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.

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.

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.

scholarly journals A Unification of Ensemble Square Root Kalman Filters

2012 ◽  
Vol 140 (7) ◽  
pp. 2335-2345 ◽  
Author(s):  
Lars Nerger ◽  
Tijana Janjić ◽  
Jens Schröter ◽  
Wolfgang Hiller
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Numerical Experiments ◽  
Computational Cost ◽  
Square Root ◽  
Symmetric Square ◽  
Ensemble Transform Kalman Filter ◽  
Filter Algorithms ◽  
Ensemble Transform

Abstract In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular “evolutive” interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

scholarly journals Direct Torque Control of Sensorless Induction Machine Drives: A Two-Stage Kalman Filter Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Jinliang Zhang ◽  
Longyun Kang ◽  
Lingyu Chen ◽  
Boyu Yi ◽  
Zhihui Xu
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Computational Cost ◽  
Direct Torque Control ◽  
Induction Machine ◽  
Torque Control ◽  
Two Stage ◽  
Torque Estimation ◽  
Filter Approach ◽  
Stator Flux

Extended Kalman filter (EKF) has been widely applied for sensorless direct torque control (DTC) in induction machines (IMs). One key problem associated with EKF is that the estimator suffers from computational burden and numerical problems resulting from high order mathematical models. To reduce the computational cost, a two-stage extended Kalman filter (TEKF) based solution is presented for closed-loop stator flux, speed, and torque estimation of IM to achieve sensorless DTC-SVM operations in this paper. The novel observer can be similarly derived as the optimal two-stage Kalman filter (TKF) which has been proposed by several researchers. Compared to a straightforward implementation of a conventional EKF, the TEKF estimator can reduce the number of arithmetic operations. Simulation and experimental results verify the performance of the proposed TEKF estimator for DTC of IMs.

scholarly journals ESPEE: Event-Based Sensor Pose Estimation Using an Extended Kalman Filter

Sensors ◽  
2021 ◽  
Vol 21 (23) ◽  
pp. 7840
Author(s):  
Fabien Colonnier ◽  
Luca Della Vedova ◽  
Garrick Orchard
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Pose Estimation ◽  
Computational Cost ◽  
Great Promise ◽  
Low Latency ◽  
Worst Case ◽  
Mapping Algorithm ◽  
Multiple Sensors ◽  
Event Based

Event-based vision sensors show great promise for use in embedded applications requiring low-latency passive sensing at a low computational cost. In this paper, we present an event-based algorithm that relies on an Extended Kalman Filter for 6-Degree of Freedom sensor pose estimation. The algorithm updates the sensor pose event-by-event with low latency (worst case of less than 2 μs on an FPGA). Using a single handheld sensor, we test the algorithm on multiple recordings, ranging from a high contrast printed planar scene to a more natural scene consisting of objects viewed from above. The pose is accurately estimated under rapid motions, up to 2.7 m/s. Thereafter, an extension to multiple sensors is described and tested, highlighting the improved performance of such a setup, as well as the integration with an off-the-shelf mapping algorithm to allow point cloud updates with a 3D scene and enhance the potential applications of this visual odometry solution.

scholarly journals State Estimation of Common Emitter Amplifier using Iterated Extended Kalman Filters

2019 ◽  
Vol 8 (9) ◽  
pp. 1784-1789
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
Signal To Noise Ratio ◽  
State Space Model ◽  
Large Signal ◽  
Extended Kalman Filters ◽  
Bipolar Junction Transistor ◽  
Junction Transistor ◽  
Transistor Model

This paper presents the output voltage estimation of bipolar junction transistor (BJT) common emitter (CE) using iterated extended Kalman filter (IEKF). For this, state space model has been derived using Kirchhoff's current law (KCL) and Ebers-Moll model of the transistor. The performance of IEKF has been compared with extended Kalman filter (EKF). The simulation results show large signal to noise ratio (SNR) and small root mean square error (RMSE) using IEKF as compared to EKF, as IEKF considers the error due to linearization. The advantage of the proposed method is that the derived extended state space equation can be used for parameter estimation of both, the transistor state and transistor parameters as the derivation includes transistor model

CALIBRATION OF MULTIFACTOR MODELS IN ELECTRICITY MARKETS

2004 ◽  
Vol 07 (02) ◽  
pp. 101-120 ◽  
Author(s):  
MARTIN BARLOW ◽  
YURI GUSEV ◽  
MANPO LAI
Keyword(s):  
Kalman Filter ◽  
Stochastic Processes ◽  
Extended Kalman Filter ◽  
Electricity Markets ◽  
Kalman Filters ◽  
Historical Data ◽  
Spot Price ◽  
Market Data ◽  
Multifactor Models ◽  
Spot Prices

Spot prices of electricity and other energy commodities are often modeled by multifactor stochastic processes. This poses a problem of estimating models' parameters based on historical data, i.e. calibrating them to markets. Here we show how a traditional tool of Kalman Filters can be successfuly applied to do this task. We study two mean-reverting log-spot price models and the Pilipovic model using correspondingly Kalman Filter the extended Kalman Filter. The results of applying this method to market data from several power exchanges are discussed.

scholarly journals Incorporating neuro-fuzzy with extended Kalman filter for simultaneous localization and mapping

2019 ◽  
Vol 16 (5) ◽  
pp. 172988141987464 ◽  
Author(s):  
Cong Hung Do ◽  
Huei-Yung Lin
Keyword(s):  
Kalman Filter ◽  
Mobile Robot ◽  
Extended Kalman Filter ◽  
Optimization Technique ◽  
Computational Cost ◽  
Simultaneous Localization And Mapping ◽  
Mobile Robot Navigation ◽  
Filter Technique ◽  
Localization And Mapping ◽  
Neuro Fuzzy

Extended Kalman filter is well-known as a popular solution to the simultaneous localization and mapping problem for mobile robot platforms or vehicles. In this article, the development of a neuro-fuzzy-based adaptive extended Kalman filter technique is presented. The objective is to estimate the proper values of the R matrix at each step. We design an adaptive neuro-fuzzy extended Kalman filter to minimize the difference between the actual and theoretical covariance matrices of the innovation consequence. The parameters of the adaptive neuro-fuzzy extended Kalman filter is then trained offline using a particle swarm optimization technique. With this approach, the advantages of high-dimensional search space can be exploited and more effective training can be achieved. In the experiments, the mobile robot navigation with a number of landmarks under two benchmark situations is evaluated. The results have demonstrated that the proposed adaptive neuro-fuzzy extended Kalman filter technique provides the improvement in both performance efficiency and computational cost.

scholarly journals ISOGEOMETRIC COLLOCATION METHODS

2010 ◽  
Vol 20 (11) ◽  
pp. 2075-2107 ◽  
Author(s):  
F. AURICCHIO ◽  
L. BEIRÃO DA VEIGA ◽  
T. J. R. HUGHES ◽  
A. REALI ◽  
G. SANGALLI
Keyword(s):  
Theoretical Analysis ◽  
Isogeometric Analysis ◽  
Computational Cost ◽  
Basis Functions ◽  
Three Dimensions ◽  
Collocation Methods ◽  
One Dimensional ◽  
Numerical Tests ◽  
Low Computational Cost ◽  
Theoretical Results

We initiate the study of collocation methods for NURBS-based isogeometric analysis. The idea is to connect the superior accuracy and smoothness of NURBS basis functions with the low computational cost of collocation. We develop a one-dimensional theoretical analysis, and perform numerical tests in one, two and three dimensions. The numerical results obtained confirm theoretical results and illustrate the potential of the methodology.

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