Filter is used only when the system is linear, but almost all practical systems have non linearity. If the dynamic model is non linear, then the Extended Kalman filter is used to eliminate the non linearity [3]. Extended Kalman Filter is the extended form of Kalman Filter, which is based on linearization of first order Taylor series expansion. By using Gaussian random variable the state distribution has been approximated [4]. The other derivative of Kalman Filter, i.e. Unscented Kalman Filter (UKF) is also used when the system is non linear and it also gives better results than Extended Kalman Filter but it suffers from the problem of divergence. So, Extended Kalman filter is the famous state estimation technique because of its simplicity [5]. Extended Kalman Filter gives an approximation of the optimal estimate. But, it suffers from different problems like divergence, initialization and linearization error and covariance estimation [6]. Therefore, it is necessary to tune the filter parameters of the Extended Kalman Filter, i.e. process noise covariance (Q) and measurement noise (R) covariance matrices. Almost all the filters require the tuning process after the implementation. In Filter tuning process, the measurement noise and dynamic noise statistics are selected to get better performance [2]. There are different methods used to tune the measurement noise covariance (R) matrix and process noise covariance (Q) matrix. Earlier, an adaptive Kalman filtering approach is used to tune the measurement noise covariance matrix and process noise covariance matrix. Three different schemes of adaptation have been used by the Adaptive Kalman Filter. These include: measurement noise covariance matrix (R), process noise covariance matrix (Q) and the initial values of error covariance matrix (P) [7]. There are two adaptive methods used, i.e. multiple model adaptive estimation in which multiple Kalman filters runs parallel, and innovative adaptive estimation in which the Q and R matrices are adapted by themselves [8]. But these methods have problem of lack of convergence, and large window requirement. There are different optimization techniques used to tune the Q and R matrices of Extended Kalman Filter. In this paper Particle Swarm Optimization technique is used to tune the Extended Kalman Filter for non linear state estimation. Particle Swarm Optimization is a metamorphic technique which is influenced by the flocks of birds or schools of fishes [10]. Using fitness function the fitness of the particle is calculated. In Section 2, the Extended Kalman Filter is presented. Section 3 presents the particle swarm optimization Technique and section 4 describes the problem formulation and system design. Section 5 describes the methodology used. Section 6 shows the simulation results. At the end, conclusion is there. II. Extended Kalman Filter By considering the following equation, the non linear system model can be described as given in [9],