Tag Archives: Ekf

A possibly interesting paper on the estimation and adaptation of EKF-SLAM to actual models of the system and the noise that I have been unable to read due to its painful syntax

Yingzhong Tian, Heru Suwoyo, Wenbin Wang, Dziki Mbemba, Long Li, An AEKF-SLAM Algorithm with Recursive Noise Statistic Based on MLE and EM, Journal of Intelligent & Robotic Systems (2020) 97:339–355, DOI: 10.1007/s10846-019-01044-8.

Extended Kalman Filter (EKF) has been popularly utilized for solving Simultaneous Localization and Mapping (SLAM)
problem. Essentially, it requires the accurate system model and known noise statistic. Nevertheless, this condition can
be satisfied in simulation case. Hence, EKF has to be enhanced when it is applied in the real-application. Mainly, this
improvement is known as adaptive-based approach. In many different cases, it is indicated by some manners of estimating
for either part or full noise statistic. This paper present a proposed method based on the adaptive-based solution used for
improving classical EKF namely An Adaptive Extended Kalman Filter. Initially, the classical EKF was improved based on
Maximum Likelihood Estimation (MLE) and Expectation-Maximization (EM) Creation. It aims to equips the conventional
EKF with ability of approximating noise statistic and its covariance matrices recursively. Moreover, EKF was modified and
improved to tune the estimated values given by MLE and EM creation. Besides that, the recursive noise statistic estimators
were also estimated based on the unbiased estimation. Although it results high quality solution but it is followed with some
risks of non-positive definite matrices of the process and measurement noise statistic covariances. Thus, an addition of
Innovation Covariance Estimation (ICE) was also utilized to depress this possibilities. The proposed method is applied for
solving SLAM problem of autonomous wheeled mobile robot. Henceforth, it is termed as AEKF-SLAM Algorithm. In order
to validate the effectiveness of proposed method, some different SLAM-Based algorithm were compared and analyzed.
The different simulation has been showing that the proposed method has better stability and accuracy compared to the
conventional filter in term of Root Mean Square Error (RMSE) of Estimated Map Coordinate (EMC) and Estimated Path
Coordinate (EPC).

Using EKF estimation in a PI controller for improving its performance under noise

Y. Zhou, Q. Zhang, H. Wang, P. Zhou and T. Chai, EKF-Based Enhanced Performance Controller Design for Nonlinear Stochastic Systems, IEEE Transactions on Automatic Control, vol. 63, no. 4, pp. 1155-1162, DOI: 10.1109/TAC.2017.2742661.

In this paper, a novel control algorithm is presented to enhance the performance of the tracking property for a class of nonlinear and dynamic stochastic systems subjected to non-Gaussian noises. Although the existing standard PI controller can be used to obtain the basic tracking of the systems, the desired tracking performance of the stochastic systems is difficult to achieve due to the random noises. To improve the tracking performance, an enhanced performance loop is constructed using the EKF-based state estimates without changing the existing closed loop with a PI controller. Meanwhile, the gain of the enhanced performance loop can be obtained based upon the entropy optimization of the tracking error. In addition, the stability of the closed loop system is analyzed in the mean-square sense. The simulation results are given to illustrate the effectiveness of the proposed control algorithm.

A new method for estimating inertial sensor signals

M. Ghobadi, P. Singla and E. T. Esfahani, Robust Attitude Estimation from Uncertain Observations of Inertial Sensors Using Covariance Inflated Multiplicative Extended Kalman Filter, IEEE Transactions on Instrumentation and Measurement, vol. 67, no. 1, pp. 209-217, DOI: 10.1109/TIM.2017.2761230.

This paper presents an attitude estimation method from uncertain observations of inertial sensors, which is highly robust against different uncertainties. The proposed method of covariance inflated multiplicative extended Kalman filter (CI-MEKF) takes the advantage of non-singularity of covariance in MEKF as well as a novel covariance inflation (CI) approach to fuse inconsistent information. The proposed CI approach compensates the undesired effect of magnetic distortion and body acceleration (as inherent biases of magnetometer and accelerometer sensors data, respectively) on the estimated attitude. Moreover, the CI-MEKF can accurately estimate the gyro bias. A number of simulation scenarios are designed to compare the performance of the proposed method with the state of the art in attitude estimation. The results show the proposed method outperforms the state of the art in terms of estimation accuracy and robustness. Moreover, the proposed CI-MEKF method is shown to be significantly robust against different uncertainties, such as large body acceleration, magnetic distortion, and errors, in the initial condition of the attitude.

Using EKF to estimate the state of a quadcopter in SE(3)

Goodarzi, F.A. & Lee, Global Formulation of an Extended Kalman Filter on SE(3) for Geometric Control of a Quadrotor UAV, J Intell Robot Syst (2017) 88: 395, DOI: 10.1007/s10846-017-0525-6.

An extended Kalman filter (EKF) is developed on the special Euclidean group, S E(3) for geometric control of a quadrotor UAV. It is obtained by performing an intrinsic form of linearization on S E(3) to estimate the state of the quadrotor from noisy measurements. The proposed estimator considers all of the coupling effects between rotational and translational dynamics, and it is developed in a coordinate-free fashion. The desirable features of the proposed EKF are illustrated by numerical examples and experimental results for several scenarios. The proposed estimation scheme on S E(3) has been unprecedented and these results can be particularly useful for aggressive maneuvers in GPS denied environments or in situations where parts of onboard sensors fail.

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

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.