Invariant Kalman Filtering

2018 ◽  
Vol 1 (1) ◽  
pp. 237-257 ◽  
Author(s):  
Axel Barrau ◽  
Silvère Bonnabel
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Autonomous Vehicle ◽  
Autonomous Systems ◽  
Practical Application ◽  
Extended Kalman Filtering ◽  
Industrial Implementation ◽  
Localization And Mapping ◽  
And Robotics ◽  
Insight Into

The Kalman filter—or, more precisely, the extended Kalman filter (EKF)—is a fundamental engineering tool that is pervasively used in control and robotics and for various estimation tasks in autonomous systems. The recently developed field of invariant extended Kalman filtering uses the geometric structure of the state space and the dynamics to improve the EKF, notably in terms of mathematical guarantees. The methodology essentially applies in the fields of localization, navigation, and simultaneous localization and mapping (SLAM). Although it was created only recently, its remarkable robustness properties have already motivated a real industrial implementation in the aerospace field. This review aims to provide an accessible introduction to the methodology of invariant Kalman filtering and to allow readers to gain insight into the relevance of the method as well as its important differences with the conventional EKF. This should be of interest to readers intrigued by the practical application of mathematical theories and those interested in finding robust, simple-to-implement filters for localization, navigation, and SLAM, notably for autonomous vehicle guidance.

scholarly journals Kalman Filtering Applied to Induction Motor State Estimation

2020 ◽  
Author(s):  
Yassine Zahraoui ◽  
Mohamed Akherraz
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Induction Motor ◽  
Kalman Filtering ◽  
Speed Estimation ◽  
Stochastic Algorithm ◽  
State Variables ◽  
Extended Kalman Filtering ◽  
Filtering Theory ◽  
State Observation

This chapter presents a full definition and explanation of Kalman filtering theory, precisely the filter stochastic algorithm. After the definition, a concrete example of application is explained. The simulated example concerns an extended Kalman filter applied to machine state and speed estimation. A full observation of an induction motor state variables and mechanical speed will be presented and discussed in details. A comparison between extended Kalman filtering and adaptive Luenberger state observation will be highlighted and discussed in detail with many figures. In conclusion, the chapter is ended by listing the Kalman filtering main advantages and recent advances in the scientific literature.

SYNCHRONIZATION THROUGH FILTERING

2000 ◽  
Vol 10 (04) ◽  
pp. 763-775 ◽  
Author(s):  
C. CRUZ ◽  
H. NIJMEIJER
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Private Communication ◽  
Extended Kalman Filtering ◽  
Extensive Simulation ◽  
Synchronization Problem

We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an EKF that is driven by a noisy drive signal from a noisy transmitter dynamics. The convergence of the filter dynamics towards the transmitter dynamics is rigorously shown using recent results in extended Kalman filtering. Two extensive simulation examples show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to private communication is also given.

scholarly journals Extended Kalman filter approach to electric arc furnace forecasting

2021 ◽  
Author(s):  
Ali Hosseignholizadeh
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Kalman Filtering ◽  
Past History ◽  
Multivariate Time Series ◽  
Arc Furnace ◽  
Extended Kalman Filtering ◽  
History Of ◽  
Auto Regressive ◽  
Filter Approach

In this thesis, we propose and implement a new approach for building an online self-adjusting model for prediction of v-i characteristic of a multivariate time series obtained from an operational electrical arc furnace. The proposed methodology is based on the Kalman filtering method, and is used for prediction of the arc furnace voltage using the past history of the current and voltage. The main advantage of the proposed approach over similar earlier related work is the ability to adapt during the operation of the furnace. In this study, three different hybrid models have been developed based on the extended Kalman filtering technique and one of the following methodologies: (i) a linar auto regressive model; (ii) fuzzy logic, (iii) wavelet analysis. The results compare well with those of earlier work and clearly indicate that the augmentation of the above mentioned approaches with the extended Kalman filter improves the prediction accuracy.

A Kalman Filtering Mechanism Based on Generalized Interval Probability and its Application in Process Variation Estimation

2014 ◽  
Author(s):  
Jie Hu ◽  
Yan Wang ◽  
Aiguo Cheng ◽  
Zhihua Zhong
Keyword(s):  
Kalman Filter ◽  
Systematic Error ◽  
Kalman Filtering ◽  
Extended Kalman Filtering ◽  
Interval Probability ◽  
State Identification ◽  
Random Intervals ◽  
Controllable Systems ◽  
Special Case

The Kalman filter has been widely applied for state identification in controllable systems. As a special case of hidden Markov model, it is based on the assumption of linear dependency relationships and Gaussian noises. The classical Kalman filter does not differentiate systematic error from random error associated with observations. In this paper, we propose an extended Kalman filtering mechanism based on generalized interval probability, where systematic error is represented by intervals, state and observable variables are random intervals, and interval-valued Gaussian distributions model the noises. The prediction and update procedures in the new mechanism are derived. A case study of auto-body side frame assembly is used to illustrate the developed mechanism.

Slow On-Off Control of Two-State Damping for Electrically Controlled Air Suspension Based on Extended Kalman Filter

2010 ◽  
Vol 39 ◽  
pp. 504-509
Author(s):  
Xing Xu ◽  
Zhong Xin Li ◽  
Qi Yao Yang ◽  
Chao Feng Pan
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Kalman Filtering ◽  
Shock Absorber ◽  
Extended Kalman Filtering ◽  
Air Suspension ◽  
Nonlinear Character ◽  
Opening And Closing ◽  
Vehicle Testing ◽  
Speed Simulation

To improve riding performance of the bus with air suspension, the half-car nonlinear model of air suspension was created with the help of analyzing nonlinear character of spring-pneumatic. Slow on-off control of two-state damping was proposed according to the tire deformation and suspension deflection, and the shock absorber with two-state damping was designed by opening and closing the orifice of throttle. It was difficult to obtain the tire deformation directly, and the state-observer of air suspension was proposed based on Extended Kalman Filtering (EKF) algorithm, namely the tire deformation was estimated by the suspension deflection and its relative changing speed. Simulation shows EKF algorithm can estimate the running states well, and the estimating error of RMS is below 10% in 3 seconds and the whole vehicle testing validate that the slow on-off control can enhance the capability of air suspension.

scholarly journals COMPARISON OF GPS SMOOTHENING METHODS BETWEEN EXTENDED KALMAN FILTER AND PARTICLE FILTER FOR UAV

2017 ◽  
Keyword(s):  
Numerical Simulation ◽  
Kalman Filter ◽  
Particle Filter ◽  
Extended Kalman Filter ◽  
Kalman Filtering ◽  
Particle Filtering ◽  
State Vector ◽  
The State ◽  
Gps Data ◽  
Extended Kalman Filtering

This paper presents a method for smoothing GPS data from a UAV using Extended Kalman filtering and particle filtering for navigation or position control. A key requirement for navigation and control of any autonomous flying or moving robot is availability of a robust attitude estimate. Consider a dynamic system such as a moving robot. The unknown parameters, e.g., the coordinates and the velocity, form the state vector. This time dependent vector may be predicted for any instant time by means of system equations. The predicted values can be improved or updated by observations containing information on some components of the state vector. The whole procedure is known as Kalman filtering. On the other hand, the particle filtering algorithm is to perform a recursive Bayesian filter by Monte Carlo simulations. The key is to represent the required posterior density function by a set of random samples, which is called particles with associated weights, and to compute estimates based on these samples as well as weights. We compare the two GPS smoothening methods: Extended Kalman Filter and Particle Filter for mobile robots applications. Validity of the smoothing methods is verified from the numerical simulation and the experiments. The numerical simulation and experimental results show the good GPS data smoothing performance using Extended Kalman filtering and particle filtering.

scholarly journals Observer Design for Nonlinear Systems with Equivariance

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Robert Mahony ◽  
Pieter van Goor ◽  
Tarek Hamel
Keyword(s):  
State Space ◽  
Kalman Filtering ◽  
High Performance ◽  
Autonomous Systems ◽  
Observer Design ◽  
Annual Review ◽  
Publication Date ◽  
Navigation Systems ◽  
Extended Kalman Filtering ◽  
Wide Range

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high-performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a global intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of the system dynamics for the observer internal model, we show that the error dynamics have a particularly nice form. Applying the methodology of extended Kalman filtering to the equivariant error state yields a filter we term the equivariant filter. The geometry of the state-space manifold appears naturally as a curvature modification to the classical Riccati equation for extended Kalman filtering. The equivariant filter exploits the symmetry and respects the geometry of an equivariant system model, and thus yields high-performance, robust filters for a wide range of mechatronic and navigation systems. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

An Extended Kalman Filtering Mechanism Based on Generalized Interval Probability

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Jie Hu ◽  
Yan Wang ◽  
Aiguo Cheng ◽  
Zhihua Zhong
Keyword(s):  
Kalman Filter ◽  
Systematic Error ◽  
Kalman Filtering ◽  
Extended Kalman Filtering ◽  
Interval Probability ◽  
State Identification ◽  
Random Intervals ◽  
Efficient Alternative ◽  
Controllable Systems ◽  
Special Case

Kalman filter has been widely applied for state identification in controllable systems. As a special case of the hidden Markov model, it is based on the assumption of linear dependency relationships and Gaussian noise. The classical Kalman filter does not differentiate systematic error from random error associated with observations. In this paper, we propose an extended Kalman filtering mechanism based on generalized interval probability, where state and observable variables are random intervals, and interval-valued Gaussian distributions model the noises. The prediction and update procedures in the new mechanism are derived. Two examples are used to illustrate the developed mechanism. It is shown that the method is an efficient alternative to sensitivity analysis for assessing the effect of systematic error.

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