M-estimator based robust unscented Kalman filter through statistical linearization

2018 ◽  
Vol 41 (7) ◽  
pp. 2016-2025 ◽  
Author(s):  
Guobin Chang ◽  
Tianhe Xu ◽  
Haitao Wang
Keyword(s):  
Kalman Filter ◽  
Gaussian Distribution ◽  
Unscented Kalman Filter ◽  
Weighted Least Squares ◽  
Point Of View ◽  
Tuning Parameter ◽  
Statistical Linearization ◽  
Unscented Transformation ◽  
Actual Distribution ◽  
M Estimator

The robust unscented Kalman filter (UKF) is revisited in this paper from a new point of view, namely the statistical linear regression (SLR) perspective of the unscented transformation (UT). When the actual distribution of the observation noise deviates from the assumed Gaussian distribution, the performance of the filter may degrade significantly owing to lacking robustness. After linearizing the nonlinear observation equation using the SLR perspective, the M-estimator is employed to replace the weighted least-squares one, resulting in the robust UKF. Besides providing new theoretical aspects, the advantageous performance of the proposed filter is re-emphasized in terms of the following three: (1) robust, the proposed filter is robust against deviations from the assumed Gaussian distribution; (2) efficient, by elaborately selecting the tuning parameter of the M-estimator, the robust filter will have a slight efficiency loss compared with the UKF when the Gaussian assumption does hold; (3) accurate, the proposed filter achieves robustness without compromising the accuracy of the UT.

scholarly journals Performance Evaluation of GPS Auto-Surveying Techniques

Sensors ◽  
2021 ◽  
Vol 21 (21) ◽  
pp. 7374
Author(s):  
João Manito ◽  
José Sanguino
Keyword(s):  
Kalman Filter ◽  
Least Squares ◽  
Unscented Kalman Filter ◽  
Weighted Least Squares ◽  
Base Station ◽  
Global Navigation Satellite Systems ◽  
Precise Position ◽  
Satellite Systems ◽  
Global Navigation Satellite ◽  
Position Estimate

With the increase in the widespread use of Global Navigation Satellite Systems (GNSS), increasing numbers of applications require precise position data. Of all the GNSS positioning methods, the most precise are those that are based in differential systems, such as Differential GNSS (DGNSS) and Real-Time Kinematics (RTK). However, for absolute positioning, the precision of these methods is tied to their reference position estimates. With the goal of quickly auto-surveying the position of a base station receiver, four positioning methods are analyzed and compared, namely Least Squares (LS), Weighted Least Squares (WLS), Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), using only pseudorange measurements, as well as the Hatch Filter and position thresholding. The research results show that the EKF and UKF present much better mean errors than LS and WLS, with an attained precision below 1 m after about 4 h of auto-surveying. The methods that presented the best results are then tested against existing implementations, showing them to be very competitive, especially considering the differences between the used receivers. Finally, these results are used in a DGNSS test, which verifies a significant improvement in the position estimate as the base station position estimate improves.

scholarly journals The Nonsequential Fusion Method for Localization from Unscented Kalman Filter by Multistation Array Buoys

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Gou Yanni ◽  
Wang Qi
Keyword(s):  
Kalman Filter ◽  
Nonlinear Filtering ◽  
Target Location ◽  
Unscented Kalman Filter ◽  
Research Field ◽  
Measuring Error ◽  
Engineering Practice ◽  
Relevant Parameter ◽  
Unscented Transformation ◽  
Target Track

Based on special features of array buoy and the research field of location and tracking of underwater target, the research combines the highly adaptive nonlinear filtering algorithm unscented Kalman filter with the nonlinear programming of multistation array buoy positioning system. In accordance with the model of nonsequential target location, the research utilizes Unscented Transformation to update the measuring error and covariance matrix of state error, aiming at estimating the filtering of state variable and acquiring the object’s current state of motion. The research analyzes the positioning performance of algorithm, pursuit path, astringency, and other performance indexes of target-relevant parameter through numerical simulation experiment. From the result, the conclusion that multistation array buoy can complete the task of tracing target track very well can be reached, which provides theoretical foundation for putting the algorithm into engineering practice.

scholarly journals A Discussion Related to Orbit Determination Using Nonlinear Sigma Point Kalman Filter

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Paula Cristiane Pinto Mesquita Pardal ◽  
Helio Koiti Kuga ◽  
Rodolpho Vilhena de Moraes
Keyword(s):  
Kalman Filter ◽  
Dynamic Model ◽  
Extended Kalman Filter ◽  
Orbit Determination ◽  
Unscented Kalman Filter ◽  
Satellite Orbit ◽  
Observation Model ◽  
Gps Measurements ◽  
Unscented Transformation ◽  
Sigma Point

Herein, the purpose is to present a Kalman filter based on the sigma point unscented transformation development, aiming at real-time satellite orbit determination using GPS measurements. First, a brief review of the extended Kalman filter will be done. After, the sigma point Kalman filter will be introduced as well as the basic idea of the unscented transformation, in which this filter is based. Following, the unscented Kalman filter applied to orbit determination will be explained. Such explanation encloses formulations about the orbit determination through GPS; the dynamic model; the observation model; the unmodeled acceleration estimation; also an application of this new filter approaches on orbit determination using GPS measurements discussion.

scholarly journals CONDITION MONITORING IN A HYDRAULIC SYSTEM OF AN INDUSTRIAL MACHINE USING UNSCENTED KALMAN FILTER

2010 ◽  
Vol 07 (03) ◽  
pp. 177-192 ◽  
Author(s):  
BEHNAM RAZAVI ◽  
CLARENCE W. DE SILVA
Keyword(s):  
Kalman Filter ◽  
Condition Monitoring ◽  
Hydraulic System ◽  
Unscented Kalman Filter ◽  
Moving Average ◽  
Hydraulic Cylinder ◽  
Minimal Set ◽  
Unscented Transformation ◽  
On Line ◽  
The Mean

This paper develops a model-based technique based on the Unscented Kalman Filter (UKF) for on-line condition monitoring, and applies it to the hydraulic system of an automated industrial fish processing machine. First an analytical model of the hydraulic system is developed and the system parameters are identified (determined). Then the developed UKF approach is implemented in the machine. The UKF employs an unscented transformation to select a minimal set of sample points around the mean, which are then propagated through nonlinear functions, from which the mean and covariance of the estimate are recovered. This approach is known to be more accurate for nonlinear systems. For experimental investigation of the performance of the approach, four common hydraulic faults are deliberately introduced into the machine. The four faults are external leakage in the two chambers of the hydraulic cylinder; internal leakage; and dry friction build-up at the moving support plate of the cutter carriage. Three levels of leakage are manually introduced to the system for each fault scenario using needle valves. The criteria that are considered in fault diagnosing are residual moving average of the errors, chamber pressures, and actuator characteristics. The experimental results show that the developed technique is able to accurately determine the fault conditions of the machine.

scholarly journals Continuous Estimation of Speed and Torque of Induction Motors Using the Unscented Kalman Filter under Voltage Sag

DYNA ◽  
2019 ◽  
Vol 86 (208) ◽  
pp. 37-45
Author(s):  
Amin Darvishi ◽  
Aref Doroudi
Keyword(s):  
Kalman Filter ◽  
Induction Motors ◽  
Unscented Kalman Filter ◽  
Rapid Change ◽  
Input Voltage ◽  
Motor Speed ◽  
Unscented Transformation ◽  
Torque Estimation ◽  
State Estimators ◽  
Continuous Estimation

Due to sensor limitations in some applications, induction motors state estimators are widely used in industries. One of the most powerful tools available for estimation is the Kalman filter. In this paper, unscented Kalman filter (UKF) and extended Kalman filter (EKF) is used to estimate the speed and torque of an induction motor. In the UKF algorithm, three types of unscented transformation (UT): basic, general and spherical types are presented and compared. It will be shown that the spherical UKF presents good estimation performance. Speed and torque Estimation approach is applied at both steady state conditions and at the time of sudden and rapid change in the motor input voltage. It will be shown that, EKF cannot trace the motor speed at the time of a large disturbance. Finally, experimental validation is presented to show the effectiveness of UKF for continuous estimation of torque and speed of induction motors.

Hybrid consensus sigma point approximation nonlinear filter using statistical linearization

2018 ◽  
Vol 40 (8) ◽  
pp. 2517-2525 ◽  
Author(s):  
Guoqing Wang ◽  
Ning Li ◽  
Yonggang Zhang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Nonlinear Filter ◽  
Statistical Linearization ◽  
Nonlinear Functions ◽  
Central Difference ◽  
Sigma Point ◽  
Point Approximation ◽  
Cubature Kalman Filter ◽  
Central Difference Kalman Filter

In this paper, a hybrid consensus sigma point approximation nonlinear filter is proposed for state estimation in collaborative sensor network, where hybrid consensus of both measurement and information is utilised. Statistical linearization of nonlinear functions is used in sigma point filters, that is, unscented Kalman filter (UKF), cubature Kalman filter (CKF), and central difference Kalman filter (CDKF). Stability of the proposed algorithm is also analysed with the help of linearization operation and some conservative assumptions. Two typical target tracking examples are used to demonstrate the effectiveness of the proposed algorithms. Simulation results show that the proposed algorithms are more stable than existing algorithms, and among our proposed algorithms, CKF- and CDKF-based algorithms are more accurate and stable than the UKF-based one.

The Unscented Kalman Filter Estimators for High Dynamic Doppler Shift Environments

2012 ◽  
Vol 532-533 ◽  
pp. 1487-1491
Author(s):  
Kun Zhao ◽  
Ke Gang Pan ◽  
Ai Jun Liu ◽  
Dao Xing Guo
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Doppler Shift ◽  
Unscented Kalman Filter ◽  
The State ◽  
Extend Kalman Filter ◽  
Unscented Transformation ◽  
High Dynamic ◽  
Simulation Results ◽  
Dynamic Trajectory

The Extend Kalman Filter (EKF) is widely used in the tracking of high dynamic Doppler shift trajectories, but it has some flows when it is used to estimate the state of nonlinear systems. In this paper, we apply the Unscented Transformation (UT) based Unscented Kalman Filter (UKF) to the state estimation in the high dynamic Doppler environments. Two versions of the UKF estimators, augmented UKF estimator and nonaugemented UKF estimator are designed. To compare the performance of them, they are applied to tracking a common high dynamic trajectory, and simulation results declare that given different conditions, the performance of the estimators will be different.

Power System State Estimation by Novel Approach of Kalman Filter

2017 ◽  
Vol 6 (2) ◽  
pp. 241
Author(s):  
Arpit Khandelwal ◽  
Ankush Tandon ◽  
Akash Saxena
Keyword(s):  
Kalman Filter ◽  
Power System ◽  
State Estimation ◽  
Unscented Kalman Filter ◽  
Test System ◽  
Electrical Network ◽  
Elapse Time ◽  
State Variables ◽  
Measuring Device ◽  
M Estimator

<p>The electrical network measurements by measuring device Phasor Measurement Device (PMU) are usually sent to the control centers using data acquisition system and other communication protocols available. However, these measurements contain uncertainties due to the measurements and communication noise (errors), incomplete metering or unavailability of some of measurements. The overall aim of state estimation is to calculate the state variables of the power system by minimizing errors available at the control center. Due to generate desired quantities by optimal estimate which is given the set of measurements, Kalman filters are widely used. This paper discusses the application of an Extended Kalman Filter (EKF) algorithm, the Unscented Kalman Filter (UKF) algorithm, and New EKF+M and UKF+M estimator algorithm, those are modification of EKF and UKF for enhance accuracy and elapse time is less. The effectiveness and performance of EKF+M and UKF+M Estimator over another Filtration algorithm is shown. These state estimation techniques applied on IEEE-30 bus, 14 bus and 9 bus test system.</p>

Performance Comparison of Static and Dynamic State Estimators for Electric Distribution Systems

2017 ◽  
Vol 18 (3) ◽  
Author(s):  
Fiaz Ahmad ◽  
Muhammad Abdul Kabir Rashid ◽  
Akhtar Rasool ◽  
Eşref Emre Özsoy ◽  
Asif Sabanovic ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Distribution System ◽  
Distribution Systems ◽  
Performance Metrics ◽  
Unscented Kalman Filter ◽  
Weighted Least Squares ◽  
Distribution Networks ◽  
Dynamic State ◽  
State Estimators ◽  
Electric Distribution

AbstractState estimation is an integral component of energy management systems used for the monitoring and control of operation of transmission networks worldwide. However, it has so far not yet been widely adopted in the distribution networks due to their passive nature with no active generation. But this scenario is challenged by the integration of distributed generators (DGs) at this level. Various static and dynamic state estimators have been researched for the transmission systems. These cannot be directly applied to the distribution systems due to their different philosophy of operation. Thus the performance of these estimators need to be re-evaluated for the distribution systems. This paper presents a computational and statistical performance of famous static estimator such as weighted least squares (WLS) and dynamic state estimators such as extended Kalman filter (EKF) and unscented Kalman filter (UKF) for electric distribution system. Additionally, an improved-UKF (IUKF) is also proposed which enhances the robustness and numerical stability of the existing UKF algorithm. All the estimators are tested for load variation and bad data for IEEE-30, 33 and 69 bus radial distribution networks using statistical performance metrics such as Maximum Absolute Deviation (MAD), Maximum Absolute Percent Error (MAPE), Root Mean Square Error (RMSE) and Overall Performance index (J). Based on these metrics, IUKF outperforms other estimators under the simulated noisy measurement conditions.

Sign in / Sign up

Export Citation Format

Share Document