scholarly journals Extended Kalman Filter with Reduced Computational Demands for Systems with Non-Linear Measurement Models

Sensors ◽  
2020 ◽  
Vol 20 (6) ◽  
pp. 1584 ◽  
Author(s):  
Piotr Kaniewski
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Kalman Filters ◽  
Linear Measurement ◽  
Linear Functions ◽  
Estimation Errors ◽  
Extended Kalman Filters ◽  
Measurement Models ◽  
Non Linear ◽  
Model Linearization

The paper presents a method of computational complexity reduction in Extended Kalman Filters dedicated for systems with non-linear measurement models. Extended Kalman filters are commonly used in radio-location and radio-navigation for estimating an object’s position and other parameters of motion, based on measurements, which are non-linearly related to the object’s position. This non-linearity forces designers to use non-linear filters, such as the Extended Kalman Filter mentioned, where linearization of the system’s model is performed in every run of the filter’s loop. The linearization, consisting of calculating Jacobian matrices for non-linear functions in the dynamics and/or observation models, significantly increases the number of operations in comparison to the linear Kalman filter. The method proposed in this paper consists of analyzing a variability of Jacobians and performing the model linearization only when expected changes of those Jacobians exceed a preset threshold. With a properly chosen threshold value, the proposed filter modification leads to a significant reduction of its computational burden and does not noticeably increase its estimation errors. The paper describes a practical simulation-based method of determining the threshold. The accuracy of the filter for various threshold values was tested for simplified models of radar systems.

scholarly journals Non-Linear Filtering for Precise Point Positioning GPS/INS integration

2014 ◽  
Vol XL-2 ◽  
pp. 127-132 ◽  
Author(s):  
M. Abd Rabbou ◽  
A. El-Rabbany
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Unscented Kalman Filter ◽  
Test Scenario ◽  
Linear Filters ◽  
Phase Measurements ◽  
Measurement Models ◽  
Nonlinear Motion ◽  
Non Linear ◽  
Tightly Coupled

This research investigates the performance of non-linear estimation filtering for GPS-PPP/MEMS-based inertial system. Although integrated GPS/INS system involves nonlinear motion state and measurement models, the most common estimation filter employed is extended Kalman filter. In this paper, both unscented Kalman filter and particle filter are developed and compared with extended Kalman filter. Tightly coupled mechanization is adopted, which is developed in the raw measurements domain. Un-differenced ionosphere-free linear combination of pseudorange and carrier-phase measurements is employed. The performance of the proposed non-linear filters is analyzed using real test scenario. The test results indicate that comparable accuracy-level are obtained from the proposed filters compared with extended Kalman filter in positioning, velocity and attitude when the measurement updates from GPS measurements are available.

Transversely Stable Extended Kalman Filters for Systems on Manifolds in Euclidean Spaces

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Jae-Hyeon Park ◽  
Karmvir Singh Phogat ◽  
Whimin Kim ◽  
Dong Eui Chang
Keyword(s):  
Kalman Filter ◽  
Euclidean Space ◽  
Extended Kalman Filter ◽  
Kalman Filters ◽  
Computational Cost ◽  
Three Dimensions ◽  
Extended Kalman Filters ◽  
Body Attitude ◽  
Open Set ◽  
Low Computational Cost

Abstract In this article, we devise a variant of the extended Kalman filter that can be generally applied to systems on manifolds with simplicity and low computational cost. We extend a given system on a manifold to an ambient open set in Euclidean space and modify the system such that the extended system is transversely stable on the manifold. Then, we apply the standard extended Kalman filter derived in Euclidean space to the modified dynamics. This method is efficient in terms of computation and accurate in comparison with the standard extended Kalman filter. It has the merit that we can apply various Kalman filters derived in Euclidean space including extended Kalman filters for state estimation for systems defined on manifolds. The proposed method is successfully applied to the rigid body attitude dynamics whose configuration space is the special orthogonal group in three dimensions.

Application of Linear Observers to Estimate States of a Roll Simulator

2014 ◽  
Author(s):  
Scott B. Zagorski ◽  
Gary J. Heydinger ◽  
Dennis A. Guenther
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Kalman Filters ◽  
Disturbance Observer ◽  
Gain Scheduling ◽  
System Parameters ◽  
Scheduling Scheme

In this research, a variety of Kalman Filters are implemented in an effort to estimate sled speed of a Roll Simulator. An Extended Kalman Filter (EKF) is incorporated to capture the nonlinear dynamics of the sled-platform assembly to estimate sled speed for the entire motion, as a linear Kalman Filter was found to be inadequate. When applied to experimental data, the EKF over-estimates sled speed, which is due to a disturbance force and/or uncertainty in system parameters. In combination with the disturbance observer, the Kalman Filter adequately estimates sled speed for experimental data. For lower speed/payload applications, a Kalman Filter using an accelerometer and measured drum speed is able to accurately track sled speed when a gain scheduling scheme is employed.

Autonomous Aerial Refueling for UAVs Based on GPS/MV

2012 ◽  
Vol 433-440 ◽  
pp. 4087-4094 ◽  
Author(s):  
Long Wang ◽  
Xin Min Dong ◽  
Jun Guo ◽  
Hai Yan Jia
Keyword(s):  
Kalman Filter ◽  
Machine Vision ◽  
Extended Kalman Filter ◽  
Reference Trajectory ◽  
Sensor Failure ◽  
Aerial Refueling ◽  
Control Laws ◽  
Measurement Models ◽  
Simulation Results ◽  
Docking Control

According to the UAV autonomous aerial refueling based on GPS/Machine Vision integration, the restrictions on the sensors during docking are analyzed. An adaptive Federal Kalman Filter (AFKF) is proposed, which is based on extended Kalman filter arithmetic, after modeling the sensors measurement models. Reference trajectory of docking is planed using cubic interpolators and docking control laws are designed with LQR. Simulation results show that the controller ensure the stabilized tracking and docking, and the AFKF outputs is continuous and stabilized during sensor failure comparing to centralize Kalman filter.

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