Tuning of Extended Kalman Filter for nonlinear State Estimation

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.

Optimized tire force estimation using extended Kalman filter and fruit fly optimization

“…The plant and measurement covariance matrices are noted by Q and R respectively. Following the formulation presented in [9], the EKF action can be subdivided into the time update and measurement update steps, represented by the expressions (14)(15)(16)(17)(18). Time update…”

“…The filter gain 𝐾 𝑘 is computed from the predicted covariance matrix 𝑃 𝑘|𝑘−1 , the measurement covariance matrix 𝑅, and the jacobian of the observation vector 𝐻 𝑘 , equation (16). Once the filter gain is calculated, the measurement residuals are used to correct the states predicted in the time update stage, expression (17). Finally, the covariance matrix is updated, expression (18).…”

“…There are no design rules in place which can be used for this complex purpose and current practice relies on trial and error methods. A new trend is to tune the EKF using numerical optimization techniques [16,17]. However, this approach has not been tested before in vehicle dynamics.…”

Approaches for Long Lifetime Organic Light Emitting Diodes

“…In 2016, Kaur et al published a review paper discussing the influence of environmental factors on organic light emitting diode (OLED) displays. [71] Presence of moisture, oxygen, and impurities strongly affecting the OLED lifetime, we are discussing the same issues in the Sections 2.2.1, 2.2.2, and 2.2.10. In 2016, Fujimoto et al reported the influence of vacuum chamber impurities on the lifetime of OLEDs.…”

Spacecraft trajectory tracking and parameter estimation around a splitting contact binary asteroid

“…Filter stability depends on properly sized covariance matrices. Aside from finding stable values, optimization techniques for tuning the covariance values have been proposed to improve the filter's performance 47,48,49 , however these techniques usually require extensive computationally expensive Monte Carlo simulations. Process noise covariance values for the (𝑥, 𝑦, 𝑧) position and (𝑥, 𝑦, 𝑧) velocity for our problem are given in Table 3 For the purpose of simulation, the true asteroid splitting parameters needed to be chosen.…”