Convergence Analysis of Extended Kalman Filter in a Noisy Environment Through Difference Equations

Sebastian, Elizabeth; Jothilakshmi, R.

doi:10.12732/ijpam.v91i1.4

Cited by 10 publications

(9 citation statements)

References 13 publications

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“…In this estimation process, the system state matrix is always A n = I 2 and the system observation matrix is always C n = 1 . Hence, according to theory (3.4) in Elizabeth and Ramakrishnan (2015), the KF is a global asymptotic observer as long as the noise matrix W = ( left left b ^ left 0 left1 0 left c ^ ) has rank (2), which is always true, and ( R , Q ) are positive definite matrices.…”

Section: Qov Semi-active Suspension Problem Formulationmentioning

confidence: 99%

“…Here, | | A | | = sup { A n , n = 0 , 1 , 2 , . . } and | | C | | = sup { C n , n = 0 , 1 , 2 , . . } are bounded due to states bound limits, Q , R are positive definite, and noise matrix W = W 1 W 1 T (see Equation (12)) is of rank (5), hence the KF observer is asymptotic according to theory (3.4) in Elizabeth and Ramakrishnan (2015).…”

Section: Qov Active Suspension Problem Formulationmentioning

confidence: 99%

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Managing the handling–comfort contradiction of a quarter-car system using Kalman filter

Muhammed

Gavrilov

2021

Transactions of the Institute of Measurement and Control

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This article introduces a new approach to manage the “handling–comfort” contradiction of a vehicle suspension system. The idea is based on determining a specific time constant that reflects the percentage of suspension damping. This time constant is defined using the measurement of the sprung mass acceleration and the suspension deflection. A distinction is made between the control unit design for a semi-active suspension system and the control unit design for an active suspension system. The semi-active design is based on two sensors and a Kalman filter (KF), while the active design is based on three sensors and a dual-estimation KF. For active suspension, a third sensor was added to measure the acceleration of the unsprung mass. Simulation is carried out in Simulink and Simscape environments. The results of the proposed approach were compared with the results achieved by the hybrid-hook system. Simulation results showed a better efficiency of the proposed approach in driving safety during a “comfort” situation.

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Section: Qov Semi-active Suspension Problem Formulationmentioning

confidence: 99%

Section: Qov Active Suspension Problem Formulationmentioning

confidence: 99%

Managing the handling–comfort contradiction of a quarter-car system using Kalman filter

Muhammed

Gavrilov

2021

Transactions of the Institute of Measurement and Control

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“…where n is the total number of GPS devices, idealValue is the IDEAL weight value from CnW-S1, h fused is the fused EC and GPS heading value, h allGPS is the fused calculated heading for all the "n" number of GPS, w allGPS is the weight given to calculated combined GPS heading, h EC is the measured EC heading, w EC is the weight given to EC heading, w i is the weight given to "i th " GPS, h i is the calculated FAz heading of "i th " GPS, and * h fused is labeled as "GPSEC_yaw" in the later parts of algorithm and it will also be used in lieu of GPSn_FAz during the EKF stage when GPS data is invalid. The controllability and observability of the extended Kalman filter or Kalman filter have been extensively researched and proven in several works such as those by Elizabeth and Jothilakshmi [45], Kamrani et al [46], and Southall et al [47]. The dynamic and measurement models which are nonlinear in nature are as follows:…”

Section: Classification and Weighing-stage 1 (Cnw-s1mentioning

confidence: 99%

Design and Real-Time Implementation of a 3-Stage CnW Heading System on an Ubuntu Linux-Embedded Board

Vista

Chong

2019

Journal of Sensors

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This paper describes the design and real-time implementation of a proposed algorithm for deriving an accurate heading system by fusing data from various inexpensive sensor devices that is comparable to more expensive maritime navigation systems. The proposed algorithm is a 3-Stage Classification N’ Weighing (CnW) Heading System with forward azimuth (FAz) and extended Kalman filter (EKF). Data from three Global Positioning System devices, an inertial measurement unit, and an electronic compass were fed into the algorithm that can be generally described as Classification N’ Weighing-Stage 1 → forward azimuth → Classification N’ Weighing-Stage 2 → extended Kalman filter → Classification N’ Weighing-Stage 3. The proposed algorithm is shown to be comparably accurate as an expensive marine navigation system, and it has less processing time compared to our previous work. The Qt-anywhere-based system developed on a Linux desktop was successfully downloaded onto an Ubuntu Linux-embedded board for real-time implementation. Important notes related to device naming problems when deploying the system on a Linux-embedded board are also given as reference for those interested to address it.

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“…In [25] better convergence was obtained by using the normal form of the governing ordinary differential equations. Local asymptotic convergence of the estimation error with an assumption of observability of the nonlinear system was subsequently shown in [20], [21].…”

Section: Introductionmentioning

confidence: 98%

“…Local asymptotic convergence of the estimation error under an observability assumption of the nonlinear system has been shown in [20], [21]. In [22], conditions for asymptotic convergence are imposed on the linearization residues.…”

Section: Introductionmentioning

confidence: 99%

Extended Kalman filter based observer design for semilinear infinite-dimensional systems

Afshar¹,

Germ²,

Morris³

2022

Preprint

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In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by delay-differential equations are also infinite-dimensional systems. The full state of these systems cannot be measured. Observer design is an important tool for estimating the state from available measurements. For linear systems, both finite-and infinite-dimensional, the Kalman filter provides an estimate with minimum-variance on the error, if certain assumptions on the noise are satisfied. The extended Kalman filter (EKF) is one type of extension to nonlinear finite-dimensional systems. In this paper we provide an extension of the EKF to semilinear infinite-dimensional systems. Under mild assumptions we prove the well-posedness of equations defining the EKF. Local exponential stability of the error dynamics is shown. Only detectability is assumed, not observability, so this result is new even for finite-dimensional systems. The results are illustrated with implementation of finite-dimensional approximations of the infinite-dimensional EKF on an example.

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Convergence Analysis of Extended Kalman Filter in a Noisy Environment Through Difference Equations

Cited by 10 publications

References 13 publications

Managing the handling–comfort contradiction of a quarter-car system using Kalman filter

Managing the handling–comfort contradiction of a quarter-car system using Kalman filter

Design and Real-Time Implementation of a 3-Stage CnW Heading System on an Ubuntu Linux-Embedded Board

Extended Kalman filter based observer design for semilinear infinite-dimensional systems

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