Tag Archives: Ukf

Improving EKF and UKF when diverse precision sensors are used for localization through adaptive covariances

April 3, 2024 12:43 ,

Giseo Park, Optimal vehicle position estimation using adaptive unscented Kalman filter based on sensor fusion, Mechatronics, Volume 99, 2024 DOI: 10.1016/j.mechatronics.2024.103144.

Precise position recognition systems are actively used in various automotive technology fields such as autonomous vehicles, intelligent transportation systems, and vehicle driving safety systems. In line with this demand, this paper proposes a new vehicle position estimation algorithm based on sensor fusion between low-cost standalone global positioning system (GPS) and inertial measurement unit (IMU) sensors. In order to estimate accurate vehicle position information using two complementary sensor types, adaptive unscented Kalman filter (AUKF), an optimal state estimation algorithm, is applied to the vehicle kinematic model. Since this AUKF includes an adaptive covariance matrix whose value changes under GPS outage conditions, it has high estimation robustness even if the accuracy of the GPS measurement signal is low. Through comparison of estimation errors with both extended Kalman filter (EKF) and UKF, which are widely used state estimation algorithms, it can be confirmed how improved the estimation performance of the proposed AUKF algorithm in real-vehicle experiments is. The given test course includes roads of various shapes as well as GPS outage sections, so it is suitable for evaluating vehicle position estimation performance.

Posted in: Mobile Robot Localization , Tagged: ,

A measure of when and how much the UKF is better than the EKF

June 29, 2023 09:42 ,

Sanat K. Biswas, Li Qiao, Andrew G. Dempster, A quantified approach of predicting suitability of using the Unscented Kalman Filter in a non-linear application, . Automatica, Volume 122, 2020, DOI: 10.1016/j.automatica.2020.109241.

A mathematical framework to predict the Unscented Kalman Filter (UKF) performance improvement relative to the Extended Kalman Filter (EKF) using a quantitative measure of non-linearity is presented. It is also shown that the range of performance improvement the UKF can attain, for a given minimum probability depends on the Non-linearity Indices of the corresponding system and measurement models. Three distinct non-linear estimation problems are examined to verify these relations. A launch vehicle trajectory estimation problem, a satellite orbit estimation problem and a re-entry vehicle position estimation problem are examined to verify these relations. Using these relations, a procedure is suggested to predict the estimation performance improvement offered by the UKF relative to the EKF for a given non-linear system and measurement without designing, implementing and tuning the two Kalman Filters.

Posted in: Bayesian filtering , Tagged: ,

Comparison of EKF and UKF for robot localization and a method of selection of a subset of the available sonar sensors

October 5, 2015 09:27 ,

Luigi D’Alfonso, Walter Lucia, Pietro Muraca, Paolo Pugliese, Mobile robot localization via EKF and UKF: A comparison based on real data, Robotics and Autonomous Systems, Volume 74, Part A, December 2015, Pages 122-127, ISSN 0921-8890, DOI: 10.1016/j.robot.2015.07.007.

In this work we compare the performance of two well known filters for nonlinear models, the Extended Kalman Filter and the Unscented Kalman Filter, in estimating the position and orientation of a mobile robot. The two filters fuse the measurements taken by ultrasonic sensors located onboard the robot. The experimental results on real data show a substantial equivalence of the two filters, although in principle the approximating properties of the UKF are much better. A switching sensors activation policy is also devised, which allows to obtain an accurate estimate of the robot state using only a fraction of the available sensors, with a relevant saving of battery power.

Posted in: Mobile Robot Localization , Tagged: , , , ,

A clarification and systematization of UKF

October 2, 2015 15:37 ,

Menegaz, H.M.T.; Ishihara, J.Y.; Borges, G.A.; Vargas, A.N., A Systematization of the Unscented Kalman Filter Theory, in Automatic Control, IEEE Transactions on , vol.60, no.10, pp.2583-2598, Oct. 2015 DOI: 10.1109/TAC.2015.2404511.

In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF’s in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF). Inconsistencies are related to 1) matching the order of the transformed covariance and cross-covariance matrices of both the UT and the SUT; 2) multiple UKF definitions; 3) issue with some reduced sets of sigma points described in the literature; 4) the conservativeness of the SUT; 5) the scaling effect of the SUT on both its transformed covariance and cross-covariance matrices; and 6) possibly ill-conditioned results in SRUKF’s. With the proposed systematization, the symmetric sets of sigma points in the literature are formally justified, and we are able to provide new consistent variations for UKF’s, such as the Scaled SRUKF’s and the UKF’s composed by the minimum number of sigma points. Furthermore, our proposed SRUKF has improved computational properties when compared to state-of-the-art methods.

Posted in: Bayesian filtering , Tagged: , ,